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  • Linear systems over Z[Q32] and roots of maps of some 3-complexes into MQ32
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-30
    Claudemir Aniz

    Let Z[Q32] be the group ring where Q32=〈x,y|x8=y2,xyx=y〉 is the quaternion group of order 32 and ε the augmentation map. We show that, if PX=K(x−1) and PX=K(−xy+1) has solution over Z[Q32] and all m×m minors of ε(P) are relatively prime, then the linear system PX=K has a solution over Z[Q32]. As a consequence of such results, we show that there is no map f:W→MQ32 that is strongly surjective, i.e.,

    更新日期:2021-01-21
  • On exponent and nilpotency of [Ω(Sr+1),Ω(KPn)]
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-30
    Marek Golasiński; Daciberg Lima Gonçalves; Peter Wong

    We give estimations of the nilpotency class and the p-primary exponent of the total Cohen groups [Ω(Sr+1),Ω(X)] especially, when X is the projective space over K=R,C, the field of reals or complex numbers and H, the quaternionic skew R-algebra.

    更新日期:2021-01-21
  • Kauffman skein algebras and quantum Teichmüller spaces via factorization homology
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2021-01-20
    Juliet Cooke

    We compute the factorization homology of the four-punctured sphere and punctured torus over the quantum group 𝒰q(𝔰𝔩2) explicitly as categories of equivariant modules using the framework developed by Ben-Zvi et al. We identify the algebra of 𝒰q(𝔰𝔩2)-invariants (quantum global sections) with the spherical double affine Hecke algebra of type (C1∨,C1), in the four-punctured sphere case, and with

    更新日期:2021-01-21
  • 3-Manifolds with nilpotent embeddings in S4
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2021-01-20
    J. A. Hillman

    We consider embeddings of 3-manifolds M in S4 such that the two complementary regions X and Y each have nilpotent fundamental group. If β=β1(M) is odd then these groups are abelian and β≤3. In general π1(X) and π1(Y) have 3-generator presentations, and β≤6. We give two examples illustrating our results.

    更新日期:2021-01-21
  • Large color R-matrix for knot complements and strange identities
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2021-01-20
    Sunghyuk Park

    The Gukov–Manolescu series, denoted by FK, is a conjectural invariant of knot complements that, in a sense, analytically continues the colored Jones polynomials. In this paper we use the large color R-matrix to study FK for some simple links. Specifically, we give a definition of FK for positive braid knots, and compute FK for various knots and links. As a corollary, we present a class of “strange

    更新日期:2021-01-21
  • On the basic properties of GCn sets
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2021-01-20
    Hakop A. Hakopian; Navasard K. Vardanyan

    In this paper the simplest n-correct sets in the plane — GCn sets are studied. An n-correct node set 𝒳 is called GCn set if the fundamental polynomial of each node is a product of n linear factors. We say that a node uses a line if the line is a factor of the fundamental polynomial of this node. A line is called k-node line if it passes through exactly k nodes of 𝒳. At most n+1 nodes can be collinear

    更新日期:2021-01-21
  • Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2020-12-30
    Lorenzo Traldi

    Joyce showed that for a classical knot K, the involutory medial quandle IMQ(K) is isomorphic to the core quandle of the homology group H1(X2), where X2 is the cyclic double cover of 𝕊3, branched over K. It follows that |IMQ(K)|=|detK|. In this paper, the extension of Joyce’s result to classical links is discussed. Among other things, we show that for a classical link L of μ≥2 components, the order

    更新日期:2021-01-21
  • Most graphs are knotted
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2020-12-28
    Kazuhiro Ichihara; Thomas W. Mattman

    We present four models for a random graph and show that, in each case, the probability that a graph is intrinsically knotted goes to one as the number of vertices increases. We also argue that, for n≥18, most graphs of order n are intrinsically knotted and, for n≥2m+9, most of order n are not m-apex. We observe that p(n)=1/n is the threshold for intrinsic knotting and linking in Gilbert’s model.

