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A Primer on Mapping Class Groups (PMS-49) - Princeton Scholarship Online
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A Primer on Mapping Class Groups (PMS-49)

Benson Farb and Dan Margalit


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. It 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 ... More

Keywords: surface homeomorphism, mapping class group, Mod(S), Dehn twists, low-dimensional homology, Birman exact sequence, braid group, symplectic representation, Torelli group, Teichmüller space

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780691147949
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691147949.001.0001


Affiliations are at time of print publication.

Benson Farb, author
University of Chicago

Dan Margalit, author
Georgia Tech