Ações de convergência de produtos livres

Abstract

Let G be a finitely generated group which has a relatively hyperbolic action on the Cantor set and its representative parabolic set P is such that every element Pi ∈ P is relatively hyperbolic with respect to a set Pi , then G is relatively hyperbolic with respect to S i Pi (consequence of [10]) and its Bowditch boundary, ∂B(G, S i Pi), depends only on the spaces ∂B(Pi,Pi). In particular, if G1, ..., Gn are relatively hyperbolic then ∂B(G1 ∗ ... ∗ Gn) only depends, topologically, of the spaces ∂B(Gi) (where we omitted for simplicity the parabolic sets). Our main result generalizes [18] where the hyperbolic boundaries of free products of hyperbolic groups are characterized. However, our methods are entirely different from that of (18).