Mapping Class Groups Of Low Genus And Their Cohomology

Mapping Class Groups Of Low Genus And Their Cohomology Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Mapping Class Groups Of Low Genus And Their Cohomology book. This book definitely worth reading, it is an incredibly well-written.

Mapping Class Groups of Low Genus and Their Cohomology

David J. Benson,Frederick Ronald Cohen
Mapping Class Groups of Low Genus and Their Cohomology Book PDF

Author : David J. Benson,Frederick Ronald Cohen
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 48,7 Mb
Release : 1991
Category : Complexes
ISBN : 9780821825068

Get Book

Mapping Class Groups of Low Genus and Their Cohomology by David J. Benson,Frederick Ronald Cohen Pdf

This series of papers is aimed towards the calculation of the cohomology of the mapping class group of a closed oriented surface of genus two. This is all 2, 3, and 5-torsion. The mod 5 cohomology is given in the first paper, the mod 3 cohomology in the second, and the mod 2 cohomology in the third. Along the way, we investigate many interesting properties of mapping class groups.

A Primer on Mapping Class Groups

Benson Farb,Dan Margalit
A Primer on Mapping Class Groups Book PDF

Author : Benson Farb,Dan Margalit
Publisher : Princeton University Press
Page : 490 pages
File Size : 40,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691147949

Get Book

A Primer on Mapping Class Groups by Benson Farb,Dan Margalit Pdf

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.

Problems on Mapping Class Groups and Related Topics

Benson Farb
Problems on Mapping Class Groups and Related Topics Book PDF

Author : Benson Farb
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 47,5 Mb
Release : 2006-09-12
Category : Mathematics
ISBN : 9780821838389

Get Book

Problems on Mapping Class Groups and Related Topics by Benson Farb Pdf

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.

Topology '90

Boris N. Apanasov,Walter D. Neumann,Alan W. Reid,Laurent Siebenmann
Topology 90 Book PDF

Author : Boris N. Apanasov,Walter D. Neumann,Alan W. Reid,Laurent Siebenmann
Publisher : Walter de Gruyter
Page : 473 pages
File Size : 46,7 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9783110857726

Get Book

Topology '90 by Boris N. Apanasov,Walter D. Neumann,Alan W. Reid,Laurent Siebenmann Pdf

This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

Mapping Class Groups and Moduli Spaces of Riemann Surfaces

Carl-Friedrich Bödigheimer,Richard Martin Hain
Mapping Class Groups and Moduli Spaces of Riemann Surfaces Book PDF

Author : Carl-Friedrich Bödigheimer,Richard Martin Hain
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 41,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851678

Get Book

Mapping Class Groups and Moduli Spaces of Riemann Surfaces by Carl-Friedrich Bödigheimer,Richard Martin Hain Pdf

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.

Quantum Topology and Global Anomalies

R A Baadhio
Quantum Topology and Global Anomalies Book PDF

Author : R A Baadhio
Publisher : World Scientific
Page : 284 pages
File Size : 46,7 Mb
Release : 1996-09-03
Category : Science
ISBN : 9789814498777

Get Book

Quantum Topology and Global Anomalies by R A Baadhio Pdf

Anomalies are ubiquitous features in quantum field theories. They can ruin the consistency of such theories and put significant restrictions on their viability, especially in dimensions higher than four. Global gauge and gravitational anomalies are to date, one of the scant powerful and probing tools available to physicists in the pursuit of uniqueness. This monograph is one of the very few that specializes in the study of global anomalies in quantum field theories. A discussion of various issues associated to three dimensional physics — the Chern–Simons–Witten theories — widen the scope of this book. Topics discussed here comprises: the ongoing quest for three-manifolds invariant, the role of the mapping class groups in (a) the detection and cancellation of global anomalies, (b) formulating three-manifolds invariant; the geometric quantization of Chern-Simons-Witten theories; deformation quantization; study of chiral and gravitational anomalies; anomalies and the Atiyah-Patodi-Singer Index theorem; exotic spheres; global gravitational anomalies in some six and ten dimensional supergravity and superstring theories, with an additional case study of Witten SU(2) Global Gauge Anomalies. In addition, five chapters lay out the mathematical basis for a thorough use of the topics above. One chapter focuses on the relationship between Teichmüller spaces, moduli spaces and mapping class groups. Another chapter is devoted to mapping class groups and arithmetic groups. Gauge theories on Riemann surfaces are studies in well over two chapters, the first one centered on the theory of bundles and the second on connections. Many readers will find this a useful book, especially theoretical physicists and mathematicians. The material presented here will be of interest to both the experts who will find complete, detailed and precise descriptions of important topics of current interest in mathematical physics, and to students and newcomers to the field, who will appreciate the vast amount of information provided here, especially on global anomalies. Contents:The Ongoing Quest for Three-Manifold InvariantsMapping Class Groups and 3-Manifold InvariantsTeichmüller Spaces and Mapping Class GroupsMapping Class Groups and Arithmetic GroupsWeil-Petersson Geometry of Teichmüller SpacesGauge Theories on Riemann Surfaces I: BundlesGauge Theories on Riemann Surfaces II: ConnectionsGeometric Quantization of Chern–Simons–Witten TheoriesDeformation QuantizationChiral and Gravitational AnomaliesAnomalies and the Index TheoremGlobal AnomaliesMapping Class Groups and Global AnomaliesExotic Spheres Readership: Mathematicians and physicists. keywords:

Advances in Topological Quantum Field Theory

John M. Bryden
Advances in Topological Quantum Field Theory Book PDF

Author : John M. Bryden
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 52,7 Mb
Release : 2007-09-27
Category : Mathematics
ISBN : 9781402027727

Get Book

Advances in Topological Quantum Field Theory by John M. Bryden Pdf

This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on 'New Techniques in Topological Quantum Field Theory'. This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields. The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a paper by M. Asaeda and J. Przytycki on the torsion conjecture for Khovanov homology by Shumakovitch. Moreover, there are articles on more classical topics related to manifolds and braid groups by such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.

