Hyperbolic groups with 1-dimensional boundary

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.

Keywords

Group Theory, Geometric Topology

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/77030

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9806059
 http://arxiv.org/abs/math/9806059

Collections

arXiv