Non-positively curved complexes of groups and boundaries

Martin, Alexandre¹

¹ IRMA, Université de Strasbourg, 7 rue René-Descartes, 67084 Cedex Strasbourg, France

Geometry & topology, Tome 18 (2014) no. 1, pp. 31-102.

Résumé

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.

Détail

DOI : 10.2140/gt.2014.18.31

Classification : 20F65, 20F67, 20F69
Keywords: complexes of groups, boundaries of groups, hyperbolic groups

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