03877nam 22007335 450 991029996850332120200707012725.01-4939-1844-310.1007/978-1-4939-1844-7(CKB)3710000000269881(SSID)ssj0001372638(PQKBManifestationID)11888488(PQKBTitleCode)TC0001372638(PQKBWorkID)11304636(PQKB)10302634(DE-He213)978-1-4939-1844-7(MiAaPQ)EBC6314948(MiAaPQ)EBC5594391(Au-PeEL)EBL5594391(OCoLC)896821995(PPN)182098788(EXLCZ)99371000000026988120141031d2014 u| 0engurnn|008mamaatxtccrFundamentals of Algebraic Topology /by Steven H. Weintraub1st ed. 2014.New York, NY :Springer New York :Imprint: Springer,2014.1 online resource (X, 163 p. 82 illus.) Graduate Texts in Mathematics,0072-5285 ;270Bibliographic Level Mode of Issuance: Monograph1-4939-1843-5 Includes bibliographical references and index.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.Graduate Texts in Mathematics,0072-5285 ;270Algebraic topologyManifolds (Mathematics)Complex manifoldsCategory theory (Mathematics)Homological algebraAlgebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Manifolds and Cell Complexes (incl. Diff.Topology)https://scigraph.springernature.com/ontologies/product-market-codes/M28027Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Algebraic topology.Manifolds (Mathematics).Complex manifolds.Category theory (Mathematics).Homological algebra.Algebraic Topology.Manifolds and Cell Complexes (incl. Diff.Topology).Category Theory, Homological Algebra.514.2Weintraub Steven Hauthttp://id.loc.gov/vocabulary/relators/aut59613MiAaPQMiAaPQMiAaPQBOOK9910299968503321Fundamentals of algebraic topology1410131UNINA