Overview
- Covers the essential results of algebraic topology in a concise and pragmatic manner
- Provides an introduction to manifolds, CW complexes, and homotopy theory
- Explains applications of algebraic topology to problems in topology and algebra
- Reveals the logical structure of the subject by illuminating the separate roles of algebra and topology
Part of the book series: Graduate Texts in Mathematics (GTM, volume 270)
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Table of contents (7 chapters)
Keywords
About this book
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.
Reviews
“Weinberg front-loads the Eilenberg-Steenrod axioms, thus rendering singular homology, where most authors start, merely an important example that emerges well on in the text. Certain readers either primarily interested in making calculations or in ‘extraordinary’ theories such as K-theories or (co)bordism will appreciate this emphasis. Summing Up: Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 52 (10), June, 2015)
“The fundamental group, covering spaces, a heavy dose of homology theory, applications to manifolds, and the higher homotopy groups is what the book is all about. … The exposition is exquisite, making reading the book very enjoyable. The book certainly has its place among the existing literature, as it offers something different from its peers. … All in all, what the book does it does very well, and it achieves a lot. … Certainly a recommended read.” (Ittay Weiss, MAA Reviews, March, 2015)
“This new booklet by the renowned textbook author Steven H. Weintraub is to serve as a quick guide to the fundamental concepts and results of classical algebraic topology. … the present book is certainly a highly useful and valuable companion for a first-year graduate course in algebraic topology, as well for ambitious students as for instructors.” (Werner Kleinert, zbMATH, Vol. 1305, 2015)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Fundamentals of Algebraic Topology
Authors: Steven H. Weintraub
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4939-1844-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2014
Hardcover ISBN: 978-1-4939-1843-0Published: 01 November 2014
Softcover ISBN: 978-1-4939-4885-7Published: 10 September 2016
eBook ISBN: 978-1-4939-1844-7Published: 31 October 2014
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: X, 163
Number of Illustrations: 82 b/w illustrations
Topics: Algebraic Topology, Manifolds and Cell Complexes (incl. Diff.Topology), Category Theory, Homological Algebra