An Introduction to Teichmuller Spaces
Springer Verlag, Japan
978-4-431-70088-3 (ISBN)
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This book offers an easy and compact access to the theory of Teichmuller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. Teichmuller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, Teichmuller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of Teichmuller theory. The book will be an excellent source of information for graduate students and reserachers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory.
1 Teichmuller Space of Genus g.- 1.1 Riemann Surfaces.- 1.2 Teichmuller Space of Genus 1.- 1.3 Teichmuller Space of Genus g.- 1.4 Quasiconformal Mappings and Teichmuller Space.- 1.5 Complex Structures and Conformal Structures.- Notes.- 2 Frike Space.- 2.1 Uniformization Theorem.- 2.2 Universal Coverings.- 2.3 Mobius Transformations.- 2.4 Fuchsian Models.- 2.5 Fricke Space.- Notes.- 3 Hyperbolic Geometry and Fenchel-Nielsen Coordinates.- 3.1 Poincare Metric and Hyperbolic Geometry.- 3.2 Fenchel-Nielsen Coordinates.- 3.3 Fricke-Klein Embedding.- 3.4 Thurston's Compactification.- Notes.- 4 Quasiconformal Mappings.- 4.1 Definitions and Elementary Properties.- 4.2 Existence Theorems on Quasiconformal Mappings.- 4.3 Dependence on Beltrami Coefficients.- 4.4 Proof of Calderon-Zygmund Theorem.- Notes.- 5 Teichmuller Spaces.- 5.1 Analytic Construction of Teichmuller Spaces.- 5.2 Teichmuller Mappings and Teichmuller's Theorerms.- 5.3 Proof of Teichmuller's Uniqueness Theorem.- Notes.- 6 Complex Analytic Theory of Teichmuller Spaces.- 6.1 Bers' Embedding.- 6.2 Invariance of Complex Structure of Teichmuller Space.- 6.3 Teichmuller Modular Groups.- 6.4 Royden's Theorems.- 6.5 Classification of Teichmuller Modular Transformations.- Notes.- 7 Weil-Petersson Metric.- 7.1 Petersson Scalar Product and Bergman Projection.- 7.2 Infinitesimal Theory of Teichmuller Spaces.- 7.3 Weil-Petersson Metric.- Notes.- 8 Fenchel-Nielsen Deformations and Weil-Petersson Metric.- 8.1 Fenchel-Nielsen Deformations.- 8.2 A Variational Formula for Geodesic Length Functions.- 8.3 Wolpert's Formula.- Notes.- Appendices.- A Classical Variations on Riemann Surfaces.- Notes.- B Compactification of the Moduli Space.- Notes.- References.- List of Symbols.
| Zusatzinfo | biography |
|---|---|
| Verlagsort | Tokyo |
| Sprache | englisch |
| Gewicht | 680 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 4-431-70088-9 / 4431700889 |
| ISBN-13 | 978-4-431-70088-3 / 9784431700883 |
| Zustand | Neuware |
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