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  • Tangle Floer homology and cobordisms between tangles
    J. Topol. (IF 1.642) Pub Date : 2020-09-24
    Akram Alishahi; Eaman Eftekhary

    We introduce a generalization of oriented tangles, which are still called tangles, so that they are in one‐to‐one correspondence with the sutured manifolds. We define cobordisms between sutured manifolds (tangles) by generalizing cobordisms between oriented tangles. For every commutative algebra A over Z / 2 Z , we define A - Tangles to be the category consisting of A ‐tangles, which are balanced tangles

    更新日期:2020-09-25
  • A generalized Blakers–Massey theorem
    J. Topol. (IF 1.642) Pub Date : 2020-09-07
    Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal

    We prove a generalization of the classical connectivity theorem of Blakers–Massey, valid in an arbitrary higher topos and with respect to an arbitrary modality, that is, a factorization system ( L , R ) in which the left class is stable by base change. We explain how to rederive the classical result, as well as the recent generalization of Chachólski, Scherer and Werndli (Ann. Inst. Fourier 66 (2016)

    更新日期:2020-09-07
  • Comparison of models for (∞,n)‐categories, II
    J. Topol. (IF 1.642) Pub Date : 2020-09-07
    Julia E. Bergner, Charles Rezk

    In this paper we complete a chain of explicit Quillen equivalences between the model category for Θ n + 1 ‐spaces and the model category of small categories enriched in Θ n ‐spaces. The Quillen equivalences given here connect Segal category objects in Θ n ‐spaces, complete Segal objects in Θ n ‐spaces, and Θ n + 1 ‐spaces.

    更新日期:2020-09-07
  • Topological restrictions on Anosov representations
    J. Topol. (IF 1.642) Pub Date : 2020-08-26
    Richard Canary, Konstantinos Tsouvalas

    We characterize groups admitting Anosov representations into SL ( 3 , R ) , projective Anosov representations into SL ( 4 , R ) , and Borel Anosov representations into SL ( 4 , R ) . More generally, we obtain bounds on the cohomological dimension of groups admitting P k ‐Anosov representations into SL ( d , R ) and offer several characterizations of Benoist representations.

    更新日期:2020-08-26
  • Tropical Lagrangian hypersurfaces are unobstructed
    J. Topol. (IF 1.642) Pub Date : 2020-07-21
    Jeffrey Hicks

    We produce for each tropical hypersurface V ( ϕ ) ⊂ Q = R n a Lagrangian L ( ϕ ) ⊂ ( C ∗ ) n whose moment map projection is a tropical amoeba of V ( ϕ ) . When these Lagrangians are admissible in the Fukaya–Seidel category, we show that they are unobstructed objects of the Fukaya category, and mirror to sheaves supported on complex hypersurfaces in a toric mirror.

    更新日期:2020-07-21
  • Generalized cusps in real projective manifolds: classification
    J. Topol. (IF 1.642) Pub Date : 2020-07-21
    Samuel A. Ballas, Daryl Cooper, Arielle Leitner

    We study a generalized cusp C that is diffeomorphic to [ 0 , ∞ ) times a closed Euclidean manifold. Geometrically, C is the quotient of a properly convex domain in R P n by a lattice, Γ , in one of a family of affine Lie groups G ( ψ ) , parameterized by a point ψ in the (dual closed) Weyl chamber for SL ( n + 1 , R ) , and Γ determines the cusp up to equivalence. These affine groups correspond to

    更新日期:2020-07-21
  • Cosmetic two‐strand twists on fibered knots
    J. Topol. (IF 1.642) Pub Date : 2020-07-20
    Carson Rogers

    Let K be a knot in a rational homology sphere M . This paper investigates the question of when modifying K by adding m > 0 half‐twists to two oppositely oriented strands, while keeping the rest of K fixed, produces a knot isotopic to K . Such a two‐strand twist of order m , as we define it, is a generalized crossing change when m is even and a non‐coherent band surgery when m = ± 1 . A cosmetic two‐strand

