Fundamentals of Algebraic Topology

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Covers the essential results of algebraic topology in a concise and pragmatic manner
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.
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
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).

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Autor: Steven H. Weintraub
ISBN-13 :: 9781493948857
ISBN: 1493948857
Erscheinungsjahr: 10.09.2016
Verlag: Springer New York
Gewicht: 275g
Seiten: 176
Sprache: Englisch
Auflage Softcover reprint of the original 1st ed. 2014
Sonstiges: Taschenbuch, 235x155x9 mm
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