Geometry Of Riemann Surfaces And Teichmuller Spaces

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Geometry of Riemann Surfaces and Teichmüller Spaces

Author : M. Seppälä
Publisher : Elsevier
ISBN 13 : 9780080872803
Total Pages : 262 pages
Book Rating : 4.8/5 (728 download)

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Book Synopsis Geometry of Riemann Surfaces and Teichmüller Spaces by : M. Seppälä

Download or read book Geometry of Riemann Surfaces and Teichmüller Spaces written by M. Seppälä and published by Elsevier. This book was released on 2011-08-18 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moduli problem is to describe the structure of the space of isomorphism classes of Riemann surfaces of a given topological type. This space is known as the moduli space and has been at the center of pure mathematics for more than a hundred years. In spite of its age, this field still attracts a lot of attention, the smooth compact Riemann surfaces being simply complex projective algebraic curves. Therefore the moduli space of compact Riemann surfaces is also the moduli space of complex algebraic curves. This space lies on the intersection of many fields of mathematics and may be studied from many different points of view. The aim of this monograph is to present information about the structure of the moduli space using as concrete and elementary methods as possible. This simple approach leads to a rich theory and opens a new way of treating the moduli problem, putting new life into classical methods that were used in the study of moduli problems in the 1920s.

Geometry of Riemann Surfaces

Author : William J. Harvey
Publisher : Cambridge University Press
ISBN 13 : 0521733073
Total Pages : 416 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Geometry of Riemann Surfaces by : William J. Harvey

Download or read book Geometry of Riemann Surfaces written by William J. Harvey and published by Cambridge University Press. This book was released on 2010-02-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Original research and expert surveys on Riemann surfaces.

Moduli Spaces of Riemann Surfaces

Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821898876
Total Pages : 371 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moduli Spaces of Riemann Surfaces by : Benson Farb

Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Teichmüller Theory in Riemannian Geometry

Author : Anthony Tromba
Publisher : Birkhäuser
ISBN 13 : 3034886136
Total Pages : 224 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Teichmüller Theory in Riemannian Geometry by : Anthony Tromba

Download or read book Teichmüller Theory in Riemannian Geometry written by Anthony Tromba and published by Birkhäuser. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.

An Introduction to Teichmüller Spaces

Author : Yoichi Imayoshi
Publisher : Springer Science & Business Media
ISBN 13 : 4431681744
Total Pages : 291 pages
Book Rating : 4.4/5 (316 download)

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Book Synopsis An Introduction to Teichmüller Spaces by : Yoichi Imayoshi

Download or read book An Introduction to Teichmüller Spaces written by Yoichi Imayoshi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry and Spectra of Compact Riemann Surfaces

Author : Peter Buser
Publisher : Springer Science & Business Media
ISBN 13 : 0817649921
Total Pages : 473 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometry and Spectra of Compact Riemann Surfaces by : Peter Buser

Download or read book Geometry and Spectra of Compact Riemann Surfaces written by Peter Buser and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Families of Riemann Surfaces and Weil-Petersson Geometry

Author : Scott A. Wolpert
Publisher : American Mathematical Soc.
ISBN 13 : 0821849867
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Families of Riemann Surfaces and Weil-Petersson Geometry by : Scott A. Wolpert

Download or read book Families of Riemann Surfaces and Weil-Petersson Geometry written by Scott A. Wolpert and published by American Mathematical Soc.. This book was released on 2010 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a generally self-contained course for graduate students and postgraduates on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. It also offers an update for researchers; material not otherwise found in a single reference is included; and aunified approach is provided for an array of results.

Compact Riemann Surfaces

Author : Jürgen Jost
Publisher : Springer Science & Business Media
ISBN 13 : 3662034468
Total Pages : 304 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Compact Riemann Surfaces by : Jürgen Jost

Download or read book Compact Riemann Surfaces written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Topological, Differential and Conformal Geometry of Surfaces

Author : Norbert A'Campo
Publisher : Springer Nature
ISBN 13 : 3030890325
Total Pages : 282 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Topological, Differential and Conformal Geometry of Surfaces by : Norbert A'Campo

Download or read book Topological, Differential and Conformal Geometry of Surfaces written by Norbert A'Campo and published by Springer Nature. This book was released on 2021-10-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
ISBN 13 : 9783037190555
Total Pages : 888 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topology And Teichmuller Spaces - Proceedings Of The 37th Taniguchi Symposium

Author : Sadayoshi Kojima
Publisher : World Scientific
ISBN 13 : 981460254X
Total Pages : 305 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Topology And Teichmuller Spaces - Proceedings Of The 37th Taniguchi Symposium by : Sadayoshi Kojima

Download or read book Topology And Teichmuller Spaces - Proceedings Of The 37th Taniguchi Symposium written by Sadayoshi Kojima and published by World Scientific. This book was released on 1996-11-09 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings is a collection of articles on Topology and Teichmüller Spaces. Special emphasis is being put on the universal Teichmüller space, the topology of moduli of algebraic curves, the space of representations of discrete groups, Kleinian groups and Dehn filling deformations, the geometry of Riemann surfaces, and some related topics.

Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces

Author : Maurizio Cornalba
Publisher : World Scientific
ISBN 13 : 9814590878
Total Pages : 716 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces by : Maurizio Cornalba

Download or read book Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces written by Maurizio Cornalba and published by World Scientific. This book was released on 1989-06-01 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

Author : John Hamal Hubbard
Publisher :
ISBN 13 : 9781943863013
Total Pages : 576 pages
Book Rating : 4.8/5 (63 download)

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Book Synopsis Teichmüller Theory and Applications to Geometry, Topology, and Dynamics by : John Hamal Hubbard

Download or read book Teichmüller Theory and Applications to Geometry, Topology, and Dynamics written by John Hamal Hubbard and published by . This book was released on 2022-02 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
ISBN 13 : 9783037190296
Total Pages : 812 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Primer on Mapping Class Groups

Author : Benson Farb
Publisher : Princeton University Press
ISBN 13 : 0691147949
Total Pages : 490 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Primer on Mapping Class Groups by : Benson Farb

Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Lectures on Riemann Surfaces

Author : Maurizio Cornalba
Publisher :
ISBN 13 : 9789814503365
Total Pages : 0 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Lectures on Riemann Surfaces by : Maurizio Cornalba

Download or read book Lectures on Riemann Surfaces written by Maurizio Cornalba and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first College on Riemann Surfaces centered on the theory of Riemann surfaces and their moduli and its applications to physics. This volume contains revised versions of the notes distributed at the College.

Mostly Surfaces

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
ISBN 13 : 0821853686
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mostly Surfaces by : Richard Evan Schwartz

Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.