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Homotopy of manifolds stabilized by projective spaces J. Topol. (IF 1.1) Pub Date : 2023-09-06 Ruizhi Huang, Stephen Theriault
We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space, and provide concrete examples. To do this, we trace the effect in homotopy theory of surgery on certain product manifolds by showing a loop homotopy decomposition
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On the motivic Segal conjecture J. Topol. (IF 1.1) Pub Date : 2023-09-06 Thomas Gregersen, John Rognes
We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group μ ℓ $\mu _\ell$ of ℓ $\ell$ th roots of unity, where ℓ $\ell$ is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group S ℓ $S_\ell$ and to μ ℓ $\mu _\ell$ , and introduce a delayed limit Adams spectral sequence
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Lagrangian cobordism functor in microlocal sheaf theory I J. Topol. (IF 1.1) Pub Date : 2023-09-04 Wenyuan Li
Let Λ ± $\Lambda _\pm$ be Legendrian submanifolds in the cosphere bundle T ∗ , ∞ M $T^{*,\infty }M$ . Given a Lagrangian cobordism L $L$ of Legendrians from Λ − $\Lambda _-$ to Λ + $\Lambda _+$ , we construct a functor Φ L * : Sh Λ + c ( M ) → Sh Λ − c ( M ) ⊗ C − * ( Ω * Λ − ) C − * ( Ω * L ) ${\mathrm{\Phi}}_{L}^{\ast}:{{\rm Sh}}_{{\mathrm{\Lambda}}_{+}}^{c}(M)\to {{\rm Sh}}_{{\mathrm{\Lambda}}_
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Equivariant knots and knot Floer homology J. Topol. (IF 1.1) Pub Date : 2023-09-05 Irving Dai, Abhishek Mallick, Matthew Stoffregen
We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose equivariant slice genus grows arbitrarily large, answering a question of Boyle and Issa. We also apply our formalism to several seemingly nonequivariant questions. In particular
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Smoothing finite-order bilipschitz homeomorphisms of 3-manifolds J. Topol. (IF 1.1) Pub Date : 2023-09-02 Lucien Grillet
We show that, for ε = 1 4000 $\varepsilon =\frac{1}{4000}$ , any action of a finite cyclic group by ( 1 + ε ) $(1+\varepsilon )$ -bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.
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The top homology group of the genus 3 Torelli group J. Topol. (IF 1.1) Pub Date : 2023-08-26 Igor A. Spiridonov
The Torelli group of a genus g $g$ oriented surface Σ g $\Sigma _g$ is the subgroup I g $\mathcal {I}_g$ of the mapping class group Mod ( Σ g ) ${\rm Mod}(\Sigma _g)$ consisting of all mapping classes that act trivially on H 1 ( Σ g , Z ) ${\rm H}_1(\Sigma _g, \mathbb {Z})$ . The quotient group Mod ( Σ g ) / I g ${\rm Mod}(\Sigma _g) / \mathcal {I}_g$ is isomorphic to the symplectic group Sp ( 2 g
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Dynamical properties of convex cocompact actions in projective space J. Topol. (IF 1.1) Pub Date : 2023-08-02 Theodore Weisman
We give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger–Guéritaud–Kassel: we show that convex cocompactness in R P d $\mathbb {R}\mathrm{P}^d$ is equivalent to an expansion property of the group about its limit set, occurring in different Grassmannians. As an application, we give a sufficient and necessary condition
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Automorphisms of procongruence curve and pants complexes J. Topol. (IF 1.1) Pub Date : 2023-07-19 Marco Boggi, Louis Funar
In this paper we study the automorphism group of the procongruence mapping class group through its action on the associated procongruence curve and pants complexes. Our main result is a rigidity theorem for the procongruence completion of the pants complex. As an application we prove that moduli stacks of smooth algebraic curves satisfy a weak anabelian property in the procongruence setting.