    更新日期:2020-07-20
  • Rational L‐space surgeries on satellites by algebraic links
    J. Topol. (IF 1.642) Pub Date : 2020-07-16
    Sarah Dean Rasmussen

    Given an n ‐component link L in any 3‐manifold M , the space L ⊂ ( Q ∪ { ∞ } ) n of rational surgery slopes yielding L‐spaces is already fully characterized in joint work by the author when n = 1 and L is nontrivial. For n > 1 , however, there are no previous results for L as a rational subspace, and only limited results for integer surgeries L ∩ Z n on S 3 . Herein, we provide the first nontrivial

    更新日期:2020-07-16
  • Engel groups and universal surgery models
    J. Topol. (IF 1.642) Pub Date : 2020-06-30
    Michael Freedman, Vyacheslav Krushkal

    We introduce a collection of 1 2 ‐ π 1 ‐null four‐dimensional surgery problems. This is an intermediate notion between the classically studied universal surgery models and the π 1 ‐null kernels which are known to admit a solution in the topological category. Using geometric applications of the group‐theoretic 2‐Engel relation, we show that the 1 2 ‐ π 1 ‐null surgery problems are universal, in the

    更新日期:2020-06-30
  • Stably slice disks of links
    J. Topol. (IF 1.642) Pub Date : 2020-06-26
    Anthony Conway, Matthias Nagel

    We define the stabilizing number sn ( K ) of a knot K ⊂ S 3 as the minimal number n of S 2 × S 2 connected summands required for K to bound a null‐homologous locally flat disk in D 4 # n S 2 × S 2 . This quantity is defined when the Arf invariant of K is zero. We show that sn ( K ) is bounded below by signatures and Casson–Gordon invariants and bounded above by the topological 4‐genus g 4 top ( K )

    更新日期:2020-06-26
  • Splitting of the homology of the punctured mapping class group
    J. Topol. (IF 1.642) Pub Date : 2020-05-20
    Andrea Bianchi

    Let Γ g , 1 m be the mapping class group of the orientable surface Σ g , 1 m of genus g with one parametrized boundary curve and m permutable punctures; when m = 0 we omit it from the notation. Let β m ( Σ g , 1 ) be the braid group on m strands of the surface Σ g , 1 . We prove that H ∗ ( Γ g , 1 m ; Z 2 ) ≅ H ∗ ( Γ g , 1 ; H ∗ ( β m ( Σ g , 1 ) ; Z 2 ) ) . The main ingredient is the computation of

    更新日期:2020-05-20
  • Product set growth in groups and hyperbolic geometry
    J. Topol. (IF 1.642) Pub Date : 2020-05-19
    Thomas Delzant, Markus Steenbock

    Generalising results of Razborov and Safin, and answering a question of Button, we prove that for every hyperbolic group there exists a constant α > 0 such that for every finite subset U that is not contained in a virtually cyclic subgroup | U n | ⩾ ( α | U | ) [ ( n + 1 ) / 2 ] . Similar estimates are established for groups acting acylindrically on trees or hyperbolic spaces.

    更新日期:2020-05-19
  • Locally discrete expanding groups of analytic diffeomorphisms of the circle
    J. Topol. (IF 1.642) Pub Date : 2020-05-19
    Bertrand Deroin

    We show that a finitely generated subgroup of Diff ω ( S 1 ) that is expanding and locally discrete in the analytic category is analytically conjugated to a uniform lattice in PGL ∼ 2 k ( R ) acting on the k th covering of R P 1 for a certain integer k > 0 .

