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IRMA Lectures in Mathematics and Theoretical Physics Vol. 13

ISBN 978-3-03719-055-5

DOI 10.4171/055

March 2009, 883 pages, hardcover, 17 x 24 cm.

98.00 Euro

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:

#### Handbook of Teichmüller Theory, Volume II

*Editor:*

Athanase Papadopoulos (IRMA, Strasbourg, France)Athanase Papadopoulos (IRMA, Strasbourg, France)

ISBN 978-3-03719-055-5

DOI 10.4171/055

March 2009, 883 pages, hardcover, 17 x 24 cm.

98.00 Euro

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).

#### Further Information

Review in Zentralblatt MATH 1158.30001