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A Primer on Mapping Class Groups (PMS-49) on Hardback by Benson Farb
A Primer on Mapping Class Groups (PMS-49) on Hardback by Benson Farb
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A Primer on Mapping Class Groups (PMS-49)

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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.

Author Biography:

Benson Farb is professor of mathematics at the University of Chicago. He is the editor of "Problems on Mapping Class Groups and Related Topics" and the coauthor of "Noncommutative Algebra". Dan Margalit is assistant professor of mathematics at Georgia Institute of Technology.
Release date NZ
October 16th, 2011
Audiences
  • Professional & Vocational
  • Tertiary Education (US: College)
Illustrations
115 line illus.
Pages
488
Dimensions
152x229x38
ISBN-13
9780691147949
Product ID
10218278

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