#### Volume 18, issue 1 (2014)

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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 $E\phantom{\rule{0.3em}{0ex}}\mathsc{Z}$–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