    更新日期:2021-01-21
  • Homotopy types of gauge groups of $$\mathrm {PU}(p)$$ PU ( p ) -bundles over spheres
    J. Homotopy Relat. Struct. (IF 0.537) Pub Date : 2021-01-21
    Simon Rea

    We examine the relation between the gauge groups of \(\mathrm {SU}(n)\)- and \(\mathrm {PU}(n)\)-bundles over \(S^{2i}\), with \(2\le i\le n\), particularly when n is a prime. As special cases, for \(\mathrm {PU}(5)\)-bundles over \(S^4\), we show that there is a rational or p-local equivalence \(\mathcal {G}_{2,k}\simeq _{(p)}\mathcal {G}_{2,l}\) for any prime p if, and only if, \((120,k)=(120,l)\)

    更新日期:2021-01-21
  • On 3-braids and L-space knots
    Geom. Dedicata. (IF 0.584) Pub Date : 2021-01-21
    Christine Ruey Shan Lee, Faramarz Vafaee

    We classify closed 3-braids which are L-space knots.

    更新日期:2021-01-21
  • Making holes in the hyperspace of subcontinua of a continuum having property (b)
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-05
    José G. Anaya; Rosa I. Carranza; David Maya; Fernando Orozco-Zitli

    Let C(X) be the hyperspace of all subcontinua of a metric continuum X. An element A∈C(X) makes a hole in C(X) if C(X)−{A} is not unicoherent. In this paper, we characterize the elements A∈C(X) satisfying that A makes a hole in C(X) when X has property (b).

    更新日期:2021-01-20
  • Discrete line fields on surfaces
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-11
    Tiago Novello; João Paixão; Carlos Tomei; Thomas Lewiner

    Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse–Smale decomposition of a (generic) field plays a fundamental role, relating the geometric structure of phase space to a combinatorial object consisting of critical points and separatrices. Such concepts

    更新日期:2021-01-20
  • The ring of stable homotopy classes of self-maps of An2-polyhedra
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-12
    David Méndez

    We raise the problem of realisability of rings as {X,X} the ring of stable homotopy classes of self-maps of a space X. By focusing on An2-polyhedra, we show that the direct sum of three endomorphism rings of abelian groups, one of which must be free, is realisable as {X,X} modulo the acyclic maps. We also show that Fp3 is not realisable in the setting of finite type An2-polyhedra, for p any prime.

    更新日期:2021-01-20
  • Algebraic fibrations of certain hyperbolic 4-manifolds
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-07
    Jiming Ma; Fangting Zheng

    An algebraically fibering group is an algebraic generalization of the fibered 3-manifold group in higher dimensions. Let M(P) and M(E) be the cusped and compact hyperbolic real moment-angled manifolds associated with the hyperbolic right-angled 24-cell P and the hyperbolic right-angled 120-cell E, respectively. Jankiewicz, Norin, and Wise recently showed that π1(M(P)) and π1(M(E)) are algebraically

    更新日期:2021-01-20
  • Simple homotopy theory and nerve theorem for categories
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-20
    Kohei Tanaka

    We study a combinatorial homotopy theory for small categories without a loop (loopfree categories) which is closely related to Whitehead's simple homotopy theory for regular CW-complexes with triangular cells. Quillen's theorem A and the nerve theorem for loopfree categories are considered from the viewpoint of the simple homotopy theory. Moreover, we extend the classical nerve theorem and discuss

    更新日期:2021-01-20
  • Super-rigidity of certain skeleta using relative symplectic cohomology
    J. Topol. Anal. (IF 0.817) Pub Date : 2021-01-18
    Dmitry Tonkonog; Umut Varolgunes

    This paper uses relative symplectic cohomology, recently studied by Varolgunes, to understand rigidity phenomena for compact subsets of symplectic manifolds. As an application, we consider a symplectic crossings divisor in a Calabi–Yau symplectic manifold M whose complement is a Liouville manifold. We show that, for a carefully chosen Liouville structure, the skeleton as a subset of M exhibits strong

    更新日期:2021-01-19
  • Unknotting numbers and crossing numbers of spatial embeddings of a planar graph
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2021-01-18
    Yuta Akimoto; Kouki Taniyama

    It is known that the unknotting number u(L) of a link L is less than or equal to half the crossing number c(L) of L. We show that there are a planar graph G and its spatial embedding f such that the unknotting number u(f) of f is greater than half the crossing number c(f) of f. We study relations between unknotting number and crossing number of spatial embedding of a planar graph in general.

