GT Vol 7 (2003) Paper 27 (Abstract)

Geometry & Topology, Vol. 7 (2003) Paper no. 27, pages 933--963.

Combination of convergence groups

Francois Dahmani

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

AMS subject classification. Primary: 20F67. Secondary: 20E06.

DOI: 10.2140/gt.2003.7.933

E-print: arXiv:math.GR/0203258

Submitted to GT on 5 June 2002. (Revised 4 November 2003.) Paper accepted 5 December 2003. Paper published 11 December 2003.

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Francois Dahmani
Forschungsinstitut fur Mathematik
ETH Zentrum, Ramistrasse, 101
8092 Zurich, Switzerland.
Email: dahmani@math.ethz.ch

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