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.
Citation
Francois Dahmani. "Combination of convergence groups." Geom. Topol. 7 (2) 933 - 963, 2003. https://doi.org/10.2140/gt.2003.7.933
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