## Geometry & Topology

### Non-positively curved complexes of groups and boundaries

Alexandre Martin

#### 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.

#### Article information

Source
Geom. Topol., Volume 18, Number 1 (2014), 31-102.

Dates
Revised: 20 March 2013
Accepted: 16 July 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732719

Digital Object Identifier
doi:10.2140/gt.2014.18.31

Mathematical Reviews number (MathSciNet)
MR3158772

Zentralblatt MATH identifier
1315.20041

#### Citation

Martin, Alexandre. Non-positively curved complexes of groups and boundaries. Geom. Topol. 18 (2014), no. 1, 31--102. doi:10.2140/gt.2014.18.31. https://projecteuclid.org/euclid.gt/1513732719

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