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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Vector fields on Singular Varieties (Paperback, 2010 ed.)
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Vector fields on Singular Varieties (Paperback, 2010 ed.)
Series: Lecture Notes in Mathematics, 1987
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Vector?eldsonmanifoldsplaymajorrolesinmathematicsandothersciences.
In particular, the Poincar' e-Hopf index theorem and its geometric
count- part,the Gauss-Bonnettheorem, giveriseto the theoryof
Chernclasses,key invariants of manifolds in geometry and topology.
One has often to face problems where the underlying space is no
more a manifold but a singular variety. Thus it is natural to ask
what is the "good"
notionofindexofavector?eld,andofChernclasses,ifthespaceacquiress-
gularities.Thequestionwasexploredbyseveralauthorswithvariousanswers,
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.
Marseille Jean-Paul Brasselet Cuernavaca Jos' e Seade Tokyo Tatsuo
Suwa September 2009 v Acknowledgements Parts of this monograph were
written while the authors were staying at various institutions,
such as Hokkaido University and Niigata University in Japan, CIRM,
Universit' e de la Mediterran' ee and IML at Marseille, France, the
Instituto de Matem' aticas of UNAM at Cuernavaca, Mexico, ICTP at
Trieste, Italia, IMPA at Rio de Janeiro, and USP at S" ao Carlos in
Brasil, to name a few, and we would like to thank them for their
generous hospitality and support. Thanks are also due to people who
helped us in many ways, in particular our co-authors of results
quoted in the book: Marcelo Aguilar, Wolfgang Ebeling, Xavier G'
omez-Mont, Sabir Gusein-Zade, LeDung " Tran ' g, Daniel Lehmann,
David Massey, A.J. Parameswaran, Marcio Soares, Mihai Tibar,
Alberto Verjovsky,andmanyother colleagueswho helped usin
variousways.
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