Spherical CR geometry and Dehn surgery / Richard Evan Schwartz.

Format:

Book

Author/Creator:

Schwartz, Richard Evan, author.

Series:

Annals of mathematics studies ; number 165.

Annals of mathematics studies ; number 165

Language:

English

Subjects (All):

CR submanifolds.

Dehn surgery (Topology).

Three-manifolds (Topology).

Physical Description:

1 online resource (199 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, 2007.

Language Note:

English

Summary:

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible and straightforward manner, Richard Evan Schwartz also presents a large amount of useful information on complex hyperbolic geometry and discrete groups. Schwartz relies on elementary proofs and avoids "ations of preexisting technical material as much as possible. For this reason, this book will benefit graduate students seeking entry into this emerging area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.

Contents:

Frontmatter

Contents

Preface

Part 1. Basic Material

Part 2. Proof of the HST

Part 3. The Applications

Part 4. Structure of Ideal Triangle Groups

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (pages [181]-184) and index.

Description based on print version record.

ISBN:

9781400837199

1400837197

9780691128108

0691128103

OCLC:

979579583