    更新日期:2021-01-19
  • On 2-twist-spun spherical Montesinos knots
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2021-01-18
    Yeonhee Jang; Misaki Kataoka; Rika Miyakoshi

    We give a classification of 2-twist-spun spherical Montesinos knots.

    更新日期:2021-01-19
  • Gauss diagram formulas of Vassiliev invariants of 2-bouquet graphs
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-08
    Noboru Ito; Natsumi Oyamaguchi

    We introduce new formulas that are Vassiliev invariants of flat vertex isotopy classes of 2-bouquet graphs. Although any Gauss diagram formula of Vassiliev invariants of 2-bouquet graphs in a 3-space has been unknown explicitly, this paper gives the first and simple example.

    更新日期:2021-01-19
  • The Segal conjecture for topological Hochschild homology of Ravenel spectra
    J. Homotopy Relat. Struct. (IF 0.537) Pub Date : 2021-01-19
    Gabriel Angelini-Knoll, J. D. Quigley

    In the 1980’s, Ravenel introduced sequences of spectra X(n) and T(n) which played an important role in the proof of the Nilpotence Theorem of Devinatz–Hopkins–Smith. In the present paper, we solve the homotopy limit problem for topological Hochschild homology of X(n), which is a generalized version of the Segal Conjecture for the cyclic groups of prime order. This result is the first step towards computing

    更新日期:2021-01-19
  • A Characterization of Unimodal Maps with Embedded Adding Machines
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-15
    Lori Alvin

    This paper investigates a constructive characterization of kneading sequences belonging to unimodal maps with embedded adding machines. It takes the concept of a {0,1}-regular scheme, which can be used to generate all kneading sequences of unimodal maps for which the turning point is regularly recurrent, and adds an extra condition that guarantees the constructed kneading sequence will additionally

    更新日期:2021-01-18
  • Rationality is decidable for nearly Euclidean Thurston maps
    Geom. Dedicata. (IF 0.584) Pub Date : 2021-01-16
    William Floyd, Walter Parry, Kevin M. Pilgrim

    Nearly Euclidean Thurston (NET) maps are described by simple diagrams which admit a natural notion of size. Given a size bound C, there are finitely many diagrams of size at most C. Given a NET map F presented by a diagram of size at most C, the problem of determining whether F is equivalent to a rational function is, in theory, a finite computation. We give bounds for the size of this computation

    更新日期:2021-01-18
  • The homotopy types of PSp(n)-gauge groups over S2m
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-09
    Sajjad Mohammadi

    Let Gk(PSp(2)) and Gk(PSp(3)) be the gauge groups of principal PSp(2)-bundles over S8 and principal PSp(3)-bundles over S4 classified by kε1′ and kε2′, where ε1′ and ε2′ are generators of π8(BPSp(2))≅Z and π4(BPSp(3))≅Z, respectively. In this article we partially classify the homotopy types for these gauge groups.

    更新日期:2021-01-14
  • Productivity of cellular-Lindelöf spaces
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-08
    Alan Dow; R.M. Stephenson

    The main purpose of this note is to prove that the product of a cellular-Lindelöf space with a space of countable spread need not be cellular-Lindelöf.

    更新日期:2021-01-13
  • Kashaev invariants of twice-iterated torus knots
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-08
    Hitoshi Murakami; Anh T. Tran

    We calculate the asymptotic behavior of the Kashaev invariant of a twice-itarated torus knot and obtain topological interpretation of the formula in terms of the Chern–Simons invariant and the twisted Reidemeister torsion.

