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010   $a3-642-05205-3
024 7 $a10.1007/978-3-642-05205-7
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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   $a20100301d2009      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aVector fields on Singular Varieties$b[electronic resource] /$fby Jean-Paul Brasselet, José Seade, Tatsuo Suwa
205   $a1st ed. 2009.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009.
215   $a1 online resource (XX, 232 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1987
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-05204-5 
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,$x0075-8434 ;$v1987
606   $aFunctions of complex variables
606   $aDynamics
606   $aErgodic theory
606   $aManifolds (Mathematics)
606   $aComplex manifolds
606   $aGlobal analysis (Mathematics)
606   $aAlgebraic geometry
606   $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
615  0$aFunctions of complex variables.
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aManifolds (Mathematics).
615  0$aComplex manifolds.
615  0$aGlobal analysis (Mathematics).
615  0$aAlgebraic geometry.
615 14$aSeveral Complex Variables and Analytic Spaces.
615 24$aDynamical Systems and Ergodic Theory.
615 24$aManifolds and Cell Complexes (incl. Diff.Topology).
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aAlgebraic Geometry.
676   $a515.94
700   $aBrasselet$b Jean-Paul$4aut$4http://id.loc.gov/vocabulary/relators/aut$060570
702   $aSeade$b José$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aSuwa$b Tatsuo$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a996466494003316
996   $aVector fields on Singular Varieties$92831000
997   $aUNISA