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A Primer on Mapping Class Groups (Pms-49)
Hardcover - English

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 Teichm├╝ller 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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ADDITIONAL INFO

ISBN
0691147949
EAN
9780691147949
Publication Date
16/10/2011
Pages
488
Dimension
23.88cm x 16.26cm x 3.30cm
Age Group
NA to NA
Grades
Not Applicable to Not Applicable
Lexile Level
0
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About Author

Farb, Benson
Benson Farb is professor of mathematics at the "University " of Chicago " ." He is the author of"Problems on Mapping Class Groups and Related Topics "and coauthor of "Noncommutative Algebra."




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