A Primer on Mapping Class Groups is popular PDF and ePub book, written by Benson Farb in 2012, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, A Primer on Mapping Class Groups can be Read Online from any device for your convenience.
A Primer on Mapping Class Groups Book PDF Summary
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.
Detail Book of A Primer on Mapping Class Groups PDF
- Author : Benson Farb
- Release : 20 September 2024
- Publisher : Princeton University Press
- ISBN : 9780691147949
- Genre : Mathematics
- Total Page : 490 pages
- Language : English
- PDF File Size : 20,9 Mb
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