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25 Remote Warehouse Mathematics- Algebraic Geometry

Hyperbolic Manifolds and Kleinian Groups (Oxford Mathematical Monographs)

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Hyperbolic Manifolds and Kleinian Groups (Oxford Mathematical Monographs) Cover

 

Synopses & Reviews

Publisher Comments:

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers produced important work which helped make Kleinian groups an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought about a revolution in the field with his profound investigation of hyperbolic manifolds, and Sullivan developed an important complex dynamical approach. This book provides the fundamental results and key theorems necessary for access to the frontiers of the theory from a modern viewpoint.

Synopsis:

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space. This book aims to provide a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis, giving fundamental results and important theorems.

Table of Contents

0. Hyperbolic surfaces and Fuchsian groups: summary

1. Hyperbolic 3-manifolds

2. The basis of Kleinian group theory

3. Geometrically finite Kleinian groups

4. Finitely generated Kleinian groups

5. The sphere at infinity

6. Infinite ends of hyperbolic manifolds

7. Algebraic and geometric convergences

Appendix

References

Product Details

ISBN:
9780198500629
Author:
Matsuzaki, Katsuhiko
Publisher:
OUP Oxford
Author:
null, Katsuhiko
Author:
null, Masahiko
Author:
Taniguchi, Masahiko
Location:
Oxford :
Subject:
Group Theory
Subject:
Geometry - Algebraic
Subject:
Three-manifolds (Topology)
Subject:
Geometry, Hyperbolic
Subject:
Topology - General
Subject:
Mathematics | Computational Mathematics
Subject:
Kleinian groups.
Subject:
Mathematics-Algebraic Geometry
Edition Number:
2
Edition Description:
Includes bibliographical references and index.
Series:
Oxford Mathematical Monographs
Publication Date:
19980431
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
162 illus.
Pages:
264
Dimensions:
9.3 x 6.1 x 0.7 in 1.2 lb

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Related Subjects

Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Topology

Hyperbolic Manifolds and Kleinian Groups (Oxford Mathematical Monographs) New Hardcover
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Product details 264 pages Oxford University Press - English 9780198500629 Reviews:
"Synopsis" by , A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space. This book aims to provide a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis, giving fundamental results and important theorems.
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