Results 31 to 40 of about 102,917 (274)
Separation of Relatively Quasiconvex Subgroups [PDF]
, 2009 Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically
Alperin +8 more
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, 2015 We introduce and systematically study the concept of a growth tight action. This generalizes growth tightness for word metrics as initiated by Grigorchuk and de la Harpe.
Arzhantseva, Goulnara N. +2 more
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Specializing cubulated relatively hyperbolic groups
Journal of Topology, 2022 In arXiv:1204.2810 Agol proved the Virtual Haken and Virtual Fibering Conjectures by confirming a conjecture of Wise: Every cubulated hyperbolic group is virtually special. We extend this result to cocompactly cubulated relatively hyperbolic groups with minimal assumptions on the parabolic subgroups.
Groves, Daniel, Manning, Jason Fox
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Floyd maps for relatively hyperbolic groups [PDF]
Geometric and Functional Analysis, 2012 Given a finitely generated group \(G\) and a finite generating set, the edges in the Cayley graph have length \(1\). W. J. Floyd conformally deformed the metric to get a metric space with finite diameter. Let \(f\colon\mathbb N\to (0,\infty)\) be a non-increasing function with \(\sum_{n=0}^\infty f(n)0\) so that \(Mf(r)\leq f(kr)\leq Nf(r)\) for all ...
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Forum of Mathematics, SigmaWe compare the marked length spectra of some pairs of proper and cocompact cubical actions of a nonvirtually cyclic group on $\mathrm {CAT}(0)$ cube complexes.
Stephen Cantrell, Eduardo Reyes
doaj +1 more source
Relative Rigidity, Quasiconvexity and C-Complexes [PDF]
, 2008 We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$ where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of parabolics 3) $X$ is a ...
Mj, Mahan
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Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2004 We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group with $\integers$, given through an automorphism $\alpha{:}\, G \,{\to}\, G$, is a hyperbolic group relative to certain canonical subgroups of $G$ on which $\alpha$ acts periodically or with linear growth.
Gautero, François, Lustig, Martin
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A Cartan-Hadamard type result for relatively hyperbolic groups [PDF]
, 2013 In this article, we prove that if a finitely presented group has an asymptotic cone which is tree-graded with respect to a precise set of pieces then it is relatively hyperbolic. This answers a question of M.
Coulon, Rémi +2 more
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Quasi-hyperbolic planes in relatively hyperbolic groups
Annales Academiae Scientiarum Fennicae Mathematica, 2020 We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the hyperbolic plane. In natural situations, the specific embeddings we find remain quasi-isometric embeddings when composed with the inclusion map from the Cayley graph to the ...
Mackay, John, Sisto, Alessandro
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Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
, 2014 We introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the later one provides a ...
Dahmani, F., Guirardel, V., Osin, D.
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