Non-positively curved complexes of groups and boundaries

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 $E\mathcal{Z}$–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.