03434nam a22005415i 4500 978-1-4939-1844-7 DE-He213 20210621154732.0 cr nn 008mamaa 141031s2014 xxu| s |||| 0|eng d 9781493918447 978-1-4939-1844-7 10.1007/978-1-4939-1844-7 doi QA612-612.8 PBPD bicssc MAT038000 bisacsh PBPD thema 514.2 23 Weintraub, Steven H. author. aut http://id.loc.gov/vocabulary/relators/aut Fundamentals of Algebraic Topology [electronic resource] / by Steven H. Weintraub. 1st ed. 2014. New York, NY : Springer New York : Imprint: Springer, 2014. X, 163 p. 82 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Graduate Texts in Mathematics, 0072-5285 ; 270 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. Algebraic topology. Manifolds (Mathematics). Complex manifolds. Category theory (Mathematics). Homological algebra. Algebraic Topology. https://scigraph.springernature.com/ontologies/product-market-codes/M28019 Manifolds and Cell Complexes (incl. Diff.Topology). https://scigraph.springernature.com/ontologies/product-market-codes/M28027 Category Theory, Homological Algebra. https://scigraph.springernature.com/ontologies/product-market-codes/M11035 SpringerLink (Online service) Springer Nature eBook Printed edition: 9781493918430 Printed edition: 9781493918454 Printed edition: 9781493948857 Graduate Texts in Mathematics, 0072-5285 ; 270 https://doi.org/10.1007/978-1-4939-1844-7 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)