Boundaries of geometrically finite groups
Bowditch, B.H. (1999) Boundaries of geometrically finite groups. Mathematische Zeitschrift, 230, (3), 509-527.
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We show that the limit set of a relatively hyperbolic group with no separating horoball is locally connected if it is connected. On the other hand, if there is a separating horoball centred on a parabolic point, one obtains a non-trivial splitting of the group over a parabolic subgroup relative to the maximal parabolic subgroups. Together with results from elsewhere, one deduces that if $ \Gamma $ is a relatively hyperbolic group such that each maximal parabolic subgroup is one-or-two ended, finitely presented, and contains no infinite torsion subgroup, then the boundary of $ \Gamma $ is locally connected if it is connected. As a corollary, we see that the limit set of a geometrically finite group acting on a complete simply connected manifold of pinched negative curvature must be locally connected if it is connected.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Pure Mathematics
|Date Deposited:||27 Jul 2006|
|Last Modified:||31 May 2011 23:52|
|Contributors:||Bowditch, B.H. (Author)
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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