Problems on Mapping Class Groups and Related Topics (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
371
Utgivningsdatum
2006-10-01
Upplaga
illustrated ed
Förlag
American Mathematical Society
Illustrationer
Illustrations
Dimensioner
260 x 184 x 25 mm
Vikt
834 g
Antal komponenter
1
ISSN
0082-0717
ISBN
9780821838389

Problems on Mapping Class Groups and Related Topics

av Benson Farb
Inbunden,  Engelska, 2006-10-01
2198
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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 focuses 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.
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Innehållsförteckning

Some problems on the mapping class group 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; The topology of 3-manifolds, Heegaard distances and the mapping class group of a 2-manifold; Lefschetz pencils and mapping class groups; Open problems in Grothendieck-Teichmuller theory; Geometric properties of the mapping class group; Problems on billiards, flat surfaces and translation surfaces; Problems in the geometry of surface group extensions; Surface subgroups of mapping class groups; Weil-Petersson perspectives; 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

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