Handbook of Teichmüller theory, Vol. VI, ed. A. Papadopoulos, IRMA Lectures in Mathematics and Theoretical Physics Vol. 27, Zurich
Résumé
The book is dedicated to the memory of Alexander Grothendieck, and it contains several chapters on his work related to the so-called Grothendieck-Teichmüller theory: the Grothendieck-Teichmüller group and the Teichmüller tower. There are also chapters on dessins d'enfants and Grothendieck’s construction of the complex structure of Teichmüller space. The other chapters concern compactifications of Teichmüller spaces, Mirzakhani’s recursion formula on Weil–Petersson volumes, rigidity phenomena in mapping class groups, harmonic volume and its applications, universal families of Riemann surfaces, representation theory and generalized structures, cubic differentials in the differential geometry of surfaces, two-generator groups acting on the complex hyperbolic plane, configuration spaces of planar linkages, an overview of quasiconformal mappings on the Heisenberg group, hypergeometric Galois actions, a panaroma of the fundamental group of the modular orbifold, a survey of Grothendieck’s tame topology, commentaries on Teichmüller’s paper ``Extremale quasikonforme Abbildungen und quadratische Differentiale", and the English translations and commmentaries of the following three papers by Teichmüller: " Complete solution of an extremal problem of the quasiconformal mapping", " On extremal problems of conformal geometry" and " A displacement theorem of quasiconformal mapping." The authors of the various chapters are: Athanase Papadopoulos, Valentin Poenaru, Norbert A’Campo, Lizhen Ji, Vincent Alberge, Hideki Miyachi, Ken’ichi Ohshika, Yi Huang, Javier Aramayona, Juan Souto, Yuuki Tadokoro, Robin de Jong, John Loftin, Ian McIntosh, Pierre Will, Alexey Sossinsky, Ioannis D. Platis, Pierre Guillot, A. Muhammed Uludag, Ismail Saglam, Ayberk Zeytin, Reiner Kühnau, Manfred Karbe and Oswald Teichmüller (in English translation).