A Primer on Mapping Class Groups (PMS-49) (Princeton Mathematical Series Book 41) by Benson Farb (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The product was amazing very easy to install I am a 50-year-old woman and I did it all by myself☺️ great packaging and I got it pretty fast considering the covid situation.

⭐This is an excllent book for mapping class goup, and some teichmuller geometry.

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