Handbook of Teichmüller Theory, Volume V [electronic resource] / Athanase Papadopoulos

Introduction to Teichmüller theory, old and new, V / Athanase Papadopoulos -- Identities on hyperbolic manifolds / Martin Bridgeman, Ser Peow Tan -- Problems on the Thurston metric / Weixu Su -- Meyer functions and the signature of fibered 4-manifolds / Yusuke Kuno -- The Goldman–Turaev Lie bialgebra and the Johnson homomorphisms / Nariya Kawazumi, Yusuke Kuno -- A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics / Takao Satoh -- Geometry and dynamics on character varieties / Inkang Kim -- Compactifications and reduction theory of geometrically finite locally symmetric spaces / Lizhen Ji -- Representations of fundamental groups of 2-manifolds / Lisa Jeffrey -- Extremal quasiconformal mappings and quadratic differentials / Oswald Teichmüller -- A commentary on Teichmüller’s paper Extremale quasikonforme Abbildungen und quadratische Differentiale / Vincent Alberge, Athanase Papadopoulos, Weixu Su -- Determination of extremal quasiconformal mappings of closed oriented Riemann surfaces / Oswald Teichmüller -- A commentary on Teichmüller’s paper Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen / Annette A’Campo-Neuen, Norbert A’Campo, Vincent Alberge, Athanase Papadopoulos.

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This volume is the fifth in a series dedicated to Teichmüller theory in a broad sense, including the study of various deformation spaces and of mapping class group actions. It is divided into four parts: Part A: The metric and the analytic theory Part B: The group theory Part C: Representation theory and generalized structures Part D: Sources The topics that are covered include identities for the hyperbolic geodesic length spectrum, Thurston's metric, the cohomology of moduli space and mapping class groups, the Johnson homomorphisms, Higgs bundles, dynamics on character varieties, and there are many others. Besides surveying important parts of the theory, several chapters contain conjectures and open problems. The last part contains two fundamental papers by Teichmüller, translated into English and accompanied by mathematical commentaries. The chapters, like those of the other volumes in this collection, are written by experts who have a broad view on the subject. They have an expository character (which fits with the original purpose of this handbook), but some of them also contain original and new material. The Handbook is addressed to researchers and to graduate students.