Outer circles : an introduction to hyperbolic 3-manifolds
著者
書誌事項
Outer circles : an introduction to hyperbolic 3-manifolds
Cambridge University Press, 2007
大学図書館所蔵 全26件
注記
Includes bibliographical references (p. 393-410) and index
内容説明・目次
内容説明
We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.
目次
- List of illustrations
- Preface
- 1. Hyperbolic space and its isometries
- 2. Discrete groups
- 3. Properties of hyperbolic manifolds
- 4. Algebraic and geometric convergence
- 5. Deformation spaces and the ends of manifolds
- 6. Hyperbolization
- 7. Line geometry
- 8. Right hexagons and hyperbolic trigonometry
- Bibliography
- Index.
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