Hardcover ISBN:  9783037190296 
Product Code:  EMSILMTP/11 
List Price:  $128.00 
AMS Member Price:  $102.40 

Book DetailsEMS IRMA Lectures in Mathematics and Theoretical PhysicsVolume: 11; 2007; 802 ppMSC: Primary 30; 32; Secondary 57; 53; 20;
The Teichmüller space of a surface was introduced by O. Teichmüller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics.
The original setting of Teichmüller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmüller space and its asymptotic geometry. Teichmüller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group \(G\), most notably \(G=\mathrm{PSL}(2,\mathbb{R})\) and \(G=\mathrm{PSL}(2,\mathbb{C})\). In the 1980s, there evolved an essentially combinatorial treatment of the Teichmüller and moduli spaces involving techniques and ideas from highenergy physics, namely from string theory. The current research interests include the quantization of Teichmüller space, the WeilPetersson symplectic and Poisson geometry of this space as well as gaugetheoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3manifolds.
The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmüller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are selfcontained and have a pedagogical character. They are written by leading experts in the subject.ReadershipGraduate students and research mathematicians interested in analysis.

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The Teichmüller space of a surface was introduced by O. Teichmüller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics.
The original setting of Teichmüller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmüller space and its asymptotic geometry. Teichmüller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group \(G\), most notably \(G=\mathrm{PSL}(2,\mathbb{R})\) and \(G=\mathrm{PSL}(2,\mathbb{C})\). In the 1980s, there evolved an essentially combinatorial treatment of the Teichmüller and moduli spaces involving techniques and ideas from highenergy physics, namely from string theory. The current research interests include the quantization of Teichmüller space, the WeilPetersson symplectic and Poisson geometry of this space as well as gaugetheoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3manifolds.
The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmüller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are selfcontained and have a pedagogical character. They are written by leading experts in the subject.
Graduate students and research mathematicians interested in analysis.