A primer on mapping class groups / Benson Farb, Dan Margalit.

By:

Farb, Benson

Contributor(s):

Margalit, Dan, 1976-

Material type: Text

TextSeries: Princeton mathematical seriesPublication details: Princeton, NJ : Princeton University Press, 2012 .Description: xiv, 472 p. : ill. ; 24 cmISBN:

9780691147949 (hardback)

Subject(s):

DDC classification:

512.74 22 FAR

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.The book 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©ơller 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"-- Provided by publisher.

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Holdings ( 1 )
Title notes ( 2 )

Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Notes	Date due	Barcode	Item holds
Reference	IIT Goa Central Library	Reference	512.74 /FAR (Browse shelf(Opens below))	1	Reference	CB/10564\|\| 19-11-22\|\| 25.00%\|\| USD 90		4096

Total holds: 0

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Includes bibliographical references and index.

"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.The book 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©ơller 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"-- Provided by publisher.