Groups acting on tree-graded spaces and splittings of relatively hyperbolic group

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Tree-graded spaces are generalizations of R-trees. They appear as asymptotic cones of groups (when the cones have cut points). Since many questions about endomorphisms and automorphisms of groups, solving equations over groups, studying embeddings of a group into another group, etc. lead to actions of groups on the asymptotic cones, it is natural to consider actions of groups on tree-graded spaces. We develop a theory of such actions which generalizes the well known theory of groups acting on R-trees. As applications of our theory, we describe, in particular, relatively hyperbolic groups with infinite groups of outer automorphisms, and co-Hopfian relatively hyperbolic groups.
01/30/06 The paper is submitted. 53 pages; Implemented several suggestions from the readers, added some results

Keywords

Group Theory, Geometric Topology, 05C25, 20A15, 20E08, 20DF05, 20F15, 20F28, 20F32, 20F38, 20F65, 20F67, 20F69

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/107529

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601305
 http://arxiv.org/abs/math/0601305

Collections

arXiv