Mapping Class Groups And Moduli Spaces Of Riemann Surfaces

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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.

Mapping Class Groups and Moduli Spaces of Riemann Surfaces

Author : Carl-Friedrich Bödigheimer
Publisher : American Mathematical Soc.
ISBN 13 : 0821851675
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mapping Class Groups and Moduli Spaces of Riemann Surfaces by : Carl-Friedrich Bödigheimer

Download or read book Mapping Class Groups and Moduli Spaces of Riemann Surfaces written by Carl-Friedrich Bödigheimer and published by American Mathematical Soc.. This book was released on 1993 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.

Problems on Mapping Class Groups and Related Topics

Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821838385
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Problems on Mapping Class Groups and Related Topics by : Benson Farb

Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

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.

Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics

Author : Aaron Wootton
Publisher : American Mathematical Society
ISBN 13 : 1470460254
Total Pages : 366 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics by : Aaron Wootton

Download or read book Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics written by Aaron Wootton and published by American Mathematical Society. This book was released on 2022-02-03 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.

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.

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.

Homotopy Theory via Algebraic Geometry and Group Representations

Author : Mark E. Mahowald
Publisher : American Mathematical Soc.
ISBN 13 : 0821808052
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopy Theory via Algebraic Geometry and Group Representations by : Mark E. Mahowald

Download or read book Homotopy Theory via Algebraic Geometry and Group Representations written by Mark E. Mahowald and published by American Mathematical Soc.. This book was released on 1998 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.

The Moduli Space of Curves

Author : Robert H. Dijkgraaf
Publisher : Springer Science & Business Media
ISBN 13 : 1461242649
Total Pages : 570 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Moduli Space of Curves by : Robert H. Dijkgraaf

Download or read book The Moduli Space of Curves written by Robert H. Dijkgraaf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

The Geometry of Moduli Spaces of Sheaves

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts

Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Moduli Spaces of Curves, Mapping Class Groups and Field Theory

Author : Xavier Buff
Publisher : American Mathematical Soc.
ISBN 13 : 0821831674
Total Pages : 144 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moduli Spaces of Curves, Mapping Class Groups and Field Theory by : Xavier Buff

Download or read book Moduli Spaces of Curves, Mapping Class Groups and Field Theory written by Xavier Buff and published by American Mathematical Soc.. This book was released on 2003 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendick-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories."--BOOK JACKET.

A Course in Complex Analysis and Riemann Surfaces

Author : Wilhelm Schlag
Publisher : American Mathematical Society
ISBN 13 : 0821898477
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Course in Complex Analysis and Riemann Surfaces by : Wilhelm Schlag

Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag and published by American Mathematical Society. This book was released on 2014-08-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.

Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces

Author : Milagros Izquierdo
Publisher : American Mathematical Soc.
ISBN 13 : 1470410931
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces by : Milagros Izquierdo

Download or read book Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces written by Milagros Izquierdo and published by American Mathematical Soc.. This book was released on 2014-11-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.

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.

Algebraic Geometry Santa Cruz 1995

Author : János Kollár
Publisher : American Mathematical Soc.
ISBN 13 : 0821808958
Total Pages : 473 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Geometry Santa Cruz 1995 by : János Kollár

Download or read book Algebraic Geometry Santa Cruz 1995 written by János Kollár and published by American Mathematical Soc.. This book was released on 1997 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometry of Algebraic Curves

Author : Enrico Arbarello
Publisher : Springer Science & Business Media
ISBN 13 : 3540693920
Total Pages : 983 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Geometry of Algebraic Curves by : Enrico Arbarello

Download or read book Geometry of Algebraic Curves written by Enrico Arbarello and published by Springer Science & Business Media. This book was released on 2011-03-10 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.

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.