Results 41 to 50 of about 17,194 (132)

Simple homotopy theory for Fukaya categories

Journal of Topology, Volume 19, Issue 3, September 2026.
Abstract We develop a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. When the first Chern class vanishes, we show that any isomorphism in the Fukaya category of a Weinstein manifold has trivial Whitehead torsion.
Yonghwan Kim
wiley   +1 more source

An EZ${\mathcal {E}\mathcal {Z}}$‐structure for the mapping class group

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We construct a boundary for the mapping class group Mod(S)${\rm Mod}(S)$ of a surface S$S$ of finite type. The action of Mod(S)${\rm Mod}(S)$ on this boundary is minimal, strongly proximal and topologically free. The boundary is the boundary of an EZ${\mathcal {E}\mathcal {Z}}$‐structure for Mod(S)${\rm Mod}(S)$.
Ursula Hamenstädt
wiley   +1 more source

Gromov hyperbolic groups and the Macaev norm [PDF]

Pacific Journal of Mathematics, 2006
Let \(\Gamma\) be a Gromov hyperbolic group with a finite set \(A\) of generators. One can consider three quantities: the Coornaert-Papadopoulos topological entropy \(h_{top}(\Sigma(\infty))\) of the subshift associated to \((\Gamma,A)\), Voiculescu's invariant \(k^-_\infty(\lambda_A)\), and the growth entropy \(\text{gr}(\Gamma,A)\). The author proves
openaire   +2 more sources

Horofunctions and symbolic dynamics on Gromov hyperbolic groups [PDF]

Glasgow Mathematical Journal, 2001
Let X be a proper geodesic metric space which is \delta-hyperbolic in the sense of Gromov. We study a class of functions on X, called horofunctions, which generalize Busemann functions. To each horofunction is associated a point in the boundary at infinity of X. Horofunctions are used to give a description of the boundary.
Coornaert, Michel, Papadopoulos, Athanase   +1 more
openaire   +1 more source

A new characterization of Gromov hyperbolicity for negatively curved surfaces

, 2021
In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or, Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a
Tourís, E., Rodríguez, J. M.
core  

Quasi‐convex surface subgroups in some one‐relator groups with torsion

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract We find surface subgroups in certain one‐relator groups with torsion and use this to deduce a profinite criterion for a word in the free group to be primitive.
Andrew Ng
wiley   +1 more source

An extended definition of Anosov representation for relatively hyperbolic groups

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich–Leeb and Zhu, and Zhu–Zimmer, as well as holonomy representations of various ...
Theodore Weisman
wiley   +1 more source

Towards the boundary of the fine curve graph

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper, we study the Gromov boundary of this space and the local topology near points associated with certain foliations and laminations. We then give several applications including finding dynamically explicit elements with positive stable ...
Jonathan Bowden, Sebastian Hensel, Richard Webb   +2 more
wiley   +1 more source

The quasi‐redirecting boundary

Journal of Topology, Volume 19, Issue 2, June 2026.
Abstract We generalize the notion of Gromov boundary to a larger class of metric spaces beyond Gromov hyperbolic spaces. Points in this boundary are classes of quasi‐geodesic rays and the space is equipped with a topology that is naturally invariant under quasi‐isometries.
Yulan Qing, Kasra Rafi
wiley   +1 more source

HNN extensions and embedding theorems for groups

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract The Higman–Neumann–Neumann (HNN) paper of 1949 is a landmark of group theory in the 20th century. The proof of its main theorem covers less than a page and uses only pre‐existing technology, but the construction that it introduced, the HNN extension, quickly became one of the principal tools of combinatorial group theory, widely used to build ...
Martin R. Bridson, Carl‐Fredrik Nyberg‐Brodda   +1 more
wiley   +1 more source