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 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.

60 pages, 4 figures

References in corpus (4)

• At infinity of finite-dimensional CAT(0) spaces
• A Combination Theorem for Metric Bundles
• Z-Structures on Product Groups
• Boundaries of systolic groups

Cited by in corpus (9)

• Quasi-isometries Between Groups with Two-Ended Splittings
• Finite-Dimensionality of Z-Boundaries
• Boundaries of Baumslag-Solitar Groups
• Complex of Relatively Hyperbolic Groups
• Equivariant blowups of bounded parabolic points
• Combination of classifying spaces for proper actions
• Proper homotopy types and Z-boundaries of spaces admitting geometric group actions
• Research announcement: A combination theorem for acylindrical complexes of hyperbolic groups and Cannon-Thurston maps
• Coarse $\mathcal{Z}$-Boundaries for Groups