Problems on Mapping Class Groups And Related Topics (Proceedings of Symposia in Pure Mathematics, 74) - Hardcover

Benson Farb

Hardcover

ISBN 10: 0821838385 ISBN 13: 9780821838389

Publisher: American Mathematical Society, 2006

Synopsis

The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmüller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2006
• Language: English
• ISBN 10: 0821838385
• ISBN 13: 9780821838389
• Binding: Hardcover
• Number of pages: 371
• Editor: Benson Farb