Handbook of Algebraic Topology

Author: I.M. James
Publisher: Elsevier
ISBN: 0080532985
Release Date: 1995-07-18
Genre: Mathematics

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 Algebra and Algebraic Topology

Author: Joe Kaminski
ISBN: 1781540853
Release Date: 2012-09
Genre: Algebra

In algebra the topics covered generally included operations with literal expressions, the solving of both linear and quadratic equations, the use of these techniques to find answers to problems, and practice with ratios, proportions, powers, and roots. Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. This book examines this topic.

Homotopy Methods in Algebraic Topology

Author: Nicholas Kuhn
Publisher: American Mathematical Soc.
ISBN: 9780821826218
Release Date: 2001-04-25
Genre: Mathematics

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 Algebra

Author: M. Hazewinkel
Publisher: Elsevier
ISBN: 0080532969
Release Date: 2000-04-06
Genre: Mathematics

Handbook of Algebra

Handbook of the History of General Topology

Author: C.E. Aull
Publisher: Springer Science & Business Media
ISBN: 0792344790
Release Date: 1997-03-31
Genre: Mathematics

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.

Homology Theory

Author: P. J. Hilton
Publisher: CUP Archive
ISBN: 0521094224
Release Date: 1967
Genre: Mathematics

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 Mathematics

Author: Vialar Thierry
Publisher: BoD - Books on Demand
ISBN: 9782955199015
Release Date: 2017-04-04

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.

Topological and Algebraic Structures in Fuzzy Sets

Author: S.E. Rodabaugh
Publisher: Springer Science & Business Media
ISBN: 9789401702317
Release Date: 2013-03-14
Genre: Mathematics

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 Categorical Algebra Volume 2 Categories and Structures

Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 052144179X
Release Date: 1994-11-03
Genre: Mathematics

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: 1568810016
Release Date: 1993-02-28
Genre: Mathematics

"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.

Homotopy Type and Homology

Author: Hans J. Baues
Publisher: Oxford University Press
ISBN: 0198514824
Release Date: 1996
Genre: Mathematics

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.

Computer Algebra Handbook

Author: Johannes Grabmeier
Publisher: Springer Science & Business Media
ISBN: 9783642558269
Release Date: 2012-12-06
Genre: Computers

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Handbook of Geometric Topology

Author: R.B. Sher
Publisher: Elsevier
ISBN: 0080532853
Release Date: 2001-12-20
Genre: Mathematics

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.

Handbook of Tilting Theory

Author: Lidia Angeleri Hügel
Publisher: Cambridge University Press
ISBN: 052168045X
Release Date: 2007-01-04
Genre: Mathematics

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