Graduate Texts in Mathematics

Fundamentals of Algebraic Topology

Authors: Weintraub, Steven

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  • ​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  
  • Illuminates the separate roles of algebra and topology
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eBook $54.99
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  • ISBN 978-1-4939-1844-7
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Hardcover $69.99
price for USA in USD
  • ISBN 978-1-4939-1843-0
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  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA in USD
  • ISBN 978-1-4939-4885-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

Steven H. Weintraub is Professor of Mathematics at Lehigh University. He is the author of Galois Theory and Algebra: An Approach via Module Theory (with W. A. Adkins).

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)

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Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-1-4939-1844-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-1-4939-1843-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA in USD
  • ISBN 978-1-4939-4885-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fundamentals of Algebraic Topology
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
270
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-1-4939-1844-7
DOI
10.1007/978-1-4939-1844-7
Hardcover ISBN
978-1-4939-1843-0
Softcover ISBN
978-1-4939-4885-7
Series ISSN
0072-5285
Edition Number
1
Number of Pages
X, 163
Number of Illustrations
82 b/w illustrations
Topics