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Combination of convergence groups

Francois Dahmani

Geometry & Topology 7 (2003) 933–963

arXiv: math.GR/0203258

Abstract

We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to contruct a boundary for a group that is an acylindrical amalgamation of relatively hyperbolic groups over a fully quasi-convex subgroup. We apply our result to Sela’s theory on limit groups and prove their relative hyperbolicity. We also get a proof of the Howson property for limit groups.

Keywords
relatively hyperbolic groups, geometrically finite convergence groups, combination theorem, limit groups
Mathematical Subject Classification 2000
Primary: 20F67
Secondary: 20E06
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Publication
Received: 5 June 2002
Revised: 4 November 2003
Accepted: 5 December 2003
Published: 11 December 2003
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Walter Neumann
Authors
Francois Dahmani
Forschungsinstitut für Mathematik
ETH Zentrum
Rämistrasse, 101
8092 Zürich
Switzerland