Corpus ID: 216144537

# Local simple connectedness of boundaries of hyperbolic groups

@article{Barrett2020LocalSC,
title={Local simple connectedness of boundaries of hyperbolic groups},
author={Benjamin Barrett},
journal={arXiv: Geometric Topology},
year={2020}
}
In this paper we prove a theorem describing the local topology of the boundary of a hyperbolic group in terms of its global topology: the boundary is locally simply connected if and only if the complement of any point in the boundary is simply connected. This generalises a theorem of Bestvina and Mess.

#### References

SHOWING 1-10 OF 22 REFERENCES
Boundaries of strongly accessible hyperbolic groups
We consider splittings of groups over finite and two-ended subgroups. We study the combinatorics of such splittings using generalisations of Whitehead graphs. In the case of hyperbolic groups, weExpand
Boundaries of right-angled hyperbolic buildings
• Mathematics
• 2006
We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. Corollary: the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.
On hyperbolic groups
Abstract We prove that a δ-hyperbolic group for δ < ½ is a free product F * G 1 * … * Gn where F is a free group of finite rank and each Gi is a finite group.
Boundaries of Coxeter groups and simplicial complexes with given links
Abstract 1. (1) We construct hyperbolic Coxeter groups with boundaries homeomorphic to Pontryagin surfaces. 2. (2) For any given finite simplicial complex L we construct a finite simplicial complex KExpand
Boundaries of hyperbolic groups
• Mathematics
• 2002
In this paper we survey the known results about boundaries of word-hyperbolic groups.
On the cut point conjecture
We sketch a proof of the fact that the Gromov boundary of a hyperbolic group does not have a global cut point if it is connected. This implies, by a theorem of Bestvina and Mess, that the boundary isExpand
Convergence groups and configuration spaces
We give an account of convergence groups from the point of view of groups which act properly discontinuously on spaces of distinct triples. We give a proof of the equivalence of this characterisationExpand
Convergence groups are Fuchsian groups
A group of homeomorphisms of the circle satisfying the "convergence property" is shown to be the restriction of a discrete group of Mobius transformations of the unit disk. This completes the proofExpand
Topology of Manifolds
Elementary concepts characterizations of $\overline E^1$ and $S^1$ Locally connected spaces fundamental properties of the euclidean $n$-sphere Peano spaces characterizations of $S^2$ and theExpand
Homeomorphic conjugates of Fuchsian groups.
By a Fuchsian group we mean a discrete subgroup of M. It may contain also orientation reversing elements. Usually a Fuchsian group is thought to act on I) but this is not a problem since the actionExpand