Relative Hyperbolicity and Relative Quasiconvexity for Countable Groups

  title={Relative Hyperbolicity and Relative Quasiconvexity for Countable Groups},
  • Published 2008
We lay the foundations for the study of relatively quasiconvex subgroups of relatively hyperbolic groups. These foundations require that we first work out a coherent theory of countable relatively hyperbolic groups (not necessarily finitely generated). We prove the equivalence of Gromov, Osin, and Bowditch’s definitions of relative hyperbolicity for countable groups. We then give several equivalent definitions of relatively quasiconvex subgroups in terms of various natural geometries on a… CONTINUE READING
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