    更新日期:2020-05-19
  • Elliptic classes of Schubert varieties via Bott–Samelson resolution
    J. Topol. (IF 1.642) Pub Date : 2020-05-14
    Richárd Rimányi, Andrzej Weber

    Based on recent advances on the relation between geometry and representation theory, we propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic characteristic classes of Schubert varieties of the generalized full flag variety G / B . For this first we need to twist the notion of elliptic characteristic class of Borisov–Libgober by a line bundle, and thus allow the elliptic

    更新日期:2020-05-14
  • Corrigendum: A flexible construction of equivariant Floer homology and applications
    J. Topol. (IF 1.642) Pub Date : 2020-05-13
    Kristen Hendricks, Robert Lipshitz, Sucharit Sarkar

    We correct a mistake regarding almost complex structures on Hilbert schemes of points in surfaces in Hendricks, Lipshitz and Sarkar (J. Topol. 9 (2016) 1153–1236). The error does not affect the main results of the paper, and only affects the proofs of invariance of equivariant symplectic Khovanov homology and reduced symplectic Khovanov homology. We give an alternate proof of the invariance of equivariant

    更新日期:2020-05-13
  • Maximal contact and symplectic structures
    J. Topol. (IF 1.642) Pub Date : 2020-05-04
    Oleg Lazarev

    We study the relationship on Weinstein domains given by Weinstein cobordism. Our main result is that any finite collection of high‐dimensional Weinstein domains with the same topology is Weinstein subdomains of a ‘maximal’ Weinstein domain also with the same topology. As applications, we construct many new exotic Weinstein structures, for example, exotic cotangent bundles containing many closed regular

    更新日期:2020-05-04
  • Relations in bounded cohomology
    J. Topol. (IF 1.642) Pub Date : 2020-05-04
    James Farre

    We explain some interesting relations in the degree 3 bounded cohomology of surface groups. Specifically, we show that if two faithful Kleinian surface group representations are quasi‐isometric, then their bounded fundamental classes are the same in bounded cohomology. This is novel in the setting that one end is degenerate, while the other end is geometrically finite. We also show that a difference

    更新日期:2020-05-04
  • Property FW, differentiable structures and smoothability of singular actions
    J. Topol. (IF 1.642) Pub Date : 2020-05-04
    Yash Lodha, Nicolás Matte Bon, Michele Triestino

    We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group Γ has the fixed point property FW for walls (for example, if it has property ( T ) ), every aperiodic action of Γ by diffeomorphisms that are of class C r with countably many singularities is conjugate to an action by true diffeomorphisms of class C r on a homeomorphic (possibly

    更新日期:2020-05-04
  • Eigenvalues of the Thurston operator
    J. Topol. (IF 1.642) Pub Date : 2020-05-02
    Xavier Buff, Adam L. Epstein, Sarah Koch

    Let f : C ̂ → C ̂ be a postcritically finite rational map, and let Q ( C ̂ ) be the space of meromorphic quadratic differentials on C ̂ with simple poles. We study the set of eigenvalues of the pushforward operator f ∗ : Q ( C ̂ ) → Q ( C ̂ ) . In particular, we show that when f : C → C is a unicritical polynomial of degree D with periodic critical point, the eigenvalues of f ∗ : Q ( C ̂ ) → Q ( C

    更新日期:2020-05-02
  • Taut foliations, positive 3‐braids, and the L‐space conjecture
    J. Topol. (IF 1.642) Pub Date : 2020-05-02
    Siddhi Krishna

    We construct taut foliations in every closed 3‐manifold obtained by r ‐framed Dehn surgery along a positive 3‐braid knot K in S 3 , where r < 2 g ( K ) − 1 and g ( K ) denotes the Seifert genus of K . This confirms a prediction of the L‐space Conjecture. For instance, we produce taut foliations in every non‐L‐space obtained by surgery along the pretzel knot P ( − 2 , 3 , 7 ) , and indeed along every

    更新日期:2020-05-02
  • Distances between surfaces in 4‐manifolds
    J. Topol. (IF 1.642) Pub Date : 2020-05-02
    Oliver Singh

    If Σ and Σ ′ are homotopic embedded surfaces in a 4‐manifold, then they may be related by a regular homotopy (at the expense of introducing double points) or by a sequence of stabilisations and destabilisations (at the expense of adding genus). This naturally gives rise to two integer‐valued notions of distance between the embeddings: the singularity distance d sing ( Σ , Σ ′ ) and the stabilisation

    更新日期:2020-05-02
  • The circle action on topological Hochschild homology of complex cobordism and the Brown–Peterson spectrum
    J. Topol. (IF 1.642) Pub Date : 2020-04-29
    John Rognes

