Peripheral Splittings of Groups

  title={Peripheral Splittings of Groups},
  author={Brian H. Bowditch},
We define the notion of a “peripheral splitting” of a group. This is essentially a representation of the group as the fundamental group of a bipartite graph of groups, where all the vertex groups of one colour are held fixed—the “peripheral subgroups”. We develop the theory of such splittings and prove an accessibility result. The theory mainly applies to relatively hyperbolic groups with connected boundary, where the peripheral subgroups are precisely the maximal parabolic subgroups. We show… CONTINUE READING
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