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Low-dimensional linear representations of mapping class groups J. Topol. (IF 1.1) Pub Date : 2023-07-14 Mustafa Korkmaz
Let S $S$ be a compact orientable surface of genus g $g$ with marked points in the interior. Franks–Handel (Proc. Amer. Math. Soc. 141 (2013) 2951–2962) proved that if n < 2 g $n<2g$ then the image of a homomorphism from the mapping class group Mod ( S ) ${\rm Mod}(S)$ of S $S$ to GL ( n , C ) ${\rm GL}(n,{\mathbb {C}})$ is trivial if g ⩾ 3 $g\geqslant 3$ and is finite cyclic if g = 2 $g=2$ . The first
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Symplectic mapping class groups of blowups of tori J. Topol. (IF 1.1) Pub Date : 2023-07-11 Gleb Smirnov
Let ω $\omega$ be a Kähler form on the real 4-torus T 4 $T^4$ . Suppose that ω $\omega$ satisfies an irrationality condition that can be achieved by an arbitrarily small perturbation of ω $\omega$ . This note shows that the smoothly trivial symplectic mapping class group of the one-point symplectic blowup of ( T 4 , ω ) $(T^4,\omega )$ is infinitely generated.
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Nonnegative scalar curvature on manifolds with at least two ends J. Topol. (IF 1.1) Pub Date : 2023-06-30 Simone Cecchini, Daniel Räde, Rudolf Zeidler
Let M $M$ be an orientable connected n $n$ -dimensional manifold with n ∈ { 6 , 7 } $n\in \lbrace 6,7\rbrace$ and let Y ⊂ M $Y\subset M$ be a two-sided closed connected incompressible hypersurface that does not admit a metric of positive scalar curvature (abbreviated by psc). Moreover, suppose that the universal covers of M $M$ and Y $Y$ are either both spin or both nonspin. Using Gromov's μ $\mu$
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Group and Lie algebra filtrations and homotopy groups of spheres J. Topol. (IF 1.1) Pub Date : 2023-06-01 Laurent Bartholdi, Roman Mikhailov
We establish a bridge between homotopy groups of spheres and commutator calculus in groups, and solve in this manner the “dimension problem” by providing a converse to Sjogren's theorem: every abelian group of bounded exponent can be embedded in the dimension quotient of a group. This is proven by embedding for arbitrary s , d $s,d$ the torsion of the homotopy group π s ( S d ) $\pi _s(S^d)$ into a
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The taut polynomial and the Alexander polynomial J. Topol. (IF 1.1) Pub Date : 2023-05-30 Anna Parlak
Landry, Minsky and Taylor defined the taut polynomial of a veering triangulation. Its specialisations generalise the Teichmüller polynomial of a fibred face of the Thurston norm ball. We prove that the taut polynomial of a veering triangulation is equal to a certain twisted Alexander polynomial of the underlying manifold. Thus, the Teichmüller polynomials are just specialisations of twisted Alexander
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Split link detection for sl(P)$\mathfrak {sl}(P)$ link homology in characteristic P$P$ J. Topol. (IF 1.1) Pub Date : 2023-05-31 Joshua Wang
We provide a sufficient condition for splitness of a link in terms of its reduced sl ( N ) $\mathfrak {sl}(N)$ link homology with arbitrary field coefficients. The proof of sufficiency uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. If N $N$ is prime and the coefficient field is of characteristic N $N$ , then the sufficient condition for splitness is also necessary
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Extensions of Veech groups I: A hyperbolic action J. Topol. (IF 1.1) Pub Date : 2023-05-31 Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger, Alessandro Sisto
Given a lattice Veech group in the mapping class group of a closed surface S $S$ , this paper investigates the geometry of Γ $\Gamma$ , the associated π 1 S $\pi _1S$ -extension group. We prove that Γ $\Gamma$ is the fundamental group of a bundle with a singular Euclidean-by-hyperbolic geometry. Our main result is that collapsing “obvious” product regions of the universal cover produces an action of
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Strong A1${\mathbb {A}}^1$-invariance of A1${\mathbb {A}}^1$-connected components of reductive algebraic groups J. Topol. (IF 1.1) Pub Date : 2023-05-27 Chetan Balwe, Amit Hogadi, Anand Sawant
We show that the sheaf of A 1 ${\mathbb {A}}^1$ -connected components of a reductive algebraic group over a perfect field is strongly A 1 ${\mathbb {A}}^1$ -invariant. As a consequence, torsors under such groups give rise to A 1 ${\mathbb {A}}^1$ -fiber sequences. We also show that sections of A 1 ${\mathbb {A}}^1$ -connected components of anisotropic, semisimple, simply connected algebraic groups
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A relative version of the Turaev–Viro invariants and the volume of hyperbolic polyhedral 3-manifolds J. Topol. (IF 1.1) Pub Date : 2023-05-28 Tian Yang
We define a relative version of the Turaev–Viro invariants for an ideally triangulated compact 3-manifold with nonempty boundary and a coloring on the edges, generalizing the Turaev–Viro invariants [36] of the manifold. We also propose the volume conjecture for these invariants whose asymptotic behavior is related to the volume of the manifold in the hyperbolic polyhedral metric [22, 23] with singular
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Positive scalar curvature and homology cobordism invariants J. Topol. (IF 1.1) Pub Date : 2023-05-29 Hokuto Konno, Masaki Taniguchi
We give an obstruction to positive scalar curvature metrics on 4-manifolds with the homology S 1 × S 3 $S^{1} \times S^{3}$ described in terms of homology cobordism invariants from Seiberg–Witten theory. The main tool of the proof is a relative Bauer–Furuta-type invariant on a periodic-end 4-manifold.
