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 IRMA Lectures in Mathematics and Theoretical Physics 2009; 883 pp; hardcover Volume: 13 ISBN-10: 3-03719-055-8 ISBN-13: 978-3-03719-055-5 List Price: US$128 Member Price: US$102.40 Order Code: EMSILMTP/13 This multi-volume 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, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmüller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms 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 Grothendieck-Teichmüller 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 Weil-Petersson 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 2-forms on the moduli space of Riemann surfaces Part B. The group theory, 2 K. Fujiwara -- Quasi-homomorphisms on mapping class groups M. Korkmaz and A. Stipsicz -- Lefschetz fibrations on 4-manifolds 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 Grothendieck-Teichmüller theory F. Luo -- Grothendieck's reconstruction principle and 2-dimensional 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