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The Complex Analytic Theory Of Teichmuller Spaces

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The Complex Analytic Theory Of Teichmuller Spaces

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Author : Subhashis Nag
language : en
Publisher: Wiley-Interscience
Release Date : 1988-03-03

The Complex Analytic Theory Of Teichmuller Spaces written by Subhashis Nag and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-03 with Mathematics categories.

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 Contains much material previously unpublished.

Geometry Of Riemann Surfaces And Teichm Ller Spaces

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Author : M. Seppälä
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Geometry Of Riemann Surfaces And Teichm Ller Spaces written by M. Seppälä and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years. In spite of its age, this fieldstill attracts a lot of attention, the smooth compact Riemannsurfaces being simply complex projective algebraic curves.Therefore the moduli space of compact Riemann surfaces is alsothe moduli space of complex algebraic curves. This space lieson the intersection of many fields of mathematics and may bestudied from many different points of view.The aim of thismonograph is to present information about the structure of themoduli space using as concrete and elementary methods aspossible. This simple approach leads to a rich theory andopens a new way of treating the moduli problem, putting newlife into classical methods that were used in the study ofmoduli problems in the 1920s.

An Introduction To Teichm Ller Spaces

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Author : Yoichi Imayoshi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To Teichm Ller Spaces written by Yoichi Imayoshi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Handbook Of Teichm Ller Theory

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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007

Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Handbook Of Teichm Ller Theory

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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007

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.

Quasiconformal Mappings Riemann Surfaces And Teichmuller Spaces

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Author : Yunping Jiang
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Quasiconformal Mappings Riemann Surfaces And Teichmuller Spaces written by Yunping Jiang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.

Weil Petersson Metric On The Universal Teichmuller Space

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Author : Leon Armenovich Takhtadzhi︠a︡n
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Weil Petersson Metric On The Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).