Combination of quasiconvex subgroups of relatively hyperbolic groups

Abstract

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups $Q$ and $R$ is quasiconvex and isomorphic to $Q{\ast }_{Q\cap R}R$. Our results generalized known combination theorems for quasiconvex subgroups of word-hyperbolic groups. Some applications are presented.

25 pages, 12 figures. v2: Improved the exposition. Rewriting of parts due to referee's comments. Version to appear in "Groups, Geometry and Dynamics"

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