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 IRMA Lectures in Mathematics and Theoretical Physics 2012; 874 pp; hardcover Volume: 17 ISBN-10: 3-03719-103-1 ISBN-13: 978-3-03719-103-3 List Price: US$128 Member Price: US$102.40 Order Code: EMSILMTP/17 See also: Handbook of Teichmüller Theory: Volume I - Athanase Papadopoulos Handbook of Teichmüller Theory: Volume II - Athanase Papadopoulos Handbook of Teichmüller Theory: Volume IV - Athanase Papadopoulos The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $$3$$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmüller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in metric and analytic theory, group theory, algebraic topology of mapping class groups and moduli spaces, Teichmüller theory, and mathematicial physics. Table of Contents A. Papadopoulos -- Introduction to Teichmüller theory, old and new, III Part A. The metric and the analytic theory, 3 J.-P. Otal -- Quasiconformal and BMO-quasiconformal homeomorphisms J. Hu -- Earthquakes on the hyperbolic plane C. Series -- Kerckhoff's lines of minima in Teichmüller space Part B. The group theory, 3 L. Ji -- A tale of two groups: arithmetic groups and mapping class groups J. D. McCarthy and A. Papadopoulos -- Simplicial actions of mapping class groups V. Disarlo -- On the coarse geometry of the complex of domains M. Korkmaz -- Minimal generating sets for the mapping class group of a surface K. Habiro and G. Massuyeau -- From mapping class groups to monoids of homology cobordisms: A survey T. Sakasai -- A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces L. Funar, C. Kapoudjian, and V. Sergiescu -- Asymptotically rigid mapping class groups and Thompson's groups Part C. The algebraic topology of mapping class groups and their intersection theory D. Zvonkine -- An introduction to moduli spaces of curves and their intersection theory I. Madsen -- Homology of the open moduli space of curves L. Ji and S. Zucker -- On the $$L^p$$-cohomology and the geometry of metrics on moduli spaces of curves Part D. Teichmüller theory and mathematical physics K. Krasnov and J.-M. Schlenker -- The Weil-Petersson metric and the renormalized volume of hyperbolic 3-manifolds R. M. Kashaev -- Discrete Liouville equation and Teichmüller theory Corrigenda List of contributors Index