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Primer on Mapping Class Groups (PMS-49)

Name: Primer on Mapping Class Groups (PMS-49)
Brand: Princeton University Press
SKU: 04641786
Price: 46046 HUF
Availability: InStock
Author: Benson Farb
ISBN: 9780691147949

Benson Farb

Dan Margalit

Language

English

Book Hardback

Libristo code: 04641786

Publishers Princeton University Press, October 2011

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance.... Full description

Libristo code: 04641786

312 b

46 046 Ft

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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 Teichmller 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.