ENGLISH

Vector fields on Singular Varieties

By Jean-Paul Brasselet , José Seade , Tatsuo Suwa (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2009
ISBN
3642052045, 9783642052040
DOI
10.1007/978-3-642-05205-7
ISSN
0075-8434
Google Books ID
mmK0mlG3RLIC
Language
english
Format
PDF
Filesize
2 MB (2383135 bytes)
Series
Lecture Notes in Mathematics 1987
Edition
1
Pages
232\253
Orientation
yes
Scanned
no
Time added
2011-08-31 04:54:40
Several Complex Variables and Analytic Spaces; Dyn

Description

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.

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