| Description |
xiv, 472 p. : ill. |
| Series |
Princeton mathematical series ; 49 |
|
Princeton mathematical series ; 49.
|
| Bibliography |
Includes bibliographical references and index. |
| Contents |
pt. 1. Mapping class groups -- pt. 2. Teichmuller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory. |
| Summary |
"The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.The book begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmoller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification"--Provided by publisher. |
| Reproduction |
Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. |
| Subject |
Mappings (Mathematics)
|
|
Class groups (Mathematics)
|
| Genre/Form |
Electronic books.
|
| Added Author |
Margalit, Dan, 1976-
|
|
ProQuest (Firm)
|
| ISBN |
9780691147949 |
|
9781400839049 (electronic bk.) |
|