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Stable isoperimetric ratios and the Hodge Laplacian of hyperbolic manifolds J. Topol. (IF 1.1) Pub Date : 2023-05-05 Cameron Gates Rudd
We show that for a closed hyperbolic 3-manifold, the size of the first eigenvalue of the Hodge Laplacian acting on coexact 1-forms is comparable to an isoperimetric ratio relating geodesic length and stable commutator length with comparison constants that depend polynomially on the volume and on a lower bound on injectivity radius, refining estimates of Lipnowski and Stern. We use this estimate to
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Semisimple four-dimensional topological field theories cannot detect exotic smooth structure J. Topol. (IF 1.1) Pub Date : 2023-04-11 David Reutter
We prove that semisimple four-dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth four-manifolds and homotopy equivalent simply connected closed oriented smooth four-manifolds. We show that all currently known four-dimensional field theories are semisimple, including unitary field theories, and
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The Segal conjecture for smash powers J. Topol. (IF 1.1) Pub Date : 2023-04-11 Håkon Schad Bergsaker, John Rognes
We prove that the comparison map from G $G$ -fixed points to G $G$ -homotopy fixed points, for the G $G$ -fold smash power of a bounded below spectrum B $B$ , becomes an equivalence after p $p$ -completion if G $G$ is a finite p $p$ -group and H ∗ ( B ; F p ) $H_*(B; \mathbb {F}_p)$ is of finite type. We also prove that the map becomes an equivalence after I ( G ) $I(G)$ -completion if G $G$ is any
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Simplicial descent for Chekanov–Eliashberg dg-algebras J. Topol. (IF 1.1) Pub Date : 2023-04-08 Johan Asplund
We introduce a type of surgery decomposition of Weinstein manifolds that we call simplicial decompositions. The main result of this paper is that the Chekanov–Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a descent (cosheaf) property with respect to a simplicial decomposition. Simplicial decompositions generalize the notion of Weinstein connected sum and we show that
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Holonomy of complex projective structures on surfaces with prescribed branch data J. Topol. (IF 1.1) Pub Date : 2023-03-13 Thomas Le Fils
We characterize the representations of the fundamental group of a closed surface to ◂⋅▸PSL2(C)$\mathrm{PSL}_2(\mathbb {C})$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces
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Augmentations and immersed Lagrangian fillings J. Topol. (IF 1.1) Pub Date : 2023-02-28 Yu Pan, Dan Rutherford
For a Legendrian link ◂⊂▸Λ⊂J1M$\Lambda \subset J^1M$ with M=R$M = \mathbb {R}$ or S1$S^1$, immersed exact Lagrangian fillings L⊂Symp◂≅▸(J1M)≅T∗◂()▸(R>0×M)$L \subset \mbox{Symp}(J^1M) \cong T^*(\mathbb {R}_{>0} \times M)$ of Λ$\Lambda$ can be lifted to conical Legendrian fillings ◂⊂▸Σ⊂J1◂()▸(R>0×M)$\Sigma \subset J^1(\mathbb {R}_{>0} \times M)$ of Λ$\Lambda$. When Σ$\Sigma$ is embedded, using the
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Toroidal integer homology three-spheres have irreducible SU(2)$SU(2)$-representations J. Topol. (IF 1.1) Pub Date : 2023-02-18 Tye Lidman, Juanita Pinzón-Caicedo, Raphael Zentner
We prove that if an integer homology three-sphere contains an embedded incompressible torus, then its fundamental group admits irreducible ◂⋅▸SU(2)$SU(2)$-representations.