    We specify exterior generators in π ∗ T H H ( M U ) = π ∗ ( M U ) ⊗ E ( λ n ′ ∣ n ⩾ 1 ) and π ∗ T H H ( B P ) = π ∗ ( B P ) ⊗ E ( λ n ∣ n ⩾ 1 ) , and calculate the action of the σ ‐operator on these graded rings. In particular, σ ( λ n ′ ) = 0 and σ ( λ n ) = 0 , while the actions on π ∗ ( M U ) and π ∗ ( B P ) are expressed in terms of the right units η R in the Hopf algebroids ( π ∗ ( M U ) , π ∗

    更新日期:2020-04-29
  • Surgery, polygons and SU(N)‐Floer homology
    J. Topol. (IF 1.642) Pub Date : 2020-03-19
    Lucas Culler, Aliakbar Daemi, Yi Xie

    Surgery exact triangles in various 3‐manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3‐manifolds, obtained by three different Dehn surgeries on a fixed knot. In this paper, the behavior of SU ( N ) ‐instanton Floer homology with respect to Dehn surgery is studied. In particular, it

    更新日期:2020-03-19
  • A Chekanov–Eliashberg algebra for Legendrian graphs
    J. Topol. (IF 1.642) Pub Date : 2020-03-19
    Byung Hee An, Youngjin Bae

    We define a differential graded algebra for Legendrian graphs and tangles in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas from Legendrian contact homology. The construction is distinguished from other versions of Legendrian contact algebra by the vertices of Legendrian graphs. A set of countably many generators and a generalized notion of equivalence

    更新日期:2020-03-19
  • The rational homotopy type of (n−1)‐connected manifolds of dimension up to 5n−3
    J. Topol. (IF 1.642) Pub Date : 2020-03-18
    Diarmuid Crowley, Johannes Nordström

    We define the Bianchi–Massey tensor of a topological space X to be a linear map B → H ∗ ( X ) , where B is a subquotient of H ∗ ( X ) ⊗ 4 determined by the algebra H ∗ ( X ) . We then prove that if M is a closed ( n − 1 ) ‐connected manifold of dimension at most 5 n − 3 (and n ⩾ 2 ) then its rational homotopy type is determined by its cohomology algebra and Bianchi–Massey tensor, and that M is formal

    更新日期:2020-03-18
  • Distortion and the bridge distance of knots
    J. Topol. (IF 1.642) Pub Date : 2020-03-18
    Ryan Blair, Marion Campisi, Scott A. Taylor, Maggy Tomova

    We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in R 3 proportional to the minimum of the bridge distance and the bridge number of the knot. We also exhibit an infinite family of knots for which the minimum of the bridge distance and the bridge number is unbounded and Pardon's lower bound is constant.

    更新日期:2020-03-18
  • Drinfeld–Gaitsgory–Vinberg interpolation Grassmannian and geometric Satake equivalence
    J. Topol. (IF 1.642) Pub Date : 2020-03-18
    Michael Finkelberg, Vasily Krylov, Ivan Mirković

    Let G be a reductive complex algebraic group. We fix a pair of opposite Borel subgroups and consider the corresponding semi‐infinite orbits in the affine Grassmannian Gr G . We prove Simon Schieder's conjecture identifying his bialgebra formed by the top compactly supported cohomology of the intersections of opposite semi‐infinite orbits with U ( n ∨ ) (the universal enveloping algebra of the positive

    更新日期:2020-03-18
  • Tight contact structures on Seifert surface complements
    J. Topol. (IF 1.642) Pub Date : 2020-03-18
    Tamás Kálmán, Daniel V. Mathews

    We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number to be the leading coefficient of the Alexander polynomial. The Euler classes of the contact structures are identified with hypertrees in a certain hypergraph. Using

    更新日期:2020-03-18
  • Chain level loop bracket and pseudo‐holomorphic disks
    J. Topol. (IF 1.642) Pub Date : 2020-03-18
    Kei Irie

