Fundamentals of Algebraic Topology / Graduate Texts in Mathematics Bd.270 (PDF)
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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.
- Autor: Steven H. Weintraub
- 2014, 2014, 163 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 1493918443
- ISBN-13: 9781493918447
- Erscheinungsdatum: 31.10.2014
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- Dateiformat: PDF
- Größe: 3.56 MB
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“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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