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Higher homotopy normalities in topological groups J. Topol. (IF 1.1) Pub Date : 2023-02-17 Mitsunobu Tsutaya
The purpose of this paper is to introduce Nk(ℓ)$N_k(\ell )$-maps (◂,▸1⩽k,ℓ⩽∞$1\leqslant k,\ell \leqslant \infty$), which describe higher homotopy normalities, and to study their basic properties and examples. An Nk(ℓ)$N_k(\ell )$-map is defined with higher homotopical conditions. It is shown that a homomorphism is an Nk(ℓ)$N_k(\ell )$-map if and only if there exists fiberwise maps between fiberwise
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Gromov–Witten theory of complete intersections via nodal invariants J. Topol. (IF 1.1) Pub Date : 2023-02-17 Hülya Argüz, Pierrick Bousseau, Rahul Pandharipande, Dimitri Zvonkine
We provide an inductive algorithm computing Gromov–Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov–Witten classes of all smooth complete intersections in projective space belong to the tautological ring of the moduli space of stable curves. The main idea is to show that invariants with insertions of primitive
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Families of diffeomorphisms and concordances detected by trivalent graphs J. Topol. (IF 1.1) Pub Date : 2023-02-14 Boris Botvinnik, Tadayuki Watanabe
We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non-trivial elements in homotopy groups ◂f()▸π∗◂()▸(BDiff∂(Dd))⊗Q$\pi _*(B\mathrm{Diff}_{\partial }(D^d))\otimes {\mathbb {Q}}$ are lifted to homotopy groups of the moduli space of h$h$-cobordisms ◂f()▸π∗◂()
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On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance J. Topol. (IF 1.1) Pub Date : 2023-02-06 Arturo Fernández-Pérez, Gilcione Nonato Costa, Rudy Rosas Bazán
We define the Milnor number of a one-dimensional holomorphic foliation F$\mathcal {F}$ as the intersection number of two holomorphic sections with respect to a compact connected component C$C$ of its singular set. Under certain conditions, we prove that the Milnor number of F$\mathcal {F}$ on a three-dimensional manifold with respect to C$C$ is invariant by C1$C^1$ topological equivalences.
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Simplicial volume and essentiality of manifolds fibered over spheres J. Topol. (IF 1.1) Pub Date : 2023-02-06 Thorben Kastenholz, Jens Reinhold
We study the question when a manifold that fibers over a sphere can be rationally essential, or have positive simplicial volume. More concretely, we show that mapping tori of manifolds (whose fundamental groups can be quite arbitrary) of dimension ◂⩾▸2n+1⩾7$2n +1 \geqslant 7$ with non-zero simplicial volume are very common. This contrasts the case of fiber bundles over a sphere of dimension d⩾2$d\geqslant
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End-periodic homeomorphisms and volumes of mapping tori J. Topol. (IF 1.1) Pub Date : 2023-01-06 Elizabeth Field, Heejoung Kim, Christopher Leininger, Marissa Loving
Given an irreducible, end-periodic homeomorphism f:S→S$f: S \rightarrow S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, Mf$M_f$, is the interior of a compact, irreducible, atoroidal 3-manifold ◂◽.▸M¯f$\overline{M}_f$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of ◂◽.▸M¯f$\overline{M}_f$ in terms of the translation
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Large genus asymptotics for lengths of separating closed geodesics on random surfaces J. Topol. (IF 1.1) Pub Date : 2023-01-09 Xin Nie, Yunhui Wu, Yuhao Xue
In this paper, we investigate basic geometric quantities of a random hyperbolic surface of genus g$g$ with respect to the Weil–Petersson measure on the moduli space Mg$\mathcal {M}_g$. We show that as g$g$ goes to infinity, a generic surface X∈Mg$X\in \mathcal {M}_g$ satisfies asymptotically:
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Random subcomplexes of finite buildings, and fibering of commutator subgroups of right-angled Coxeter groups J. Topol. (IF 1.1) Pub Date : 2023-01-06 Eduard Schesler, Matthew C. B. Zaremsky
The main theme of this paper is higher virtual algebraic fibering properties of right-angled Coxeter groups (RACGs), with a special focus on those whose defining flag complex is a finite building. We prove for particular classes of finite buildings that their random induced subcomplexes have a number of strong properties, most prominently that they are highly connected. From this we are able to deduce
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A criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds J. Topol. (IF 1.1) Pub Date : 2022-12-28 Florent Ygouf
We define on any affine invariant orbifold M$\mathcal {M}$ a foliation FM$\mathcal {F}^{\mathcal {M}}$ that generalizes the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification
