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Kenichi Oshika, "Discrete Groups"

This book deals with geometric and topological aspects of discrete groups. The main topics are hyperbolic groups due to Gromov, automatic group theory, invented and developed by Epstein, whose subjects are groups that can be manipulated by computers, and Kleinian group theory, which enjoys the longest tradition and the richest contents within the theory of discrete subgroups of Lie groups.

What is common among these three classes of groups is that when seen as geometric objects, they have the properties of a negatively curved space rather than a positively curved space. As Kleinian groups are groups acting on a hyperbolic space of constant negative curvature, the technique employed to study them is that of hyperbolic manifolds, typical examples of negatively curved manifolds. Although hyperbolic groups in the sense of Gromov are much more general objects than Kleinian groups, one can apply for them arguments and techniques that are quite similar to those used for Kleinian groups. Automatic groups are further general objects, including groups having properties of spaces of curvature 0. Still, relationships between automatic groups and hyperbolic groups are examined here using ideas inspired by the study of hyperbolic manifolds. In all of these three topics, there is a "soul" of negative curvature upholding the theory. The volume would make a fine textbook for a graduate-level course in discrete groups.

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	Science/Engineering Hyperbolic Manifolds and Discrete Groups Hyperbolic Manifolds and Discrete Groups Birkhäuser Boston \| 2000-11-03 \| ISBN: 0817639047 \| 467 Pages \| 3.23 MB \| PDFHyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, ...
	Discrete Groups, Expanding Graphs and Invariant Measures Alexander Lubotzky “Discrete Groups, Expanding Graphs and Invariant Measures" Birkhäuser Basel \| 1994-08-01 \| ISBN: 376435075X \| 196 pages \| PDF \| 8,7 MB RS link:
	Science/Engineering Discrete Groups (Translations of Mathematical Monographs) Discrete Groups (Translations of Mathematical Monographs) Publisher: American Mathematical Society \| ISBN: 082182080X \| edition 2001 \| DJVU \| 193 pages \| 1,74 mbThis book deals with geometric and topological aspects of discrete groups. The ...
	Science/Engineering Michael Kapovich - Hyperbolic Manifolds and Discrete Groups Michael Kapovich - Hyperbolic Manifolds and Discrete GroupsBirkhäuser Boston \| 2000 \| ISBN: 0817639047 \| Pages: 467 \| PDF \| 5.58 MBHyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic ...
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