    Let L be a Lagrangian submanifold in a symplectic vector space which is closed, oriented and spin. Using virtual fundamental chains of moduli spaces of nonconstant pseudo‐holomorphic disks with boundaries on L , one can define a Maurer–Cartan element of a Lie bracket operation in string topology (the loop bracket) defined at chain level. This observation is due to Fukaya, who also pointed out its important

    更新日期:2020-03-18
  • Non‐integrality of some Steinberg modules
    J. Topol. (IF 1.642) Pub Date : 2020-03-16
    Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson, Dan Yasaki

    We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartment classes. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartment classes if and only if the ring is Euclidean. We also construct new cohomology classes in the top‐dimensional

    更新日期:2020-03-16
  • Framed transfers and motivic fundamental classes
    J. Topol. (IF 1.642) Pub Date : 2020-03-16
    Elden Elmanto, Marc Hoyois, Adeel A. Khan, Vladimir Sosnilo, Maria Yakerson

    We relate the recognition principle for infinite P 1 ‐loop spaces to the theory of motivic fundamental classes of Déglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with A n /

    更新日期:2020-03-16
  • Finite presentations for spherical/braid twist groups from decorated marked surfaces
    J. Topol. (IF 1.642) Pub Date : 2020-03-16
    Yu Qiu, Yu Zhou

    We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3‐Calabi–Yau triangulated category. The motivation/application is that the result will be used to show that the (principal component of) space of stability

    更新日期:2020-03-16
  • Regular globally hyperbolic maximal anti‐de Sitter structures
    J. Topol. (IF 1.642) Pub Date : 2020-01-29
    Andrea Tamburelli

    Let Σ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce regular globally hyperbolic anti‐de Sitter structures on Σ × R and provide two parameterisations of their deformation space: as an enhanced product of two copies of the Fricke space of Σ and as the bundle over the Teichmüller space of Σ whose fibre consists of meromorphic quadratic differentials with

    更新日期:2020-01-29
  • On the E2‐term of the bo‐Adams spectral sequence
    J. Topol. (IF 1.642) Pub Date : 2020-01-11
    A. Beaudry, M. Behrens, P. Bhattacharya, D. Culver, Z. Xu

    The E 1 ‐term of the (2‐local) bo ‐based Adams spectral sequence for the sphere spectrum decomposes into a direct sum of a v 1 ‐periodic part, and a v 1 ‐torsion part. Lellmann and Mahowald completely computed the d 1 ‐differential on the v 1 ‐periodic part, and the corresponding contribution to the E 2 ‐term. The v 1 ‐torsion part is harder to handle, but with the aid of a computer it was computed

    更新日期:2020-01-11
  • Topological concordance of knots in homology spheres and the solvable filtration
    J. Topol. (IF 1.642) Pub Date : 2019-12-04
    Christopher W. Davis

    In 2016, Levine showed that there exists a knot in a homology 3‐sphere which is not smoothly concordant to any knot in S 3 where one allows concordances in any smooth homology cobordism. Whether the same is true if one allows topological concordances is not known. One might hope that such an example might be detected by the powerful filtration of knot concordance introduced by Cochran–Orr–Teichner

    更新日期:2019-12-04
  • On minimal ideal triangulations of cusped hyperbolic 3‐manifolds
    J. Topol. (IF 1.642) Pub Date : 2019-11-22
    William Jaco, Hyam Rubinstein, Jonathan Spreer, Stephan Tillmann

    Previous work of the authors studies minimal triangulations of closed 3‐manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1‐dimensional Z 2 ‐cohomology. The underlying blueprint is now used in the study of minimal ideal triangulations. As an application, it is shown that the monodromy ideal triangulations of the hyperbolic once‐punctured torus bundles

    更新日期:2019-11-22
  • On the Chern classes of singular complete intersections
    J. Topol. (IF 1.642) Pub Date : 2019-11-11
    Roberto Callejas‐Bedregal, Michelle F. Z. Morgado, José Seade

