Hyperbolic groups with 1-dimensional boundary
Group Theory
2007-05-23 v1 Geometric Topology
Abstract
If a torsion-free hyperbolic group G has 1-dimensional boundary, then the boundary is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When the boundary of G is a Sierpinski carpet we show that G is a quasi-convex subgroup of a 3-dimensional hyperbolic Poincare duality group. We also construct a ``topologically rigid'' hyperbolic group G: any homeomorphism of the boundary of G is induced by an element of G.
Cite
@article{arxiv.math/9806059,
title = {Hyperbolic groups with 1-dimensional boundary},
author = {Michael Kapovich and Bruce Kleiner},
journal= {arXiv preprint arXiv:math/9806059},
year = {2007}
}