Fundamentals of algebraic topology / Steven H. Weintraub.
Material type:
TextSeries: Graduate texts in mathematics ; 270.Publication details: New York : Springer, 2014.Description: x, 163 p. ; illustrationsISBN: - 9781493918430
- 514.2 23 W424
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 514.2 W424 (Browse shelf(Opens below)) | Available | 135825 |
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| 514.2 W187 Introduction to Algebraic Topology | 514.2 W187 Algebraic topology : homology and cohomology | 514.2 W284 Topological rings | 514.2 W424 Fundamentals of algebraic topology / | 514.2 W924 Algebraic topology | 514.22 Al366 Combinatorial topology | 514.22 Al366 Combinatorial topology |
Includes bibliographical references and index.
1. The Basics --
2. The Fundamental Group --
3. Generalized Homology Theory --
4. Ordinary Homology Theory --
5. Singular Homology Theory --
6. Manifolds --
7. Homotopy Theory --
8. Homotopy Theory --
A. Elementary Homological Algebra --
B. Bilinear Forms.- C. Categories and Functors --
Bibliography --
Index.
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.
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