Combination of convergence groups

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

References

Forward citations

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

Volume 7, issue 2 (2003)

Francois Dahmani