    更新日期:2021-01-13
  • Clopen objects, connected objects, and normalized topological categories
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-07
    Jay Stine

    In this paper we extend the notion of a clopen subset of a topological space to that of a clopen subobject in a topological category. We relate clopen subobjects to the concept of normalized topological category via a theorem which, in turn, shows why certain subsets must be clopen in a topological space. We employ clopen subobjects to extend the topological notion of connectedness to topological categories

    更新日期:2021-01-13
  • On metrizability and compactness of certain products without the Axiom of Choice
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-07
    Paul Howard; Eleftherios Tachtsis

    We prove that there exists a model of ZF (Zermelo–Fraenkel set theory without the Axiom of Choice (AC)) in which there is a compact, metrizable, non-second countable, Cantor cube. This answers in the affirmative an open question by E. Wajch (2018) [15]. Furthermore, we strengthen a result in the above paper, namely “Countable products of metrizable spaces are quasi-metrizable implies van Douwen's Choice

    更新日期:2021-01-13
  • 2-stratifolds with fundamental group Z
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-08
    J.C. Gómez-Larrañaga; F. González-Acuña; Wolfgang Heil

    2-stratifolds are a generalization of 2-manifolds that occur as objects in applications such as in TDA. These spaces can be described by an associated bicoloured labelled graph. In previous papers we obtained a classification of 1-connected trivalent 2-stratifolds. In this paper we classify trivalent 2-stratifolds that have fundamental group Z. This classification implicitly gives an efficient algorithm

    更新日期:2021-01-13
  • Primitive, proper power, and Seifert curves in the boundary of a genus two handlebody
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-05
    Sungmo Kang

    A simple closed curve α in the boundary of a genus two handlebody H is primitive if adding a 2-handle to H along α yields a solid torus. If adding a 2-handle to H along α yields a Seifert-fibered space and not a solid torus, the curve is called Seifert. If α is disjoint from an essential separating disk in H, does not bound a disk in H, and is not primitive in H, then it is said to be proper power

    更新日期:2021-01-13
  • The hit problem for the polynomial algebra in some weight vectors
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-05
    Nguyễn Sum; Nguyễn Khắc Tín

    Let Pk:=F2[x1,x2,…,xk] be the polynomial algebra over the prime field of two elements, F2, in k variables x1,x2,…,xk, each of degree 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for Pk as a module over the mod-2 Steenrod algebra. In this paper, we extend a result in [12] on the hit problem in degree (k−1)(2d−1) with k⩾6, by explicitly computing the hit

    更新日期:2021-01-13
  • Expansive systems on lattices
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-30
    Mauricio Achigar

    We study expansive dynamical systems in the setting of distributive lattices and their automorphisms, the usual notion of expansiveness for a homeomorphism of a compact metric space being the particular case when the lattice is the topology of the phase space ordered by inclusion and the automorphism the one induced by the homeomorphism, mapping open sets to open sets. We prove in this context generalizations

    更新日期:2021-01-10
  • Effective topological complexity of orientable-surface groups
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-04
    Natalia Cadavid-Aguilar; Jesús González

    We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an orientable surface with respect to its antipodal involution. Our estimates are at most one unit from being optimal, and are closely related to the (regular) topological

    更新日期:2021-01-10
  • Menger and Menger-type star selection principles for hit-and-miss topology
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-28
    Ricardo Cruz-Castillo; Alejandro Ramírez-Páramo; Jesús F. Tenorio

    In this paper we characterize the Menger property and the selection principles star-Menger and strongly star-Menger in the hyperspaces CL(X), K(X), F(X) and CS(X), endowed with the hit-and-miss topology. To characterize the corresponding principles type star, we introduce a couple of technical selection principles, which we have denoted by SM(ΠΔ(Γ),ΠΔ(Γ)) and SM⁎(ΠΔ(Γ),ΠΔ(Γ)). Also, we give an equivalence

    更新日期:2021-01-10
  • Beyond Erdős-Kunen-Mauldin: Shift-compactness properties and Singular sets
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-09
    H.I. Miller; L. Miller-Van Wieren; A.J. Ostaszewski

    The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of R which is Baire (= has the Baire property, BP) or measurable is shift-compact: it contains some subsequence of any null sequence to within translation by an element of the set. Here effective proofs are recognized to yield (i) analogous category and Haar-measure metrizable generalizations for Baire groups and locally compact

    更新日期:2021-01-10
  • On the Hodge conjecture for hypersurfaces in toric varieties
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Ugo Bruzzo; Antonella Grassi

    We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties satisfying an effective combinatorial property the Hodge conjecture holds. This gives a connection between the Oda conjecture and Hodge conjecture. We also give an explicit criterion which depends on the degree for very general hypersurfaces for the combinatorial condition to be verified.

