LEADER 04150nam 22006735 450 001 9910254096503321 005 20251126000823.0 010 $a3-319-23488-9 024 7 $a10.1007/978-3-319-23488-5 035 $a(CKB)3710000000734692 035 $a(DE-He213)978-3-319-23488-5 035 $a(MiAaPQ)EBC5595981 035 $a(PPN)194378918 035 $a(EXLCZ)993710000000734692 100 $a20160624d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHomotopical topology /$fby Anatoly Fomenko, Dmitry Fuchs 205 $aSecond edition 210 1$aCham :$cSpringer International Publishing$d[2016]. 210 4$d©2016 215 $a1 online resource (XI, 627 p. 210 illus.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v273 311 1 $a3-319-23487-0 311 1 $a9783319234878 327 $aIntroduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories. 330 $aThis classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics?the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra?the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology?the Adams conjecture, Bott periodicity, the Hirzebruch?Riemann?Roch theorem, the Atiyah?Singer index theorem, to name a few?paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader?s mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A. T. Fomenko artistically render the wondrous beauty, and mystery, of the subject. 410 0$aGraduate texts in mathematics,$x0072-5285 ;$v273 606 $aTopologia algebraica$2lemac 606 $aÀlgebra homològica$2lemac 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aK-theory 606 $aAlgebraic topology 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 615 7$aTopologia algebraica 615 7$aÀlgebra homològica 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 0$aK-theory. 615 0$aAlgebraic topology. 615 14$aCategory Theory, Homological Algebra. 615 24$aK-Theory. 615 24$aAlgebraic Topology. 676 $a512.55 700 $aFomenko$b A. T$4aut$4http://id.loc.gov/vocabulary/relators/aut$052478 702 $aFuchs$b Dmitry$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254096503321 996 $aHomotopical topology$94458004 997 $aUNINA