Combination of convergence groups

Details Combination of convergence groups Combination of convergence groups

2002-03-25

arxiv.org/abs/math/0203258v3

Geom. Topol. 7 (2003) 933-963

Mathematics

Group Theory

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper27.abs.html

Scientific paper

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.

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