Vector Fields On Singular Varieties
- Collana:
- Lecture Notes In Mathematics
- EAN:
9783642052040
- ISBN:
3642052045
- Pagine:
- 232
- Formato:
- Paperback
- Lingua:
- Tedesco
Descrizione Vector Fields On Singular Varieties
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, L^eDung ~ Tran ¿ g, Daniel Lehmann, David Massey, A.J. Parameswaran, Marcio Soares, Mihai Tibar, Alberto Verjovsky,andmanyother colleagueswho helped usin variousways.
