Vector fields on Singular Varieties (Lecture Notes in Mathematics, 1987) - Softcover

Brasselet, Jean-Paul; Seade, José; Suwa, Tatsuo

Softcover

ISBN 10: 3642052045 ISBN 13: 9783642052040

Publisher: Springer, 2009

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2009
• Language: English
• ISBN 10: 3642052045
• ISBN 13: 9783642052040
• Binding: Paperback
• Number of pages: 252