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The correspondence induced on the pillowcase by the earring tangle J. Topol. (IF 1.1) Pub Date : 2022-11-11 Guillem Cazassus, Christopher Herald, Paul Kirk, Artem Kotelskiy
The earring tangle consists of four strands 4pt◂⊂▸×I⊂S2×I$4\text{pt} \times I \subset S^2 \times I$ and one meridian around one of the strands. Equipping this tangle with a nontrivial ◂⋅▸SO(3)$SO(3)$ bundle, we show that its traceless ◂⋅▸SU(2)$SU(2)$ flat moduli space is topologically a smooth genus three surface. We also show that the restriction map from this surface to the traceless flat moduli
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Homotopy functoriality for Khovanov spectra J. Topol. (IF 1.1) Pub Date : 2022-11-09 Tyler Lawson, Robert Lipshitz, Sucharit Sarkar
We prove that the Khovanov spectra associated to links and tangles are functorial up to homotopy and sign.
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Heegaard genus and complexity of fibered knots J. Topol. (IF 1.1) Pub Date : 2022-11-08 Mustafa Cengiz
We prove that if a fibered knot K$K$ with genus greater than 1 in a three-manifold M$M$ has a sufficiently complicated monodromy, then K$K$ induces a minimal genus Heegaard splitting P$P$ that is unique up to isotopy, and small genus Heegaard splittings of M$M$ are stabilizations of P$P$. We provide a complexity bound in terms of the Heegaard genus of M$M$. We also provide global complexity bounds
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Infinitely many virtual geometric triangulations J. Topol. (IF 1.1) Pub Date : 2022-11-01 David Futer, Emily Hamilton, Neil R. Hoffman
We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, every long Dehn filling of one cusp in this cover admits infinitely many geometric ideal triangulations. This cover is constructed in several stages, using results about separability of peripheral subgroups and their double cosets, in addition to a new conjugacy
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Decompositions of the stable module ∞$\infty$-category J. Topol. (IF 1.1) Pub Date : 2022-10-29 Joshua Hunt
We show that the stable module ∞$\infty$-category of a finite group G$G$ decomposes in three different ways as a limit of the stable module ∞$\infty$-categories of certain subgroups of G$G$. Analogously to Dwyer's terminology for homology decompositions, we call these the centraliser, normaliser, and subgroup decompositions. We construct centraliser and normaliser decompositions and extend the subgroup
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Thickness and relative hyperbolicity for graphs of multicurves J. Topol. (IF 1.1) Pub Date : 2022-10-31 Jacob Russell, Kate M. Vokes
We prove that any graph of multicurves satisfying certain natural properties is either hyperbolic, relatively hyperbolic, or thick. Further, this geometric characterization is determined by the set of subsurfaces that intersect every vertex of the graph. This extends previously established results for the pants graph and the separating curve graph to a broad family of graphs associated to surfaces
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Étale cohomology, purity and formality with torsion coefficients J. Topol. (IF 1.1) Pub Date : 2022-10-27 Joana Cirici, Geoffroy Horel
We use Galois group actions on étale cohomology to prove results of formality for dg-operads and dg-algebras with torsion coefficients. Our theory applies, among other related objects, to the dg-operad of singular chains of the operad of little disks and to the dg-algebra of singular cochains of the configuration space of points in the complex space. The formality that we obtain is only up to a certain
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Symplectic hats J. Topol. (IF 1.1) Pub Date : 2022-10-12 John B. Etnyre, Marco Golla
We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3-sphere, and hats in blow-ups of the (punctured) complex projective planes. We apply the construction to give constraints on the algebraic
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Homological stability for Iwahori–Hecke algebras J. Topol. (IF 1.1) Pub Date : 2022-10-08 Richard Hepworth
We show that the Iwahori–Hecke algebras Hn$\mathcal {H}_n$ of type An−1$A_{n-1}$ satisfy homological stability, where homology is interpreted as an appropriate Tor group. Our result precisely recovers Nakaoka's homological stability result for the symmetric groups in the case that the defining parameter is equal to 1. We believe that this paper, and our joint work with Boyd on Temperley–Lieb algebras
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The Picard group of the universal moduli stack of principal bundles on pointed smooth curves J. Topol. (IF 1.1) Pub Date : 2022-09-27 Roberto Fringuelli, Filippo Viviani
For any smooth connected linear algebraic group G$G$ over an algebraically closed field k$k$, we describe the Picard group of the universal moduli stack of principal G$G$-bundles over pointed smooth k$k$-projective curves.
