Volume 18, issue 1 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Non-positively curved complexes of groups and boundaries

Alexandre Martin

Geometry & Topology 18 (2014) 31–102
Abstract

Given a complex of groups over a finite simplicial complex in the sense of Haefliger, we give conditions under which it is possible to build an EZ–structure in the sense of Farrell and Lafont for its fundamental group out of such structures for its local groups. As an application, we prove a combination theorem that yields a procedure for getting hyperbolic groups as fundamental groups of simple complexes of hyperbolic groups. The construction provides a description of the Gromov boundary of such groups.

Keywords
complexes of groups, boundaries of groups, hyperbolic groups
Mathematical Subject Classification 2010
Primary: 20F65, 20F67, 20F69
References
Publication
Received: 22 February 2012
Revised: 20 March 2013
Accepted: 16 July 2013
Preview posted: 21 November 2013
Published: 9 January 2014
Proposed: Jean-Pierre Otal
Seconded: Walter Neumann, Martin R Bridson
Authors
Alexandre Martin
IRMA
Université de Strasbourg
7 rue René-Descartes
67084 Cedex Strasbourg
France