    更新日期:2021-01-10
  • The Richberg technique for subsolutions
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    F. Reese Harvey; H. Blaine Lawson; Szymon Pliś

    This note adapts the sophisticated Richberg technique for approximation in pluripotential theory to the $F$-potential theory associated to a general nonlinear convex subequation $F \subset J^2 (X)$ on a manifold $X$. The main theorem is the following “local to global” result. Suppose $u$ is a continuous strictly $F$-subharmonic function such that each point $x \in X$ has a fundamental neighborhood

    更新日期:2021-01-10
  • Isotropic curve flows
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Chuu-Lian Terng; Zhiwei Wu

    A smooth curve $\gamma$ in $\mathbb{R}^{n+1,n}$ is isotropic if $\gamma , \gamma_x, \dotsc , \gamma^{(2n)}_x$ are linearly independent and the span of $\gamma , \gamma_x, \dotsc , \gamma^{(n−1)}_x$ is isotropic. We construct two hierarchies of isotropic curve flows on $\mathbb{R}^{n+1,n}$, whose differential invariants are solutions of Drinfeld–Sokolov’s KdV type soliton hierarchies associated to the

    更新日期:2021-01-10
  • A Liouville-type theorem and Bochner formula for harmonic maps into metric spaces
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Brian Freidin; Yingying Zhang

    We study analytic properties of harmonic maps from Riemannian polyhedra into $\operatorname{CAT}(\kappa)$ spaces for $\kappa \in {\lbrace 0, 1 \rbrace}$. Locally, on each top-dimensional face of the domain, this amounts to studying harmonic maps from smooth domains into $\operatorname{CAT}(\kappa)$ spaces. We compute a target variation formula that captures the curvature bound in the target, and use

    更新日期:2021-01-10
  • Evolution of locally convex closed curves in the area-preserving and length-preserving curvature flows
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Natasa Sesum; Dong-Ho Tsai; Xiao-Liu Wang

    We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to infinity. For the area-preserving flow, the positivity of the enclosed algebraic area determines whether the curvature blows up in finite time or not, while for the

    更新日期:2021-01-10
  • Orthogonal Higgs bundles with singular spectral curves
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Steve Bradlow; Lucas Branco; Laura P. Schaposnik

    We examine Higgs bundles for non-compact real forms of $SO(4,\mathbb{C})$ and the isogenous complex group $SL(2,\mathbb{C}) \times SL(2,\mathbb{C})$. This involves a study of non-regular fibers in the corresponding Hitchin fibrations and provides interesting examples of non-abelian spectral data.

    更新日期:2021-01-10
  • Geodesic orbit spaces in real flag manifolds
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Brian Grajales; Lino Grama; Caio J. C. Negreiros

    We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex case, on real flag manifolds the isotropy representation can have equivalent submodules, which makes invariant metrics depend on more parameters and allows us to find

    更新日期:2021-01-10
  • On isolated umbilic points
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Brendan Guilfoyle

    Counter-examples to the famous conjecture of Carathéodory, as well as the bound on umbilic index proposed by Hamburger, are constructed with respect to Riemannian metrics that are arbitrarily close to the flat metric on Euclidean $3$-space. In particular, Riemannian metrics with a smooth strictly convex $2$-sphere containing a single umbilic point are constructed explicitly, in contradiction with any

    更新日期:2021-01-10
  • Collapsing Ricci-flat metrics on elliptic K3 surfaces
    Commun. Anal. Geom. (IF 0.62) Pub Date : 2021-01-08
    Gao Chen; Jeff Viaclovsky; Ruobing Zhang

    For any elliptic K3 surface $\mathfrak{F} : \mathcal{K} \to \mathbb{P}^1$, we construct a family of collapsing Ricci-flat Kähler metrics such that curvatures are uniformly bounded away from singular fibers, and which Gromov–Hausdorff limit to $\mathbb{P}^1$ equipped with the McLean metric. There are well-known examples of this type of collapsing, but the key point of our construction is that we can

