LEADER 03877nam 22007335 450 001 9910299968503321 005 20200707012725.0 010 $a1-4939-1844-3 024 7 $a10.1007/978-1-4939-1844-7 035 $a(CKB)3710000000269881 035 $a(SSID)ssj0001372638 035 $a(PQKBManifestationID)11888488 035 $a(PQKBTitleCode)TC0001372638 035 $a(PQKBWorkID)11304636 035 $a(PQKB)10302634 035 $a(DE-He213)978-1-4939-1844-7 035 $a(MiAaPQ)EBC6314948 035 $a(MiAaPQ)EBC5594391 035 $a(Au-PeEL)EBL5594391 035 $a(OCoLC)896821995 035 $a(PPN)182098788 035 $a(EXLCZ)993710000000269881 100 $a20141031d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFundamentals of Algebraic Topology /$fby Steven H. Weintraub 205 $a1st ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (X, 163 p. 82 illus.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v270 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-1843-5 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v270 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 14$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aCategory Theory, Homological Algebra. 676 $a514.2 700 $aWeintraub$b Steven H$4aut$4http://id.loc.gov/vocabulary/relators/aut$059613 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299968503321 996 $aFundamentals of algebraic topology$91410131 997 $aUNINA