Handbook of Algebraic Topology

Author: I.M. James

Publisher: Elsevier

ISBN: 9780080532981

Category: Mathematics

Page: 1324

View: 9801

Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Handbook of the History of General Topology

Author: C.E. Aull,R. Lowen

Publisher: Springer Science & Business Media

ISBN: 9401704708

Category: Mathematics

Page: 1223

View: 6477

This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Topological and Algebraic Structures in Fuzzy Sets

A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

Author: S.E. Rodabaugh,Erich Peter Klement

Publisher: Springer Science & Business Media

ISBN: 9401702314

Category: Mathematics

Page: 470

View: 9752

This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

Handbook of Algebra

Author: N.A

Publisher: Elsevier

ISBN: 9780080532950

Category: Mathematics

Page: 912

View: 9990

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.

Homotopy Methods in Algebraic Topology

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder, June 20-24, 1999

Author: John Patrick Campbell Greenlees,Robert Ray Bruner,Nicholas John Kuhn,Robert F Bruner

Publisher: American Mathematical Soc.

ISBN: 0821826212

Category: Mathematics

Page: 321

View: 9387

This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado (Boulder). The conference coincided with the sixtieth birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the ordinary, elliptic and real-oriented Adams spectral sequences, mapping class groups, configuration spaces, extended powers, operads, the telescope conjecture, $p$-compact groups, algebraic K theory, stable and unstable splittings, the calculus of functors, the $E_{\infty}$ tensor product, and equivariant cohomology theories. The book offers a compendious source on modern aspects of homotopy theoretic methods in many algebraic settings.

Handbook of K-Theory

Author: Eric Friedlander,Daniel R. Grayson

Publisher: Springer Science & Business Media

ISBN: 354023019X

Category: Mathematics

Page: 626

View: 4959

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Handbook of Mathematics

Author: Vialar Thierry

Publisher: BoD - Books on Demand

ISBN: 295519901X


Page: 1132

View: 7073

The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.

Homotopy Type and Homology

Author: Hans J. Baues

Publisher: Oxford University Press

ISBN: 9780198514824

Category: Mathematics

Page: 489

View: 9491

This book represents a new attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classification and includes applications to the classification of manifolds.

Handbook of Teichmüller Theory

Author: Athanase Papadopoulos

Publisher: European Mathematical Society

ISBN: 9783037191033

Category: Mathematics

Page: 866

View: 9980


Handbook of Tilting Theory

Author: Lidia Angeleri Hügel,Lidia Angeleri Hugel,Dieter Happel,Henning Krause

Publisher: Cambridge University Press

ISBN: 9780521680455

Category: Mathematics

Page: 472

View: 9078

A handbook of key articles providing both an introduction and reference for newcomers and experts alike.

Handbook of Categorical Algebra: Volume 2, Categories and Structures

Author: Francis Borceux

Publisher: Cambridge University Press

ISBN: 9780521441797

Category: Mathematics

Page: 443

View: 810

The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users.

Differential Algebras in Topology

Author: David Anik

Publisher: A K Peters, Ltd.

ISBN: 9781568810010

Category: Mathematics

Page: 274

View: 6312

"We construct an infinite family ... of spaces that generalize the odd-dimensional Moore space ... Extending some work of Cohen, Moore, and Neisendorfer, we explore the homotopy-theoretic properties of these spaces and of several closely related spaces. In the process, we develop a variety of algebraic and geometric tools and techniques that may have wide applicability in unstable p-primary homotopy theory."--abstract.

Handbook of Geometric Topology

Author: R.B. Sher,R.J. Daverman

Publisher: Elsevier

ISBN: 9780080532851

Category: Mathematics

Page: 1144

View: 7434

Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.

Homology Theory

An Introduction to Algebraic Topology

Author: P. J. Hilton,S. Wylie

Publisher: CUP Archive

ISBN: 9780521094221

Category: Mathematics

Page: 484

View: 1289

This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.

Handbook of Topological Fixed Point Theory

Author: Robert F. Brown,Massimo Furi,L. Gorniewicz,Boju Jiang

Publisher: Springer Science & Business Media

ISBN: 9781402032226

Category: Mathematics

Page: 972

View: 1123

This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

The Concise Handbook of Algebra

Author: Aleksandr Vasilʹevich Mikhalev

Publisher: Springer Science & Business Media

ISBN: 9780792370727

Category: Mathematics

Page: 618

View: 2909

Provides a succinct, but thorough treatment of algebra. In a collection that spans about 150 sections, organized in 9 chapters, algebraists are provided with a standard knowledge set for their areas of expertise.

Handbook of Enumerative Combinatorics

Author: Miklos Bona

Publisher: CRC Press

ISBN: 1482220865

Category: Mathematics

Page: 1086

View: 6044

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the award-winning Combinatorics of Permutations. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics and Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, log-concavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.

Handbook of Spatial Logics

Author: Marco Aiello,Ian Pratt-Hartmann,Johan van Benthem

Publisher: Springer Science & Business Media

ISBN: 1402055870

Category: Science

Page: 1058

View: 4578

The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.