    更新日期:2021-01-10
  • Homology Groups of Cubical Sets with Connections
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-08
    Hélène Barcelo, Curtis Greene, Abdul Salam Jarrah, Volkmar Welker

    Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of “connection” as a new kind of degeneracy. In this paper, for a cubical set with connections, we show that the connections generate an acyclic subcomplex of the chain complex of the cubical set. In particular, our results show that the homology groups of a cubical set with connections are independent of whether

    更新日期:2021-01-08
  • On M-factorizable P-groups
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-04
    Heng Zhang; Wei He; Dekui Peng; Mikhail Tkachenko

    A topological group G is M-factorizable if for every continuous real-valued function f on G, one can find a continuous homomorphism π:G→H onto a metrizable topological group H and a continuous function h on H such that f=h∘π. We continue the study of M-factorizability in topological groups started in Zhang et al. (2020) [14], with a special emphasis on P-groups, i.e., the groups in which all Gδ-sets

    更新日期:2021-01-07
  • Cofinal completion vis-á-vis Cauchy continuity and total boundedness
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-31
    Lipsy Gupta; S. Kundu

    A function f from a metric space (X,d) to another metric space (Y,ρ) is said to be Cauchy-continuous if for every Cauchy sequence (xn) in (X,d), (f(xn)) is Cauchy in (Y,ρ). It is well known that a metric space is complete if and only if every real-valued continuous function defined on it is Cauchy-continuous. Here we consider a well-studied intermediate class of metric spaces which lies between the

    更新日期:2021-01-07
  • Simple Smale flows and their templates on S3
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-07
    Xiang Liu; Xuezhi Zhao

    The embedded template is a geometric tool in dynamics being used to model knots and links as periodic orbits of 3-dimensional flows. We prove that for an embedded template in S3 with fixed homeomorphism type, its boundary as a trivalent spatial graph is a complete isotopic invariant. Moreover, we construct an invariant of embedded templates by Kauffman's invariant of spatial graphs, which is a set

    更新日期:2021-01-07
  • The algebraic K-theory of the group ring of the Klein bottle group
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-07
    Cristhian E. Hidber; Daniel Juan-Pineda

    Let K denote the Klein bottle. We compute the algebraic K-theory groups of the ring Z[π1(K)] in terms of the algebraic K-theory groups of the integers. Following the same arguments, we do the same for the ring Z[π1(Ng)], where Ng denotes a nonorientable closed surface of genus g>2.

    更新日期:2021-01-07
  • The R∞-property for right-angled Artin groups
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-07
    Karel Dekimpe; Pieter Senden

    Given a group G and an automorphism φ of G, two elements x,y∈G are said to be φ-conjugate if x=gyφ(g)−1 for some g∈G. The number of equivalence classes is the Reidemeister number R(φ) of φ, and if R(φ)=∞ for all automorphisms of G, then G is said to have the R∞-property. A finite simple graph Γ gives rise to the right-angled Artin group AΓ, which has as generators the vertices of Γ and as relations

    更新日期:2021-01-07
  • The equivariant cobordism category
    J. Topol. (IF 1.642) Pub Date : 2021-01-07
    Søren Galatius; Gergely Szűcs

    For a finite group G , we define an equivariant cobordism category C d G . Objects of the category are ( d − 1 ) ‐dimensional closed smooth G ‐manifolds and morphisms are smooth d ‐dimensional equivariant cobordisms. We identify the homotopy type of its classifying space (that is, geometric realization of its simplicial nerve) as the fixed points of the infinite loop space of a certain equivariant

    更新日期:2021-01-07
  • A Categorical Approach to Linkage
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-07
    Alexander York

    Linkage of ideals is a very well-studied topic in algebra. It has lead to the development of module linkage which looks to extend the ideas and results of the former. Although linkage has been used extensively to find many interesting and impactful results, it has only been extended to schemes and modules. This paper builds a framework in which to perform linkage from a categorical perspective. This

    更新日期:2021-01-07
  • The Grothendieck Group of an n -exangulated Category
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-06
    Johanne Haugland

