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＜電子ブック＞
Vector fields on Singular Varieties / by Jean-Paul Brasselet, José Seade, Tatsuo Suwa
(Lecture Notes in Mathematics. ISSN:16179692 ; 1987)

版	1st ed. 2009.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XX, 232 p : online resource
著者標目	*Brasselet, Jean-Paul author Seade, José author Suwa, Tatsuo author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Dynamical systems LCSH:Manifolds (Mathematics) LCSH:Global analysis (Mathematics) LCSH:Algebraic geometry FREE:Several Complex Variables and Analytic Spaces FREE:Dynamical Systems FREE:Manifolds and Cell Complexes FREE:Global Analysis and Analysis on Manifolds FREE:Algebraic Geometry
一般注記	The 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 Vector 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 HTTP:URL=https://doi.org/10.1007/978-3-642-05205-7

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