Hardcover ISBN:  9783037191033 
Product Code:  EMSILMTP/17 
List Price:  $128.00 
AMS Member Price:  $102.40 
Hardcover ISBN:  9783037191033 
Product Code:  EMSILMTP/17 
List Price:  $128.00 
AMS Member Price:  $102.40 

Book DetailsEMS IRMA Lectures in Mathematics and Theoretical PhysicsVolume: 17; 2012; 874 ppMSC: Primary 30; 32; 57; 11; 14; 20;
The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with \(3\)manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, lowdimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics.
This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems.
This volume is divided into the following four sections: The metric and the analytic theory
 The group theory
 The algebraic topology of mapping class groups and moduli spaces
 Teichmüller theory and mathematical physics
This handbook is addressed to graduate students and researchers in all the fields mentioned.ReadershipGraduate students and research mathematicians interested in metric and analytic theory, group theory, algebraic topology of mapping class groups and moduli spaces, Teichmüller theory, and mathematicial physics.

RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Requests
The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with \(3\)manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, lowdimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics.
This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems.
This volume is divided into the following four sections:
 The metric and the analytic theory
 The group theory
 The algebraic topology of mapping class groups and moduli spaces
 Teichmüller theory and mathematical physics
This handbook is addressed to graduate students and researchers in all the fields mentioned.
Graduate students and research mathematicians interested in metric and analytic theory, group theory, algebraic topology of mapping class groups and moduli spaces, Teichmüller theory, and mathematicial physics.