    We define the Grothendieck group of an n-exangulated category. For n odd, we show that this group shares many properties with the Grothendieck group of an exact or a triangulated category. In particular, we classify dense complete subcategories of an n-exangulated category with an n-(co)generator in terms of subgroups of the Grothendieck group. This unifies and extends results of Thomason, Bergh–Thaule

    更新日期:2021-01-07
  • Remarks on g-reversible topological groups
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-05
    Wei He; Dekui Peng

    Our main objective is to study g-reversible groups introduced in Chatyrko and Shakhmatov (2020) [3]. We first give a necessary and sufficient condition for a locally compact group with an open compact subgroup to be g-reversible, it can be applied to give complete solutions of Questions 8.5, 9.7, 9.8, and Problem 9.6 in the previous article [3]. We also investigate g-reversibility of some precompact

    更新日期:2021-01-06
  • The hyperspace of connected boundary subcontinua of a continuum
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-29
    Raúl Escobedo; Norberto Ordoñez; Rusell-Aarón Quiñones-Estrella; Hugo Villanueva

    Given a metric continumm X, let CB(X) be the hyperspace of subcontinua of X with connected boundary. In this paper we present results concerning CB(X), first about continua for which every subcontinuum has connected boundary. Then we study continua that only have one-point sets as connected boundary proper subcontinua. Later we include characterizations of arcs and simple closed curves. Finally we

    更新日期:2021-01-06
  • Point-countable covers and sequence-covering s-mappings at subsets
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-28
    Xuewei Ling; Shou Lin; Wei He

    A.V. Arhangel'skiı̌ introduced the notion of an almost s-mapping. It is known that the open almost s-images of metric spaces coincide with the open boundary s-images of metric spaces. In this paper, we investigate some questions related to the sequence-covering almost s-images and sequence-covering boundary s-images of metric spaces. We establish some new characterizations of the images of metric spaces

    更新日期:2021-01-06
  • An elementary proof of Euler's formula using Cauchy's method
    Topol. Appl. (IF 0.531) Pub Date : 2021-01-06
    Jean-Paul Brasselet; Nguyn̂̃n Thị Bích Thủy

    The use of Cauchy's method to prove Euler's well-known formula is an object of many controversies. The purpose of this paper is to prove that Cauchy's method applies for convex polyhedra and not only for them, but also for surfaces such as the torus, the projective plane, the Klein bottle and the pinched torus.

    更新日期:2021-01-06
  • The Adams spectral sequence for 3-local $$\mathrm {tmf}$$ tmf
    J. Homotopy Relat. Struct. (IF 0.537) Pub Date : 2021-01-06
    D. Culver

    The purpose of this article is to record the computation of the homotopy groups of 3-local \(\mathrm {tmf}\) via the Adams spectral sequence.

    更新日期:2021-01-06
  • Some strengthened versions of Klamkin’s inequality and applications
    Geom. Dedicata. (IF 0.584) Pub Date : 2021-01-05
    Quang Hung Tran

    In this paper, we establish two strengthened versions of Klamkin’s inequality for an n-dimensional simplex in Euclidean space \({E}^n\) and give some applications.

    更新日期:2021-01-05
  • On some applications of Gauduchon metrics
    Geom. Dedicata. (IF 0.584) Pub Date : 2021-01-04
    Ping Li

    We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with the implications of algebro-geometric nature under the existence of a Hermitian metric with nonnegative holomorphic sectional curvature. The second one is to show the non-existence of holomorphic sections on Hermitian vector bundles under certain conditions. The third one

    更新日期:2021-01-05
  • K-reflections of product spaces
    Topol. Appl. (IF 0.531) Pub Date : 2020-12-28
    Xiaoquan Xu

    Let Topd, Topw and Sob be the category of all d-spaces, that of all well-filtered spaces and that of all sober spaces respectively. For a full subcategory K of Topd containing Sob, it is proved that the product of an arbitrary family of K-determined sets is a K-determined set and if K is adequate, then the K-reflection preserves arbitrary products of T0 spaces. In particular, the Keimel-Lawson reflection

    更新日期:2021-01-04
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