Handbook of Teichmüller Theory, Volume VI / Athanase Papadopoulos

Format:

Book

Contributor:

Papadopoulos, Athanase

Series:

IRMA Lectures in Mathematics and Theoretical Physics (IRMA) ; 2523-5133 ; 27

Language:

English

Physical Description:

1 online resource (652 pages)

Place of Publication:

Zuerich, Switzerland : European Mathematical Society Publishing House, 2016

System Details:

text file PDF

Summary:

This volume is the sixth in a series dedicated to Teichmüller 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 Grothendieck-Teichmüller theory. Part D: Sources. The topics surveyed include Grothendieck's construction of the analytic structure of Teichmüller space, identities on the geodesic length spectrum of hyperbolic surfaces (including Mirzakhani's application to the computation of Weil-Petersson volumes), moduli spaces of configurations spaces, the Teichmüller tower with the action of the Galois group on dessins d'enfants, and several others actions related to surfaces. The last part contains three papers by Teichmüller, translated into English with mathematical commentaries, and a document that contains H. Grötzsch's comments on Teichmüller's famous paper Extremale quasikonforme Abbildungen und quadratische Differentiale. The handbook is addressed to researchers and to graduate students.

Contents:

Introduction to Teichmüller theory, old and new, VI / Athanase Papadopoulos

Alexander Grothendieck / Valentin Poénaru

On Grothendieck's construction of Teichmüller space / Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos

Null-set compactifications of Teichmüller spaces / Vincent Alberge, Hideki Miyachi, Ken'ichi Ohshika

Mirzakhani's recursion formula on Weil-Petersson volume and applications / Yi Huang

Rigidity phenomena in the mapping class group / Javier Aramayona, Juan Souto

Harmonic volume and its applications / Yuuki Tadokoro

Torus bundles and 2-forms on the universal family of Riemann surfaces / Robin de Jong

Cubic Differentials in the Differential Geometry of Surfaces / John Loftin, Ian McIntosh

Two-generator groups acting on the complex hyperbolic plane / Pierre Will

Configuration spaces of planar linkages / Alexey Sossinsky

Quasiconformal mappings on the Heisenberg group: An overview / Ioannis D. Platis

Actions of the absolute Galois group / Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos

A primer on dessins / Pierre Guillot

Hypergeometric Galois Actions / A. Muhammed Uludağ, İsmail Sağlam

A panaroma of the fundamental group of the modular orbifold / A. Muhammed Uludağ, Ayberk Zeytin

On Grothendieck's tame topology / Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos

Some historical commentaries on Teichmüller's paper Extremale quasikonforme Abbildungen und quadratische Differentiale / Reiner Kühnau

Complete solution of an extremal problem of the quasiconformal mapping / Oswald Teichmüller

A Commentary on Teichmüller's paper Vollständige Lösung einer Extremalaufgabe der quasikonformen Abbildung / Vincent Alberge, Athanase Papadopoulos

On extremal problems of conformal geometry / Oswald Teichmüller

A Commentary on Teichmüller's paper Über Extremalprobleme der konformen Geometrie / Norbert A'Campo, Athanase Papadopoulos

A displacement theorem of quasiconformal mapping / Oswald Teichmüller

A Commentary on Teichmüller's paper Ein Verschiebungssatz der quasikonformen Abbildung / Vincent Alberge.

ISBN:

3-03719-661-0