# Handbook of Teichmüller Theory: Volume IV

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*Athanase Papadopoulos*

A publication of the European Mathematical Society

For several decades, Teichmüller theory has been one of the most active
research areas in mathematics, with a very wide range of points of view,
including Riemann surface theory, hyperbolic geometry, low-dimensional
topology, several complex variables, algebraic geometry, arithmetic,
partial differential equations, dynamical systems, representation
theory, symplectic geometry, geometric group theory, and mathematical
physics.

This book is the fourth volume in a Handbook of Teichmüller
Theory project that started as an attempt to present, in a most
comprehensive and systematic way, the various aspects of this theory
with its relations to all the fields mentioned. The handbook is
addressed to researchers as well as graduate students.

This volume is divided into five parts:

- Part A: The metric and the analytic theory
- Part B: Representation theory and generalized structures
- Part C: Dynamics
- Part D: The quantum theory
- Part E: Sources

Parts A, B, and D are sequels to parts on the same theme in previous volumes. Part E contains the translation together with a commentary of an important paper by Teichmüller that is almost unknown, even to specialists. Making the original ideas of and motivations for a theory clear is crucial for many reasons, and making this translation, together with the commentary that follows, available will give readers a broader perspective on Teichmüller theory.

The various volumes in this collection are written by experts who have a broad view on the subject. In general, the chapters are expository, while some of them contain new and important results.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in metric, analytic, representation, and quantum theories.