Geometry Of Riemann Surfaces And Teichmuller Spaces
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Author | : M. Seppälä |
Publisher | : Elsevier |
Total Pages | : 269 |
Release | : 2011-08-18 |
Genre | : Mathematics |
ISBN | : 0080872808 |
Download Geometry of Riemann Surfaces and Teichmüller Spaces Book in PDF, Epub and Kindle
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.
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 371 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0821898876 |
Download Moduli Spaces of Riemann Surfaces Book in PDF, Epub and Kindle
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.
Author | : Yoichi Imayoshi |
Publisher | : Springer Science & Business Media |
Total Pages | : 291 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 4431681744 |
Download An Introduction to Teichmüller Spaces Book in PDF, Epub and Kindle
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 | : William J. Harvey |
Publisher | : Cambridge University Press |
Total Pages | : 416 |
Release | : 2010-02-11 |
Genre | : Mathematics |
ISBN | : 0521733073 |
Download Geometry of Riemann Surfaces Book in PDF, Epub and Kindle
Original research and expert surveys on Riemann surfaces.
Author | : Anthony Tromba |
Publisher | : Birkhäuser |
Total Pages | : 224 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034886136 |
Download Teichmüller Theory in Riemannian Geometry Book in PDF, Epub and Kindle
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.
Author | : Peter Buser |
Publisher | : Springer Science & Business Media |
Total Pages | : 473 |
Release | : 2010-10-29 |
Genre | : Mathematics |
ISBN | : 0817649921 |
Download Geometry and Spectra of Compact Riemann Surfaces Book in PDF, Epub and Kindle
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.
Author | : Mika Seppälä |
Publisher | : |
Total Pages | : 263 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9780444888464 |
Download Geometry of Riemann Surfaces and Teichmüller Spaces Book in PDF, Epub and Kindle
Author | : Frederick P. Gardiner |
Publisher | : American Mathematical Soc. |
Total Pages | : 396 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821819836 |
Download Quasiconformal Teichmuller Theory Book in PDF, Epub and Kindle
The Teichmüller space T(X) is the space of marked conformal structures on a given quasiconformal surface X. This volume uses quasiconformal mapping to give a unified and up-to-date treatment of T(X). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type. The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to three-dimensional manifolds through its relationship to Kleinian groups, and to one-dimensional dynamics through its relationship to quasisymmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.
Author | : Jürgen Jost |
Publisher | : Springer Science & Business Media |
Total Pages | : 304 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662034468 |
Download Compact Riemann Surfaces Book in PDF, Epub and Kindle
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.
Author | : Sadayoshi Kojima |
Publisher | : World Scientific |
Total Pages | : 305 |
Release | : 1996-11-09 |
Genre | : |
ISBN | : 981460254X |
Download Topology And Teichmuller Spaces - Proceedings Of The 37th Taniguchi Symposium Book in PDF, Epub and Kindle
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.