Results 21 to 30 of about 437,604 (285)
A non-Hopfian relatively hyperbolic group with respect to a Hopfian subgroup [PDF]
Groups, Geometry, and Dynamics, 2023 We produce an example demonstrating that every finitely generated relatively hyperbolic group with respect to a collection of Hopfian subgroups need not be Hopfian. This answers a question of Osin \cite[Problem 5.5]{Osin} in the negative.
Jan Kim, Donghi Lee
semanticscholar +1 more source
Peripheral fillings of relatively hyperbolic groups [PDF]
Inventiones mathematicae, 2006 A group-theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group G G we define a peripheral filling procedure, which produces quotients of G G by imitating the effect of the Dehn filling of a complete finite-volume hyperbolic 3-manifold M M on the ...
D. Osin
openalex +5 more sources
On cubulated relatively hyperbolic groups
Geometry & Topology, 2020 We show that properly and cocompactly cubulated relatively hyperbolic groups are virtually special, provided the peripheral subgroups are virtually special in a way that is compatible with the cubulation. This extends Agol's result for cubulated hyperbolic groups, and applies to a wide range of peripheral subgroups.
Eduardo Oregón‐Reyes
openalex +4 more sources
Relative Growth in Hyperbolic Groups [PDF]
Monatshefte für Mathematik, 2021 AbstractIn this note we obtain estimates on the relative growth of normal subgroups of non-elementary hyperbolic groups, particularly those with free abelian quotient. As a corollary, we deduce that the associated relative growth series fail to be rational.
Stephen Cantrell, Richard Sharp
openaire +3 more sources
Hyperfiniteness of boundary actions of relatively hyperbolic groups [PDF]
Groups, Geometry, and Dynamics, 2022 We show that if $G$ is a finitely generated group hyperbolic relative to a finite collection of subgroups $\mathcal{P}$, then the natural action of $G$ on the geodesic boundary of the associated relative Cayley graph induces a hyperfinite equivalence ...
Chris Karpinski
semanticscholar +1 more source
The rates of growth in an acylindrically hyperbolic group [PDF]
Groups, Geometry, and Dynamics, 2021 Let G be an acylindrically hyperbolic group on a \delta -hyperbolic space X . Assume there exists M such that for any finite generating set S of G , the set S^{M} contains a hyperbolic element on X
K. Fujiwara
semanticscholar +1 more source
Lower bound on growth of non-elementary subgroups in relatively hyperbolic groups [PDF]
Journal of group theroy, 2021 This paper proves that, in a non-elementary relatively hyperbolic group, the logarithm growth rate of any non-elementary subgroup has a linear lower bound by the logarithm of the size of the corresponding generating set.
Yu-miao Cui +2 more
semanticscholar +1 more source
Bi-exactness of relatively hyperbolic groups [PDF]
Journal of Functional Analysis, 2023 We prove that finitely generated relatively hyperbolic groups are bi-exact if and only if all peripheral subgroups are bi-exact. This is a generalization of Ozawa's result which claims that finitely generated relatively hyperbolic groups are bi-exact if all peripheral subgroups are amenable.
Koichi Oyakawa
openalex +3 more sources
AUTOMORPHISM AND OUTER AUTOMORPHISM GROUPS OF RIGHT-ANGLED ARTIN GROUPS ARE NOT RELATIVELY HYPERBOLIC [PDF]
Bulletin of the Australian Mathematical Society, 2021 We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least three vertices are not relatively hyperbolic. We then show that the outer automorphism groups are also not relatively hyperbolic, except for a few ...
Junseok Kim +2 more
semanticscholar +1 more source
Relatively hyperbolic groups with semistable peripheral subgroups [PDF]
International journal of algebra and computation, 2021 Suppose [Formula: see text] is a finitely presented group that is hyperbolic relative to [Formula: see text] a finite collection of finitely generated proper subgroups of [Formula: see text].
M. Haulmark, M. Mihalik
semanticscholar +1 more source