Expansive Convergence Groups are Relatively Hyperbolic |
| |
Authors: | Victor Gerasimov |
| |
Affiliation: | (1) Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antonio Carlos, 6627/ Caixa Postal 702, 30161-970 Belo Horizonte, MG, Brasil |
| |
Abstract: | Let a discrete group G act by homeomorphisms of a compactum in a way that the action is properly discontinuous on triples and cocompact on pairs. We prove that such an action is geometrically finite. The converse statement was proved by P. Tukia [T3]. So, we have another topological characterisation of geometrically finite convergence groups and, by the result of A. Yaman [Y2], of relatively hyperbolic groups. Further, if G is finitely generated then the parabolic subgroups are finitely generated and undistorted. This answer to a question of B. Bowditch and eliminates restrictions in some known theorems about relatively hyperbolic groups. Received: April 2007, Revision: May 2008, Accepted: August 2008 |
| |
Keywords: | KeywordHeading" > and phrases: Convergence group relatively hyperbolic group geometrically finite group expansive group |
本文献已被 SpringerLink 等数据库收录! |
|