Peripheral structures of relatively hyperbolic groups

Details Peripheral structures of relatively hyperbolic groups Peripheral structures of relatively hyperbolic groups

2011-01-15

arxiv.org/abs/1101.2990v3

Mathematics

Group Theory

30 pages

Scientific paper

In this paper, we introduce and characterize a class of parabolically extended structures for relatively hyperbolic groups. A characterization of relative quasiconvexity with respect to parabolically extended structures is obtained using dynamical methods. Some applications are discussed. The class of groups acting geometrically finitely on Floyd boundaries turns out to be easily understood. However, we also show that Dunwoody's inaccessible group does not act geometrically finitely on its Floyd boundary.

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