LEADER 02959nam 2200601Ia 450 001 9910483981803321 005 20200520144314.0 010 $a9783642052057 010 $a3642052053 024 7 $a10.1007/978-3-642-05205-7 035 $a(CKB)1000000000804406 035 $a(SSID)ssj0000372695 035 $a(PQKBManifestationID)11275434 035 $a(PQKBTitleCode)TC0000372695 035 $a(PQKBWorkID)10422920 035 $a(PQKB)10066846 035 $a(DE-He213)978-3-642-05205-7 035 $a(MiAaPQ)EBC3064908 035 $a(PPN)139962417 035 $a(EXLCZ)991000000000804406 100 $a20100209d2009 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aVector fields on singular varieties /$fJean-Paul Brasselet, Jose Seade, Tatsuo Suwa 205 $a1st ed. 2009. 210 $aHeidelberg ;$aNew York $cSpringer$dc2009 215 $a1 online resource (XX, 232 p.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v1987 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642052040 311 08$a3642052045 320 $aIncludes bibliographical references and index. 327 $aThe Case of Manifolds -- The Schwartz Index -- The GSV Index -- Indices of Vector Fields on Real Analytic Varieties -- The Virtual Index -- The Case of Holomorphic Vector Fields -- The Homological Index and Algebraic Formulas -- The Local Euler Obstruction -- Indices for 1-Forms -- The Schwartz Classes -- The Virtual Classes -- Milnor Number and Milnor Classes -- Characteristic Classes of Coherent Sheaves on Singular Varieties. 330 $aVector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ?good? notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1987. 606 $aSingularities (Mathematics) 606 $aVector fields 615 0$aSingularities (Mathematics) 615 0$aVector fields. 676 $a515.94 700 $aBrasselet$b Jean-Paul$060570 701 $aSeade$b J$g(Jose)$0368369 701 $aSuwa$b T$g(Tatsuo),$f1942-$0506827 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483981803321 996 $aVector fields on Singular Varieties$9773771 997 $aUNINA