000 03166nam a22005775i 4500
001 978-3-642-05205-7
003 DE-He213
005 20160624101836.0
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
082 0 4 _a515.94
_223
100 1 _aBrasselet, Jean-Paul.
_eauthor.
245 1 0 _aVector fields on Singular Varieties
_h[electronic resource] /
_cby Jean-Paul Brasselet, José Seade, Tatsuo Suwa.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _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 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aDifferentiable dynamical systems.
650 0 _aGlobal analysis.
650 0 _aDifferential equations, partial.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aSeveral Complex Variables and Analytic Spaces.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aAlgebraic Geometry.
700 1 _aSeade, José.
_eauthor.
700 1 _aSuwa, Tatsuo.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642052040
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1987
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-05205-7
942 _2EBK1930
_cEBK
999 _c31224
_d31224