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Characterizing divergence and thickness in right-angled Coxeter groups J. Topol. (IF 1.1) Pub Date : 2022-09-27 Ivan Levcovitz
We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential, or infinite. We prove that a RACG is strongly thick of order k$k$ if and only if its divergence function is a polynomial of degree k+1$k+1$. Moreover, we show that the exact divergence function of a RACG can
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Surface-like boundaries of hyperbolic groups J. Topol. (IF 1.1) Pub Date : 2022-09-20 Benjamin Beeker, Nir Lazarovich
We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.
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The topological modular forms of RP2$\mathbb {R}P^2$ and RP2∧CP2$\mathbb {R}P^2 \wedge \mathbb {C}P^2$ J. Topol. (IF 1.1) Pub Date : 2022-09-19 Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham, Zhouli Xu
We study the elliptic spectral sequence computing tmf∗(RP2)$tmf_*(\mathbb {R}P^2)$ and tmf∗(RP2∧CP2)$tmf_* (\mathbb {R} P^2 \wedge \mathbb {C} P^2)$. Specifically, we compute all differentials and resolve exotic extensions by 2, η$\eta$, and ν$\nu$. For tmf∗(RP2∧CP2)$tmf_* (\mathbb {R} P^2 \wedge \mathbb {C} P^2)$, we also compute the effect of the v1$v_1$-self maps of RP2∧CP2$\mathbb {R} P^2 \wedge
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Braid loops with infinite monodromy on the Legendrian contact DGA J. Topol. (IF 1.1) Pub Date : 2022-09-19 Roger Casals, Lenhard Ng
We present the first examples of elements in the fundamental group of the space of Legendrian links in (S3,ξst)$(\mathbb {S}^3,\xi _{\text{st}})$ whose action on the Legendrian contact DGA is of infinite order. This allows us to construct the first families of Legendrian links that can be shown to admit infinitely many Lagrangian fillings by Floer-theoretic techniques. These new families include the
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On the EO$\mathrm{EO}$-orientability of vector bundles J. Topol. (IF 1.1) Pub Date : 2022-09-19 P. Bhattacharya, H. Chatham
We study the orientability of vector bundles with respect to a family of cohomology theories called EO$\mathrm{EO}$-theories. The EO$\mathrm{EO}$-theories are higher height analogues of real K$\mathrm{K}$-theory KO$\mathrm{KO}$. For each EO$\mathrm{EO}$-theory, we prove that the direct sum of i$i$ copies of any vector bundle is EO$\mathrm{EO}$-orientable for some specific integer i$i$. Using a splitting
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A quantitative Birman–Menasco finiteness theorem and its application to crossing number J. Topol. (IF 1.1) Pub Date : 2022-09-11 Tetsuya Ito
Birman–Menasco proved that there are finitely many knots having a given genus and braid index. We give a quantitative version of the Birman–Menasco finiteness theorem, an estimate of the crossing number of knots in terms of genus and braid index. As applications, we give a solution of the braid index problem, the problem to determine the braid index of a given link, and provide estimates of the crossing
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R$\mathbb {R}$-motivic stable stems J. Topol. (IF 1.1) Pub Date : 2022-07-27 Eva Belmont, Daniel C. Isaksen
We compute some R$\mathbb {R}$-motivic stable homotopy groups. For s−w⩽11$s - w \leqslant 11$, we describe the motivic stable homotopy groups πs,w$\pi _{s,w}$ of a completion of the R$\mathbb {R}$-motivic sphere spectrum. We apply the ρ$\rho$-Bockstein spectral sequence to obtain R$\mathbb {R}$-motivic Ext$\operatorname{Ext}$ groups from the C$\mathbb {C}$-motivic Ext$\operatorname{Ext}$ groups, which
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Enhanced bivariant homology theory attached to six functor formalism J. Topol. (IF 1.1) Pub Date : 2022-07-26 Tomoyuki Abe
Bivariant theory is a unified framework for cohomology and Borel–Moore homology theories. In this paper, we extract an ∞$\infty$-enhanced bivariant homology theory from Gaitsgory–Rozenblyum's six functor formalism.
