Problems on mapping class groups and related topics / Benson Farb, editor.

Format:

Book

Contributor:

Farb, Benson, editor.

Series:

Proceedings of symposia in pure mathematics ; volume 74.

Proceedings of symposia in pure mathematics ; volume 74

Language:

English

Subjects (All):

Mappings (Mathematics)--Congresses.

Mappings (Mathematics).

Class groups (Mathematics)--Congresses.

Class groups (Mathematics).

Physical Description:

1 online resource (384 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

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, Teichmuller 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.

Contents:

""Contents""; ""Preface""; ""I. Cohomological, Combinatorial and Algebraic Structure""; ""Four Questions about Mapping Class Groups""; ""Some Problems on Mapping Class Groups and Moduli Space""; ""Finiteness and Torelli Spaces""; ""Fifteen Problems about the Mapping Class Groups""; ""Problems on Homomorphisms of Mapping Class Groups""; ""The Mapping Class Group and Homotopy Theory""; ""Probing Mapping Class Groups Using Arcs""; ""Relations in the Mapping Class Group""; ""II. Connections with 3-manifolds, Symplectic Geometry and Algebraic Geometry""

""Surface Subgroups of Mapping Class Groups""""Weil-Petersson Perspectives""; ""IV. Braid Groups, Out(F[sub(n)]) and other Related Groups""; ""Braid Groups and Iwahori-Heck Algebras""; ""Automorphism Groups of Free Groups, Surface Groups and Free Abelian Groups""; ""Problems: Braid Groups, Homotopy, Cohomology and Representations""; ""Cohomological Structure of the Mapping Class Group and Beyond""; ""From Braid Groups to Mapping Class Groups""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-9380-7