    We consider two classical extensions for singular varieties of the usual Chern classes of complex manifolds, namely the total Schwartz–MacPherson and Fulton–Johnson classes, c S M ( X ) and c F J ( X ) . Their difference (up to sign) is the total Milnor class M ( X ) , a gener‐alization of the Milnor number for varieties with arbitrary singular set. We get first Verdier‐Riemann–Roch type formulae for

    更新日期:2019-11-11
  • Negatively curved bundles in the Igusa stable range
    J. Topol. (IF 1.642) Pub Date : 2019-11-11
    Mauricio Bustamante, Francis Thomas Farrell, Yi Jiang

    We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of Riemannian metrics without conjugate points on a high‐dimensional manifold with hyperbolic fundamental group. As a consequence, we show that spaces of negatively curved Riemannian metrics have in general nontrivial rational homotopy groups. We also show that smooth M ‐bundles over

    更新日期:2019-11-11
  • A characterization on separable subgroups of 3‐manifold groups
    J. Topol. (IF 1.642) Pub Date : 2019-11-11
    Hongbin Sun

    In this paper, we give a complete characterization on which finitely generated subgroups of finitely generated 3‐manifold groups are separable. Our characterization generalizes Liu's spirality character on surface subgroups of closed 3‐manifold groups. A consequence of our characterization is that, for any compact, orientable, irreducible and ∂ ‐irreducible 3‐manifold M with nontrivial torus decomposition

    更新日期:2019-11-11
  • Finiteness of nonzero degree maps between 3‐manifolds
    J. Topol. (IF 1.642) Pub Date : 2019-11-11
    Yi Liu

    In this paper, it is shown that every orientable closed 3‐manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible nongeometric orientable closed 3‐manifolds. Moreover, given any nonzero integer, as a mapping degree up to sign, every orientable closed 3‐manifold maps with that degree onto only finitely many homeomorphically distinct orientable closed 3‐manifolds

    更新日期:2019-11-11
  • Structures in genus‐zero relative Gromov–Witten theory
    J. Topol. (IF 1.642) Pub Date : 2019-11-11
    H. Fan, L. Wu, F. You

    In this paper, we define genus‐zero relative Gromov–Witten invariants with negative contact orders. Using this, we construct relative quantum cohomology rings and Givental formalism. A version of Virasoro constraints also follows from it.

    更新日期:2019-11-11
  • Peculiar modules for 4‐ended tangles
    J. Topol. (IF 1.642) Pub Date : 2019-08-19
    Claudius Zibrowius

    With a 4‐ended tangle T , we associate a Heegaard Floer invariant CFT ∂ ( T ) , the peculiar module of T . Based on Zarev's bordered sutured Heegaard Floer theory (Zarev, PhD Thesis, Columbia University, 2011), we prove a glueing formula for this invariant which recovers link Floer homology H F L ̂ . Moreover, we classify peculiar modules in terms of immersed curves on the 4‐punctured sphere. In fact

    更新日期:2019-08-19
  • Lifting accessible model structures
    J. Topol. (IF 1.642) Pub Date : 2019-08-16
    Richard Garner, Magdalena Kędziorek, Emily Riehl

    A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted along either a left or a right adjoint. It follows that accessible model structures on locally presentable categories – ones admitting accessible functorial factorizations

    更新日期:2019-08-16
  • Twisted spin cobordism and positive scalar curvature
    J. Topol. (IF 1.642) Pub Date : 2019-08-14
    Fabian Hebestreit, Michael Joachim

    We show how a suitably twisted spin cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others. We then investigate this parametrised spectrum, compute its m o d 2 ‐cohomology and generalise the Anderson–Brown–Peterson splitting of the usual spin cobordism

    更新日期:2019-08-14
  • Equivalent non‐isotopic spheres in 4‐manifolds
    J. Topol. (IF 1.642) Pub Date : 2019-07-30
    Hannah R. Schwartz

    We construct infinitely many smooth oriented 4‐manifolds containing pairs of homotopic, smoothly embedded 2‐spheres that are not topologically isotopic, but that are equivalent by an ambient diffeomorphism inducing the identity on homology. These examples show that Gabai's recent ‘generalized 4D lightbulb theorem' does not generalize to arbitrary 4‐manifolds. In contrast, we also show that there are

