Fundamentals of Algebraic Topology
Seiten
2016
|
Softcover reprint of the original 1st ed. 2014
Springer-Verlag New York Inc.
978-1-4939-4885-7 (ISBN)
Springer-Verlag New York Inc.
978-1-4939-4885-7 (ISBN)
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.
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.
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).
Preface.- 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.
| Erscheinungsdatum | 22.09.2016 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; 270 |
| Zusatzinfo | 82 Illustrations, black and white |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Algebra | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | algebraic topology • Homology Theory • homotopy theory • Manifolds |
| ISBN-10 | 1-4939-4885-7 / 1493948857 |
| ISBN-13 | 978-1-4939-4885-7 / 9781493948857 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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