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Equivariant 4-genera of strongly invertible and periodic knots J. Topol. (IF 1.1) Pub Date : 2022-07-14 Keegan Boyle, Ahmad Issa
We study the equivariant genera of strongly invertible and periodic knots. Our techniques include some new strongly invertible concordance group invariants, Donaldson's theorem, and the g-signature. We find many new examples where the equivariant 4-genus is larger than the 4-genus.
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The panted cobordism groups of cusped hyperbolic 3-manifolds J. Topol. (IF 1.1) Pub Date : 2022-07-12 Hongbin Sun
For any oriented cusped hyperbolic 3-manifold M $M$ , we study its ( R , ε ) $(R,\epsilon )$ -panted cobordism group, which is the abelian group generated by ( R , ε ) $(R,\epsilon )$ -good curves in M $M$ modulo the oriented boundaries of ( R , ε ) $(R,\epsilon )$ -good pants. In particular, we prove that for sufficiently small ε > 0 $\epsilon >0$ and sufficiently large R > 0 $R>0$ , some modified
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S1$S^1$-equivariant contact homology for hypertight contact forms J. Topol. (IF 1.1) Pub Date : 2022-07-07 Michael Hutchings, Jo Nelson
In a previous paper, we showed that the original definition of cylindrical contact homology, with rational coefficients, is valid on a closed three-manifold with a dynamically convex contact form. However, we did not show that this cylindrical contact homology is an invariant of the contact structure. In the present paper, we define ‘nonequivariant contact homology’ and ‘ S 1 $S^1$ S1 -equivariant
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Heegaard genus, degree-one maps, and amalgamation of 3-manifolds J. Topol. (IF 1.1) Pub Date : 2022-07-07 Tao Li
Let M = W ∪ T V $M=\mathcal {W}\cup _\mathcal {T} \mathcal {V}$ be an amalgamation of two compact 3-manifolds along a torus, where W $\mathcal {W}$ is the exterior of a knot in a homology sphere. Let N $N$ be the manifold obtained by replacing W $\mathcal {W}$ with a solid torus such that the boundary of a Seifert surface in W $\mathcal {W}$ is a meridian of the solid torus. This means that there is
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Global fixed points of mapping class group actions and a theorem of Markovic J. Topol. (IF 1.1) Pub Date : 2022-07-02 Lei Chen, Nick Salter
We give a short and elementary proof of the nonrealizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of Thurston. With the tools established in this paper, we also obtain some rigidity results for actions of the mapping class group on Euclidean spaces.
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Global algebraic K-theory J. Topol. (IF 1.1) Pub Date : 2022-07-02 Stefan Schwede
We introduce a global equivariant refinement of algebraic K-theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global Ω $\Omega$ -spectrum that keeps track of genuine G $G$ -equivariant infinite loop spaces, for all finite groups G $G$ . The resulting global algebraic K-theory
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Rigidity of the saddle connection complex J. Topol. (IF 1.1) Pub Date : 2022-06-30 Valentina Disarlo, Anja Randecker, Robert Tang
For a half-translation surface ( S , q ) $(S,q)$ (S,q) , the associated saddle connection complex A ( S , q ) $\mathcal {A}(S,q)$ A(S,q) is the simplicial complex where vertices are the saddle connections on ( S , q ) $(S,q)$ (S,q) , with simplices spanned by sets of pairwise disjoint saddle connections. This complex can be naturally regarded as an induced subcomplex of the arc complex. We prove that
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Patchworking real algebraic hypersurfaces with asymptotically large Betti numbers J. Topol. (IF 1.1) Pub Date : 2022-06-23 Charles Arnal
In this article, we describe a recursive method for constructing a family of real projective algebraic hypersurfaces in ambient dimension n $n$ n from families of such hypersurfaces in ambient dimensions k = 1 , … , n − 1 $k=1,\ldots ,n-1$ k=1,…,n−1 . The asymptotic Betti numbers of real parts of the resulting family can then be described in terms of the asymptotic Betti numbers of the real parts of