Complexes of Groups and Boundaries

Details Complexes of Groups and Boundaries Complexes of Groups and Boundaries

2012-01-30

arxiv.org/abs/1201.6249v1

Mathematics

Geometric Topology

60 pages, 4 figures

Scientific paper

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-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.

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