IRMA Lectures in Mathematics and Theoretical Physics 2009; 883 pp; hardcover Volume: 13 ISBN10: 3037190558 ISBN13: 9783037190555 List Price: US$128 Member Price: US$102.40 Order Code: EMSILMTP/13
 This multivolume set deals with Teichmüller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmüller theory. The aim is to give a complete panorama of this generalized Teichmüller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts:  The metric and the analytic theory (uniformization, WeilPetersson geometry, holomorphic families of Riemann surfaces, infinitedimensional Teichmüller spaces, cohomology of moduli space, and the intersection theory of moduli space).
 The group theory (quasihomomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups).
 Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line).
 The GrothendieckTeichmüller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmüller theory of the solenoid).
This handbook is an essential reference for graduate students and researchers interested in Teichmüller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in analysis. Table of Contents  A. Papadopoulos  Introduction to Teichmüller theory, old and new
Part A. The metric and the analytic theory, 2  S. A. Wolpert  The WeilPetersson metric geometry
 A. Fletcher and V. Markovic  Infinite dimensional Teichmüller spaces
 Y. Imayoshi  A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy
 R. Silhol  The uniformization problem
 G. Mondello  Riemann surfaces, ribbon graphs and combinatorial classes
 N. Kawazumi  Canonical 2forms on the moduli space of Riemann surfaces
Part B. The group theory, 2  K. Fujiwara  Quasihomomorphisms on mapping class groups
 M. Korkmaz and A. Stipsicz  Lefschetz fibrations on 4manifolds
 Y. Kida  Introduction to measurable rigidity of mapping class groups
 M. Möller  Affine groups of flat surfaces
 L. Paris  Braid groups and Artin groups
Part C. Representation spaces and geometric structures, 1  D. Dumas  Complex projective structures
 S. Kojima  Circle packing and Teichmüller space
 R. Benedetti and F. Bonsante  \((2 + 1)\) Einstein spacetimes of finite type
 W. M. Goldman  Trace coordinates on Fricke spaces of some simple hyperbolic surfaces
 S. Lawton and E. Peterson  Spin networks and \(SL(2,\mathbb{C})\)character varieties
Part D. The GrothendieckTeichmüller theory  F. Luo  Grothendieck's reconstruction principle and 2dimensional topology and geometry
 F. Herrlich and G. Schmithüsen  Dessins d'enfants and origami curves
 D. Šarić  The Teichmüller theory of the solenoid
 List of contributors
 Index
