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Author: Athanase Papadopoulos | Publisher: European Mathematical Society | Category: Mathematics | Language: English | Page: 652 | ISBN: 3037191619 | ISBN13: 9783037191613 |

Description: This volume is the sixth in a series dedicated to Teichmller theory in a broad sense, including various moduli and deformation spaces, and the study of mapping class groups. It is divided into five parts: Part A: The metric and the analytic theory. Part B: The group theory. Part C: Representation theory and generalized structures. Part D: The GrothendieckTeichmller theory. Part D: Sources. The topics surveyed include Grothendiecks construction of the analytic structure of Teichmller space, identities on the geodesic length spectrum of hyperbolic surfaces (including Mirzakhanis application to the computation of WeilPetersson volumes), moduli spaces of configurations spaces, the Teichmller tower with the action of the Galois group on dessins denfants, and several others actions related to surfaces. The last part contains three papers by Teichmller, translated into English with mathematical commentaries, and a document that contains H. Grtzschs comments on Teichmllers famous paper Extremale quasikonforme Abbildungen und quadratische Differentiale. The handbook is addressed to researchers and to graduate students.

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