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Combination of convergence groups. (English) Zbl 1037.20042
Author’s summary: We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to construct 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.

MSC:
20F67 Hyperbolic groups and nonpositively curved groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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