ENGLISH

A Primer on Mapping Class Groups (PMS-49)

By Benson Farb; Dan Margalit

Book information

Publisher
Princeton University Press
Year
2011
ISBN
9781400839049
DOI
10.1515/9781400839049
Language
english
Format
PDF
Filesize
3 MB (2769414 bytes)
Series
Princeton Mathematical Series; 41
Edition
Course Book
Pages
512\488
Library
degruyter.com
Time added
2023-08-26 05:19:44

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 Teichmüller 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.

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