03044nam a22004095i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207082001500223100008000238245008900318250001800407264006700425300003600492336002600528337002600554338003600580347002400616490005300640505088400693520070201577650002402279650010002303710003402403773002602437776003602463776003602499830005302535856004602588978-1-4939-9063-4DE-He21320210118114613.0cr nn 008mamaa190629s1991 xxu| s |||| 0|eng d a9781493990634 a10.1007/978-1-4939-9063-42doi aQA564-609 aPBMW2bicssc aMAT0120102bisacsh aPBMW2thema a516.35223 aMassey, William S.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut aA Basic Course in Algebraic Topologyh[electronic resource] /cby William S. Massey. a1st ed. 1991. aNew York, NY :bSpringer New York :bImprint: Springer,c1991. aXVIII, 431 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda aGraduate Texts in Mathematics,x0072-5285 ;v127 a1: Two-Dimensional Manifolds -- 2: The Fundamental Group -- 3: Free Groups and Free Products of Groups -- 4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications -- 5: Covering Spaces -- 6: Background and Motivation for Homology Theory -- 7: Definitions and Basic Properties of Homology Theory -- 8: Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory -- 9: Homology of CW-Complexes -- 10: Homology with Arbitrary Coefficient Groups -- 11: The Homology of Product Spaces -- 12: Cohomology Theory -- 13: Products in Homology and Cohomology -- 14: Duality Theorems for the Homology of Manifolds -- 15: Cup Products in Projective Spaces and Applications of Cup Products. Appendix A: A Proof of De Rham's Theorem. -- Appendix B: Permutation Groups or Tranformation Groups. aThis textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date. . aAlgebraic geometry. aAlgebraic Geometry.0https://scigraph.springernature.com/ontologies/product-market-codes/M11019 aSpringerLink (Online service) tSpringer Nature eBook iPrinted edition:z9780387974309 iPrinted edition:z9781493990627 aGraduate Texts in Mathematics,x0072-5285 ;v127 uhttps://doi.org/10.1007/978-1-4939-9063-4