Results 1 to 10 of about 99 (73)
Stability for hyperbolic groups acting on boundary spheres
Forum of Mathematics, Sigma, 2023 A hyperbolic group G acts by homeomorphisms on its Gromov boundary. We show that if $\partial G$ is a topological n–sphere, the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard boundary ...
Kathryn Mann, Jason Fox Manning
doaj +1 more source
Deforming cubulations of hyperbolic groups
Journal of Topology, Volume 14, Issue 3, Page 877-912, September 2021., 2021 Abstract We describe a procedure to deform cubulations of hyperbolic groups by ‘bending hyperplanes’. Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in fibred hyperbolic 3‐manifolds and free‐by‐Z groups, and Hsu–Wise turns.
Elia Fioravanti, Mark Hagen
wiley +1 more source
Cusps, Kleinian groups, and Eisenstein series
Forum of Mathematics, Sigma, 2023 We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma
Beibei Liu, Shi Wang
doaj +1 more source
Density of Metric Small Cancellation in Finitely Presented Groups [PDF]
Groups, Complexity, Cryptology, 2020 Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information ...
Alex Bishop, Michal Ferov
doaj +1 more source
Packing subgroups in relatively hyperbolic groups [PDF]
, 2006 Our main result establishes the bounded packing of relatively quasiconvex subgroups of a relatively hyperbolic group, under mild hypotheses. As an application, we prove that relatively quasiconvex subgroups have finite height and width, properties that ...
G. Hruska +3 more
semanticscholar +1 more source
Hadamard spaces with isolated flats [PDF]
, 2004 We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces.
Christopher Hruska, B. Kleiner
semanticscholar +1 more source
Curve graphs for Artin–Tits groups of type B, A∼ and C∼ are hyperbolic
Transactions of the London Mathematical Society, 2021 The graph of irreducible parabolic subgroups is a combinatorial object associated to an Artin–Tits group A defined so as to coincide with the curve graph of the (n+1)‐times punctured disk when A is Artin's braid group on (n+1) strands.
Matthieu Calvez +1 more
doaj +1 more source
The Tits Alternative for Cat(0) Cubical Complexes [PDF]
, 2004 A Tits alternative theorem is proved in this paper for groups acting on CAT(0) cubical complexes. That is, a proof is given to show that if G is assumed to be a group for which there is a bound on the orders of its finite subgroups, and if G acts ...
M. Sageev, D. Wise
semanticscholar +1 more source
Combination of quasiconvex subgroups of relatively hyperbolic groups [PDF]
, 2007 For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1 Q1\Q2 Q2.
Eduardo Martínez-Pedroza
semanticscholar +2 more sources
The asymptotic geometry of right-angled Artin groups, I [PDF]
, 2007 We study atomic right-angled Artin groups ‐ those whose defining graph has no cycles of length 4, and no separating vertices, separating edges, or separating vertex stars.
M. Bestvina, B. Kleiner, M. Sageev
semanticscholar +1 more source