A Primer on Mapping Class Groups

Margalit Dan Margalit Dan\ Farb Benson

ISBN 10: 0691147949 / ISBN 13: 9780691147949

Edité par Princeton University Press, 2011

pp. 488. N° de réf. du vendeur 5419637

Synopsis :

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.

À propos de l?auteur: Benson Farb is professor of mathematics at the University of Chicago. He is the editor of Problems on Mapping Class Groups and Related Topics and the coauthor of Noncommutative Algebra. Dan Margalit is assistant professor of mathematics at Georgia Institute of Technology.

Détails bibliographiques

Titre : A Primer on Mapping Class Groups
Éditeur : Princeton University Press
Date d'édition : 2011
Reliure : Couverture rigide
Etat : New