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Record Nr. |
UNINA9910299968503321 |
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Autore |
Weintraub Steven H |
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Titolo |
Fundamentals of Algebraic Topology / / by Steven H. Weintraub |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Springer, , 2014 |
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ISBN |
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Edizione |
[1st ed. 2014.] |
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Descrizione fisica |
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1 online resource (X, 163 p. 82 illus.) |
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Collana |
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Graduate Texts in Mathematics, , 0072-5285 ; ; 270 |
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Disciplina |
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Soggetti |
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Algebraic topology |
Manifolds (Mathematics) |
Complex manifolds |
Category theory (Mathematics) |
Homological algebra |
Algebraic Topology |
Manifolds and Cell Complexes (incl. Diff.Topology) |
Category Theory, Homological Algebra |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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