The Weil-Petersson Metric for Teichmueller Space and the Jenkins-Strebel Differentials PDF Download
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Author: Scott A. Wolpert
Publisher:
ISBN:
Category : Quasiconformal mappings
Languages : en
Pages : 130
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Author: Scott A. Wolpert
Publisher:
ISBN:
Category : Quasiconformal mappings
Languages : en
Pages : 130
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Book Description
Author: Athanase Papadopoulos
Publisher: European Mathematical Society
ISBN: 9783037190296
Category : Mathematics
Languages : en
Pages : 812
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Book Description
The Teichmuller space of a surface was introduced by O. Teichmuller 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 Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller 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 Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller 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 Teichmuller 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.
Author: Yoichi Imayoshi
Publisher: Springer Science & Business Media
ISBN: 4431681744
Category : Mathematics
Languages : en
Pages : 291
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Book Description
This book offers an easy and compact access to the theory of TeichmA1/4ller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. TeichmA1/4ller 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, TeichmA1/4ller 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 TeichmA1/4ller 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.
Author: Lipman Bers
Publisher: American Mathematical Soc.
ISBN: 9780821809976
Category : Mathematics
Languages : en
Pages : 642
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Book Description
Author: Felix E. Browder
Publisher: American Mathematical Soc.
ISBN: 0821814486
Category : Mathematics
Languages : en
Pages : 449
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Book Description
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This title presents the written versions this Symposium. It contains two papers by invited speakers who were not able to attend, S S Chern and L Nirenberg.
Author: Subhashis Nag
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 456
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Book Description
An accessible, self-contained treatment of the complex structure of the Teichmüller moduli spaces of Riemann surfaces. Complex analysts, geometers, and especially string theorists (!) will find this work indispensable. The Teichmüller space, parametrizing all the various complex structures on a given surface, itself carries (in a completely natural way) the complex structure of a finite- or infinite-dimensional complex manifold. Nag emphasizes the Bers embedding of Teichmüller spaces and deals with various types of complex-analytic coördinates for them. This is the first book in which a complete exposition is given of the most basic fact that the Bers projection from Beltrami differentials onto Teichmüller space is a complex analytic submersion. The fundamental universal property enjoyed by Teichmüller space is given two proofs and the Bers complex boundary is examined to the point where totally degenerate Kleinian groups make their spectacular appearance. Contains much material previously unpublished.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1184
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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 388
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Author:
Publisher:
ISBN:
Category : Union catalogs
Languages : en
Pages : 528
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Book Description
Includes entries for maps and atlases.
Author: Athanase Papadopoulos
Publisher: Springer Nature
ISBN: 3031435109
Category :
Languages : en
Pages : 396
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Book Description
