LEADER 03960nam 22006495 450 001 9910299973503321 005 20200706071604.0 010 $a3-319-09354-1 024 7 $a10.1007/978-3-319-09354-3 035 $a(CKB)3710000000343722 035 $a(SSID)ssj0001424537 035 $a(PQKBManifestationID)11849599 035 $a(PQKBTitleCode)TC0001424537 035 $a(PQKBWorkID)11369462 035 $a(PQKB)10245699 035 $a(DE-He213)978-3-319-09354-3 035 $a(MiAaPQ)EBC6312341 035 $a(MiAaPQ)EBC5579490 035 $a(Au-PeEL)EBL5579490 035 $a(OCoLC)1083465849 035 $a(PPN)183520513 035 $a(EXLCZ)993710000000343722 100 $a20150108d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMod Two Homology and Cohomology /$fby Jean-Claude Hausmann 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (IX, 535 p. 9 illus.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-09353-3 327 $aIntroduction -- Simplicial (co)homology -- Singular and cellular (co)homologies -- Products -- Poincar´e Duality -- Projective spaces -- Equivariant cohomology -- Steenrod squares -- Stiefel-Whitney classes -- Miscellaneous applications and developments -- Hints and answers for some exercises. 330 $aCohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: It leads more quickly to the essentials of the subject, An absence of signs and orientation considerations simplifies the theory, Computations and advanced applications can be presented at an earlier stage, Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book. 410 0$aUniversitext,$x0172-5939 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics) 615 0$aComplex manifolds. 615 14$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 676 $a514.2 700 $aHausmann$b Jean-Claude$4aut$4http://id.loc.gov/vocabulary/relators/aut$060510 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299973503321 996 $aMod two homology and cohomology$91409837 997 $aUNINA