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Handbook of Teichmüller Theory, Vol...
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Papadopoulos, Athanase,
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Handbook of Teichmüller Theory, Volume I
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Handbook of Teichmüller Theory, Volume I/ Athanase Papadopoulos
其他作者:
Papadopoulos, Athanase,
出版者:
Zuerich, Switzerland :European Mathematical Society Publishing House, : 2007,
面頁冊數:
1 online resource (802 pages)
標題:
Complex analysis -
電子資源:
https://doi.org/10.4171/029
電子資源:
https://www.ems-ph.org/img/books/irma11_mini.jpg
ISBN:
9783037195291
Handbook of Teichmüller Theory, Volume I
Handbook of Teichmüller Theory, Volume I
[electronic resource] /Athanase Papadopoulos - Zuerich, Switzerland :European Mathematical Society Publishing House,2007 - 1 online resource (802 pages) - IRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;112523-5133 ;.
Introduction to Teichmüller theory, old and new /Athanase Papadopoulos --
Restricted to subscribers:https://www.ems-ph.org/ebooks.php
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 space and of the mapping class group. 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 in the study of Teichmüller space and of 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 = PSL(2,ℝ) and G = PSL(2,ℂ). In the 1980s, there evolved an essentially combinatorial treatment of the Teichmüller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmüller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. 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 self-contained and have a pedagogical character. They are written by leading experts in the subject.
ISBN: 9783037195291
Standard No.: 10.4171/029doiSubjects--Topical Terms:
3480831
Complex analysis
Handbook of Teichmüller Theory, Volume I
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Introduction to Teichmüller theory, old and new /
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Harmonic maps and Teichmüller theory /
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Georgios D. Daskalopoulos, Richard A. Wentworth --
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On Teichmüller's metric and Thurston's asymmetric metric on Teichmüller space /
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Athanase Papadopoulos, Guillaume Théret --
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Surfaces, circles, and solenoids /
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Robert C. Penner --
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About the embedding of Teichmüller space in the space of geodesic Hölder distributions /
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Jean-Pierre Otal --
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Teichmüller spaces, triangle groups and Grothendieck dessins /
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William J. Harvey --
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On the boundary of Teichmüller disks in Teichmüller and in Schottky space /
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Frank Herrlich, Gabriela Schmithüsen --
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Introduction to mapping class groups of surfaces and related groups /
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Shigeyuki Morita --
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Geometric survey of subgroups of mapping class groups /
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John Loftin --
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Deformations of Kleinian groups /
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Albert Marden --
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Geometry of the complex of curves and of Teichmüller space /
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Ursula Hamenstädt --
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Parameters for generalized Teichmüller spaces /
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Charalampos Charitos, Ioannis Papadoperakis --
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On the moduli space of singular euclidean surfaces /
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Marc Troyanov --
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Discrete Riemann surfaces /
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Christian Mercat --
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On quantizing Teichmüller and Thurston theories /
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Leonid Chekhov, Robert C. Penner --
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Dual Teichmüller and lamination spaces /
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Vladimir V. Fock, Alexander Goncharov --
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An analog of a modular functor from quantized Teichmüller theory /
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Jörg Teschner --
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On quantum moduli space of flat PSL2(ℝ)-connections on a punctured surface /
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Rinat Kashaev.
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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 space and of the mapping class group. 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 in the study of Teichmüller space and of 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 = PSL(2,ℝ) and G = PSL(2,ℂ). In the 1980s, there evolved an essentially combinatorial treatment of the Teichmüller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmüller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. 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 self-contained and have a pedagogical character. They are written by leading experts in the subject.
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