Research Catalog

Title

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

Author

Farb, Benson.

Publication

Princeton, NJ : Princeton University Press, c2012.

Items in the Library & Off-site

Details

Additional Authors

Margalit, Dan, 1976-

Description

xiv, 472 p. : ill.; 24 cm.

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©oller 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"--

Series Statement

Princeton mathematical series ; 49

Uniform Title

Princeton mathematical series ; 49.

Alternative Title

• Mapping class groups
• Class groups

Subject

• Mappings (Mathematics)
• Class groups (Mathematics)

Bibliography (note)

• Includes bibliographical references (p. [447]-463) and index.

Contents

Curves, surfaces, and hyperbolic geometry -- Mapping class group basics -- Dehn twists -- Generating the mapping class group -- Presentations and low-dimensional homology -- The symplectic representation and the Torelli group -- Torsion -- The Dehn-Nielsen-Baer theorem -- Braid groups -- Teichmüller space -- Teichmüller geometry -- Moduli space -- The Nielsen-Thurston classification -- Pseudo-Anosov theory -- Thurston's proof.

Call Number

JSE 12-245

ISBN

• 9780691147949 (hardback)
• 0691147949 (hardback)

LCCN

2011008491

OCLC

587249112

Author

Farb, Benson.

Title

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

Imprint

Princeton, NJ : Princeton University Press, c2012.

Series

Princeton mathematical series ; 49

Princeton mathematical series ; 49.

Bibliography

Includes bibliographical references (p. [447]-463) and index.

Added Author

Margalit, Dan, 1976-

Research Call Number

JSE 12-245