Title
Peripheral Structures of Relatively Hyperbolic Groups: A geometric approach from boundaries,Used
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In the 20 years since their introduction by Gromov, relatively hyperbolic groups have been receiving a great deal of attention. This class of groups encompasses many naturally occurring groups, such as geometrically finite Kleinian groups, word hyperbolic groups, limit groups, CAT(0)groups with isolated flats and many others. The objective of this book focuses on the study of relatively hyperbolic groups and their quasiconvex subgroups. 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. A result of independent interest in the thesis is that a separable subgroup has the bounded packing property. This implies that the property is true for each subgroup of a polycyclic group, answering a question of Hruska and Wise.
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