    更新日期:2019-07-30
  • The topological period–index problem over 8‐complexes, I
    J. Topol. (IF 1.642) Pub Date : 2019-07-03
    Xing Gu

    We study the Postnikov tower of the classifying space of a compact Lie group P ( n , m n ) , which gives obstructions to lifting a topological Brauer class of period n to a P U m n ‐torsor, where the base space is a CW complex of dimension 8 . Combined with the study of a twisted version of Atiyah–Hirzebruch spectral sequence, this solves the topological period–index problem for CW complexes of dimension 8

    更新日期:2019-07-03
  • Groups with infinitely many ends acting analytically on the circle
    J. Topol. (IF 1.642) Pub Date : 2019-06-24
    Sébastien Alvarez, Dmitry Filimonov, Victor Kleptsyn, Dominique Malicet, Carlos Meniño Cotón, Andrés Navas, Michele Triestino

    This article is inspired by two milestones in the study of non‐minimal group actions on the circle: Duminy's theorem about the number of ends of semi‐exceptional leaves, and Ghys' freeness result in real‐analytic regularity. Our first result concerns groups of real‐analytic diffeomorphisms with infinitely many ends: if the action is non‐expanding, then the group is virtually free. The second result

    更新日期:2019-06-24
  • Positive scalar curvature and higher‐dimensional families of Seiberg–Witten equations
    J. Topol. (IF 1.642) Pub Date : 2019-06-21
    Hokuto Konno

    We introduce an invariant of tuples of commuting diffeomorphisms on a 4‐manifold using families of Seiberg–Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1‐parameter families of Seiberg–Witten equations. Our invariant yields an application to the homotopy groups of the space of positive scalar curvature metrics on a 4‐manifold. We also study the

    更新日期:2019-06-21
  • Action dimensions of some simple complexes of groups
    J. Topol. (IF 1.642) Pub Date : 2019-06-21
    Michael W. Davis, Giang Le, Kevin Schreve

    The action dimension of a discrete group G is the minimum dimension of a contractible manifold that admits a proper G ‐action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including (1) Artin groups, (2) graph products of groups and (3) fundamental groups of aspherical complements of arrangements of affine hyperplanes.

    更新日期:2019-06-21
  • Koszul duality via suspending Lefschetz fibrations
    J. Topol. (IF 1.642) Pub Date : 2019-06-20
    Yin Li

    Let M be a Liouville 6‐manifold which is the smooth fiber of a Lefschetz fibration on C 4 constructed by suspending a Lefschetz fibration on C 3 . We prove that for many examples including stabilizations of Milnor fibers of hypersurface cusp singularities, the compact Fukaya category F ( M ) and the wrapped Fukaya category W ( M ) are related through A ∞ ‐Koszul duality, by identifying them with cyclic

    更新日期:2019-06-20
  • Comparing cyclotomic structures on different models for topological Hochschild homology
    J. Topol. (IF 1.642) Pub Date : 2019-06-18
    Emanuele Dotto, Cary Malkiewich, Irakli Patchkoria, Steffen Sagave, Calvin Woo

    The topological Hochschild homology THH ( A ) of an orthogonal ring spectrum A can be defined by evaluating the cyclic bar construction on A or by applying Bökstedt's original definition of THH to A . In this paper, we construct a chain of stable equivalences of cyclotomic spectra comparing these two models for THH ( A ) . This implies that the two versions of topological cyclic homology resulting

    更新日期:2019-06-18
  • Distortion of surfaces in 3‐manifolds
    J. Topol. (IF 1.642) Pub Date : 2019-06-17
    Hoang Thanh Nguyen

    Let g : S ↬ N be a properly immersed π 1 ‐injective surface in a non‐geometric 3‐manifold N . We compute the distortion of π 1 ( S ) in π 1 ( N ) and show that how it is related to separability of π 1 ( S ) in π 1 ( N ) . The only possibility of the distortion is linear, quadratic, exponential, and double exponential.

