Peripheral structures of relatively hyperbolic groups

2011/01/15 by Wenyuan Yang, Yang, Wenyuan
Mathematics · #20F65 #20F67 (Primary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F65 #msc:20F67

paper · pdf · doi:10.48550/arxiv.1101.2990

30 pages

arxiv created 2011/11/13 · arxiv updated 2011/11/15

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 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.

Related

• The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups
• Detecting Relatively Quasiconvex Subgroups and Their Induced Peripheral Structure
• Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity
• Quasiconvexity in the Relatively Hyperbolic Groups
• Floyd maps to the boundaries of relatively hyperbolic groups