Algebraic Topology: New Trends in Localization and Periodicity

Carles Broto,Carles Casacuberta,Guido Mislin
Algebraic Topology New Trends in Localization and Periodicity Book PDF

Author : Carles Broto,Carles Casacuberta,Guido Mislin
Publisher : Birkhäuser
Page : 405 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890182

Get Book

Algebraic Topology: New Trends in Localization and Periodicity by Carles Broto,Carles Casacuberta,Guido Mislin Pdf

Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.

Handbook of Algebra

Anonim
Handbook of Algebra Book PDF

Author : Anonim
Publisher : Elsevier
Page : 936 pages
File Size : 49,8 Mb
Release : 1995-12-18
Category : Mathematics
ISBN : 9780080532950

Get Book

Handbook of Algebra by Anonim Pdf

Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

Coarse Cohomology and Index Theory on Complete Riemannian Manifolds

John Roe
Coarse Cohomology and Index Theory on Complete Riemannian Manifolds Book PDF

Author : John Roe
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 42,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825594

Get Book

Coarse Cohomology and Index Theory on Complete Riemannian Manifolds by John Roe Pdf

``Coarse geometry'' is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which ``look the same from a great distance'' are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct ``higher indices'' for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the $K$-theory of a certain operator algebra naturally associated to the coarse structure, and this $K$-theory then pairs with the coarse cohomology. The higher indices can be calculated in topological terms thanks to the work of Connes and Moscovici. They can also be interpreted in terms of the $K$-homology of an ideal boundary naturally associated to the coarse structure. Applications to geometry are given, and the book concludes with a discussion of the coarse analog of the Novikov conjecture.

Phantom Homology

Melvin Hochster,Craig Huneke
Phantom Homology Book PDF

Author : Melvin Hochster,Craig Huneke
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 44,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825563

Get Book

Phantom Homology by Melvin Hochster,Craig Huneke Pdf

This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic $p$. The book would be suitable for use in an advanced graduate course in commutative algebra.

Eigenvalues of the Laplacian for Hecke Triangle Groups

Dennis A. Hejhal
Eigenvalues of the Laplacian for Hecke Triangle Groups Book PDF

Author : Dennis A. Hejhal
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 55,9 Mb
Release : 1992
Category : Automorphic functions
ISBN : 9780821825297

Get Book

Eigenvalues of the Laplacian for Hecke Triangle Groups by Dennis A. Hejhal Pdf

Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a discrete and continuous spectrum. This paper only examines the discrete side of the spectrum.

Invariant Subsemigroups of Lie Groups

Karl-Hermann Neeb
Invariant Subsemigroups of Lie Groups Book PDF

Author : Karl-Hermann Neeb
Publisher : American Mathematical Soc.
Page : 193 pages
File Size : 55,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825624

Get Book

Invariant Subsemigroups of Lie Groups by Karl-Hermann Neeb Pdf

This work presents the first systematic treatment of invariant Lie semi groups. Because these semi groups provide interesting models for space times in general relativity, this work will be useful to both mathematicians and physicists. It will also appeal to engineers interested in bi-invariant control systems on Lie groups. Neeb investigates closed invariant subsemigroups of Lie groups which are generated by one-parameter semi groups and the sets of infinitesimal generators of such semi groups - invariant convex cones in Lie algebras.In addition, a characterization of those finite-dimensional real Lie algebras containing such cones is obtained. The global part of the theory deals with globality problems (Lie's third theorem for semi groups), controllability problems, and the facial structure of Lie semi groups. Neeb also determines the structure of the universal compactification of an invariant Lie semigroup and shows that the lattice of idempotents is isomorphic to a lattice of faces of the cone dual to the cone of infinitesimal generators.

Categories of Modules over Endomorphism Rings

Theodore Gerard Faticoni
Categories of Modules over Endomorphism Rings Book PDF

Author : Theodore Gerard Faticoni
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 45,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0821825542

Get Book

Categories of Modules over Endomorphism Rings by Theodore Gerard Faticoni Pdf

It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital]A, ·). This memoir should be accessible to anyone who has a working knowledge of rings, modules, functors, and categories equivalent to that gained by reading Anderson and Fuller's text "Rings and Categories of Modules."

Sum of Even Powers of Real Linear Forms

Bruce Arie Reznick
Sum of Even Powers of Real Linear Forms Book PDF

Author : Bruce Arie Reznick
Publisher : American Mathematical Soc.
Page : 155 pages
File Size : 47,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825235

Get Book

Sum of Even Powers of Real Linear Forms by Bruce Arie Reznick Pdf

This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.