Foundations of Algebraic Topology
Foundations of Algebraic Topology

Author: Samuel Eilenberg

Publisher: Princeton University Press

Published: 2015-12-08

Total Pages: 345

ISBN-13: 1400877490

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The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Foundations of Algebraic Topology
Foundations of Algebraic Topology

Author: Samuel Eilenberg

Publisher:

Published: 2015-12-08

Total Pages: 0

ISBN-13: 9780691627236

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Annotation 'I have learned to be content in whatever state] I am'' (Phil. 4:11) Anyone who lacks true contentment may find it in this book. If not, it will be because that one would not follow the very clear and simple instructions given. The teaching is from the Bible, yet it must be described as unique. Nowhere else will you find such unusual, but Biblically authenticated thoughts: He will teach you that contentment lies in subtraction, not in addition; that the ABC's of Christianity are nothing like what you thought them to be; that there is a mystery of contentment, but that once you have learned the way from Christ's word, you will be able to attain such a depth of contentment as you never before dreamed existed. This is a key book for building up Christian maturity. Christian Contentment, what is it? ''It is a sweet, inward heart thing. It is a work of the Spirit indoors. It is a box of precious ointment, very comforting and useful for troubled hearts in times of troubled conditions.

Fundamentals of Algebraic Topology
Fundamentals of Algebraic Topology

Author: Steven H. Weintraub

Publisher: Springer

Published: 2014-10-31

Total Pages: 169

ISBN-13: 1493918443

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This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.

A Concise Course in Algebraic Topology
A Concise Course in Algebraic Topology

Author: J. P. May

Publisher: University of Chicago Press

Published: 1999-09

Total Pages: 262

ISBN-13: 9780226511832

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Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Foundations of Combinatorial Topology
Foundations of Combinatorial Topology

Author: L. S. Pontryagin

Publisher: Courier Corporation

Published: 2015-05-20

Total Pages: 112

ISBN-13: 0486406857

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Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.

Homology Theory
Homology Theory

Author: James W. Vick

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 258

ISBN-13: 1461208815

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This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.

More Concise Algebraic Topology
More Concise Algebraic Topology

Author: J. P. May

Publisher: University of Chicago Press

Published: 2012-02

Total Pages: 544

ISBN-13: 0226511782

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With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

Lectures on Algebraic Topology
Lectures on Algebraic Topology

Author: Sergeĭ Vladimirovich Matveev

Publisher: European Mathematical Society

Published: 2006

Total Pages: 112

ISBN-13: 9783037190234

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Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

Foundations of Topology
Foundations of Topology

Author: Gerhard Preuß

Publisher: Springer Science & Business Media

Published: 2011-06-27

Total Pages: 306

ISBN-13: 9401004897

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A new foundation of Topology, summarized under the name Convenient Topology, is considered such that several deficiencies of topological and uniform spaces are remedied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this setting semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, e.g. simple convergence, continuous convergence and uniform convergence. Various interesting results are presented which cannot be obtained by using topological or uniform spaces in the usual context. The text is self-contained with the exception of the last chapter, where the intuitive concept of nearness is incorporated in Convenient Topology (there exist already excellent expositions on nearness spaces).