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001 978-3-642-05205-7
003 DE-He213
005 20190213151517.0
007 cr nn 008mamaa
008 100301s2009 gw | s |||| 0|eng d
020 _a9783642052057
_9978-3-642-05205-7
024 7 _a10.1007/978-3-642-05205-7
_2doi
050 4 _aQA331.7
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
082 0 4 _a515.94
_223
100 1 _aBrasselet, Jean-Paul.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aVector fields on Singular Varieties
_h[electronic resource] /
_cby Jean-Paul Brasselet, José Seade, Tatsuo Suwa.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aXX, 232 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1987
505 0 _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.
520 _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.
650 0 _aDifferential equations, partial.
650 0 _aDifferentiable dynamical systems.
650 0 _aCell aggregation
_xMathematics.
650 0 _aGlobal analysis.
650 0 _aGeometry, algebraic.
650 1 4 _aSeveral Complex Variables and Analytic Spaces.
_0http://scigraph.springernature.com/things/product-market-codes/M12198
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
700 1 _aSeade, José.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSuwa, Tatsuo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642052118
776 0 8 _iPrinted edition:
_z9783642052040
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1987
856 4 0 _uhttps://doi.org/10.1007/978-3-642-05205-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10918
_d10918