A primer on mapping class groups
Author(s)
Bibliographic Information
A primer on mapping class groups
（Princeton mathematical series, 49）
Princeton University Press, c2012
- : hardback
Available at / 45 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. [447]-463) and index
Description and Table of Contents
Description
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. A Primer on Mapping Class Groups 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 Teichmuller 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.
Table of Contents
*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*Acknowledgments, pg. xiii*Overview, pg. 1*Chapter One. Curves, Surfaces, and Hyperbolic Geometry, pg. 17*Chapter Two. Mapping Class Group Basics, pg. 44*Chapter Three. Dehn Twists, pg. 64*Chapter Four. Generating The Mapping Class Group, pg. 89*Chapter Five. Presentations And Low-Dimensional Homology, pg. 116*Chapter Six. The Symplectic Representation and the Torelli Group, pg. 162*Chapter Seven. Torsion, pg. 200*Chapter Eight. The Dehn-Nielsen-Baer Theorem, pg. 219*Chapter Nine. Braid Groups, pg. 239*Chapter Ten. Teichmuller Space, pg. 263*Chapter Eleven. Teichmuller Geometry, pg. 294*Chapter Twelve. Moduli Space, pg. 342*Chapter Thirteen. The Nielsen-Thurston Classification, pg. 367*Chapter Fourteen. Pseudo-Anosov Theory, pg. 390*Chapter Fifteen. Thurston'S Proof, pg. 424*Bibliography, pg. 447*Index, pg. 465
by "Nielsen BookData"
