About this book
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.
- DOI https://doi.org/10.1007/978-3-642-05205-7
- Copyright Information Springer-Verlag Berlin Heidelberg 2009
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-642-05204-0
- Online ISBN 978-3-642-05205-7
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- About this book