    更新日期:2019-06-17
  • Braids with as many full twists as strands realize the braid index
    J. Topol. (IF 1.642) Pub Date : 2019-05-28
    Peter Feller, Diana Hubbard

    We characterize the fractional Dehn twist coefficient of a braid in terms of a slope of the homogenization of the Upsilon function, where Upsilon is the function‐valued concordance homomorphism defined by Ozsváth, Stipsicz, and Szabó. We use this characterization to prove that n ‐braids with fractional Dehn twist coefficient larger than n − 1 realize the braid index of their closure. As a consequence

    更新日期:2019-05-28
  • Cellular approximations of p‐local compact groups
    J. Topol. (IF 1.642) Pub Date : 2019-05-28
    Natàlia Castellana, Ramón Flores, Alberto Gavira‐Romero

    Let A be the classifying space of an abelian p ‐torsion group. We compute A ‐cellular approximations (in the sense of Chachólski and Farjoun) of classifying spaces of p ‐local compact groups, with special emphasis in the cases which arise from compact Lie groups.

    更新日期:2019-05-28
  • Voros symbols as cluster coordinates
    J. Topol. (IF 1.642) Pub Date : 2019-05-10
    Dylan G. L. Allegretti

    We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock–Goncharov coordinates of framed P G L 2 ( C ) ‐local systems on a marked bordered surface. Using this result, we show that these Borel sums can be extended to meromorphic functions on C ∗ , and we prove an asymptotic property of the monodromy map introduced in collaboration with Tom Bridgeland

    更新日期:2019-05-10
  • Symplectic homology of complements of smooth divisors
    J. Topol. (IF 1.642) Pub Date : 2019-04-23
    Luís Diogo, Samuel T. Lisi

    If ( X , ω ) is a closed symplectic manifold, and Σ is a smooth symplectic submanifold Poincaré dual to a positive multiple of ω , then X ∖ Σ can be completed to a Liouville manifold ( W , d λ ) .

    更新日期:2019-04-23
  • A gluing theorem for the Kapustin–Witten equations with a Nahm pole
    J. Topol. (IF 1.642) Pub Date : 2019-04-18
    Siqi He

    In the present paper, we establish a gluing construction for the Nahm pole solutions to the Kapustin–Witten equations over manifolds with boundaries and cylindrical ends. Given two Nahm pole solutions with some convergence assumptions on the cylindrical ends, we prove that there exists an obstruction class for gluing the two solutions together along the cylindrical end. In addition, we establish a

    更新日期:2019-04-18
  • Chow–Witt rings of classifying spaces for symplectic and special linear groups
    J. Topol. (IF 1.642) Pub Date : 2019-04-18
    Jens Hornbostel, Matthias Wendt

    We compute the Chow–Witt rings of the classifying spaces for the symplectic and special linear groups. In the structural description we give, contributions from real and complex realization are clearly visible. In particular, the computation of cohomology with I j ‐coefficients is done closely along the lines of Brown's computation of integral cohomology for special orthogonal groups. The computations

    更新日期:2019-04-18
  • Commuting matrices and Atiyah's real K‐theory
    J. Topol. (IF 1.642) Pub Date : 2019-04-17
    Simon Gritschacher, Markus Hausmann

    We describe the C 2 ‐equivariant homotopy type of the space of commuting n ‐tuples in the stable unitary group in terms of Real K‐theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n ‐tuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal K‐theory.

    更新日期:2019-04-17
  • On the stable Cannon Conjecture
    J. Topol. (IF 1.642) Pub Date : 2019-04-15
    Steve Ferry, Wolfgang Lück, Shmuel Weinberger

    The Cannon Conjecture for a torsion‐free hyperbolic group G with boundary homeomorphic to S 2 says that G is the fundamental group of an aspherical closed 3‐manifold M . It is known that then M is a hyperbolic 3‐manifold. We prove the stable version that for any closed manifold N of dimension greater or equal to 2 there exists a closed manifold M together with a simple homotopy equivalence M → N ×

    更新日期:2019-04-15
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