Combination of convergence groups

Dahmani, Francois¹

¹ Forschungsinstitut für Mathematik, ETH Zentrum, Rämistrasse, 101, 8092 Zürich, Switzerland

Geometry & topology, Tome 7 (2003) no. 2, pp. 933-963.

Résumé

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.

Détail

DOI : 10.2140/gt.2003.7.933

Keywords: relatively hyperbolic groups, geometrically finite convergence groups, combination theorem, limit groups

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