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 naturalto ask what is the ‘good’ notion of the index of a vector field, and of Chernclasses, 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 theframework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
- ISBN: 978-3-642-05204-0
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 250
- Fecha Publicación: 01/12/2009
- Nº Volúmenes: 1
- Idioma: Inglés