Geometry And Dynamics In Gromov Hyperbolic Metric Spaces
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Geometry and Dynamics in Gromov Hyperbolic Metric Spaces
Author: Tushar Das
language: en
Publisher: American Mathematical Soc.
Release Date: 2017-04-14
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Essays in Group Theory
Author: S.M. Gersten
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.
Geometry, Topology, and Dynamics in Negative Curvature
Author: C. S. Aravinda
language: en
Publisher: Cambridge University Press
Release Date: 2016-01-21
Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.