Handbook of Teichmüller Theory, Volume II [electronic resource] /
Athanase Papadopoulos
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2009
- 1 online resource (883 pages)
- IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 13 .
Introduction to Teichmüller theory, old and new, II / The Weil–Petersson metric geometry / Infinite dimensional Teichmüller spaces / A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy / The uniformization problem / Riemann surfaces, ribbon graphs and combinatorial classes / Canonical 2-forms on the moduli space of Riemann surfaces / Quasi-homomorphisms on mapping class groups / Lefschetz fibrations on 4-manifolds / Introduction to measurable rigidity of mapping class groups / Affine groups of flat surfaces / Braid groups and Artin groups / Complex projective structures / Circle packing and Teichmüller space / (2+1) Einstein spacetimes of finite type / Trace coordinates on Fricke spaces of some simple hyperbolic surfaces / Spin networks and SL(2,ℂ)-character varieties / Grothendieck’s reconstruction principle and 2-dimensional topology and geometry / Dessins d’enfants and origami curves / The Teichmüller theory of the solenoid / Athanase Papadopoulos -- Scott A. Wolpert -- Alastair Fletcher, Vladimir Markovic -- Yoichi Imayoshi -- Robert Silhol -- Gabriele Mondello -- Nariya Kawazumi -- Koji Fujiwara -- Mustafa Korkmaz, András I. Stipsicz -- Yoshikata Kida -- Martin Möller -- Luis Paris -- David Dumas -- Sadayoshi Kojima -- Riccardo Benedetti, Francesco Bonsante -- William M. Goldman -- Sean Lawton, Elisha Peterson -- Feng Luo -- Frank Herrlich, Gabriela Schmithüsen -- Dragomir Šarić.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
This multi-volume set deals with Teichmüller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmüller theory. The aim is to give a complete panorama of this generalized Teichmüller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The present volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil–Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmüller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck–Teichmüller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmüller theory of the soleniod). This handbook is an essential reference for graduate students and researchers interested in Teichmüller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
9783037195550
10.4171/055 doi
Complex analysis
Functions of a complex variable
Several complex variables and analytic spaces
Introduction to Teichmüller theory, old and new, II / The Weil–Petersson metric geometry / Infinite dimensional Teichmüller spaces / A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy / The uniformization problem / Riemann surfaces, ribbon graphs and combinatorial classes / Canonical 2-forms on the moduli space of Riemann surfaces / Quasi-homomorphisms on mapping class groups / Lefschetz fibrations on 4-manifolds / Introduction to measurable rigidity of mapping class groups / Affine groups of flat surfaces / Braid groups and Artin groups / Complex projective structures / Circle packing and Teichmüller space / (2+1) Einstein spacetimes of finite type / Trace coordinates on Fricke spaces of some simple hyperbolic surfaces / Spin networks and SL(2,ℂ)-character varieties / Grothendieck’s reconstruction principle and 2-dimensional topology and geometry / Dessins d’enfants and origami curves / The Teichmüller theory of the solenoid / Athanase Papadopoulos -- Scott A. Wolpert -- Alastair Fletcher, Vladimir Markovic -- Yoichi Imayoshi -- Robert Silhol -- Gabriele Mondello -- Nariya Kawazumi -- Koji Fujiwara -- Mustafa Korkmaz, András I. Stipsicz -- Yoshikata Kida -- Martin Möller -- Luis Paris -- David Dumas -- Sadayoshi Kojima -- Riccardo Benedetti, Francesco Bonsante -- William M. Goldman -- Sean Lawton, Elisha Peterson -- Feng Luo -- Frank Herrlich, Gabriela Schmithüsen -- Dragomir Šarić.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
This multi-volume set deals with Teichmüller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmüller theory. The aim is to give a complete panorama of this generalized Teichmüller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The present volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil–Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmüller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck–Teichmüller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmüller theory of the soleniod). This handbook is an essential reference for graduate students and researchers interested in Teichmüller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
9783037195550
10.4171/055 doi
Complex analysis
Functions of a complex variable
Several complex variables and analytic spaces