Peripheral structures of relatively hyperbolic groups

Abstract

Abstract. 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. The connection between the existence of a minimal relatively hyperbolic structure on a given group and the action on its Floyd boundary is examined. It is shown that Dunwoody's inaccessible group that has no minimal relatively hyperbolic structure turns out to be acting non-geometrically finitely on its Floyd boundary.