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

Many authors have questioned the use of the index of the vector field, and of the Chern classes, if the underlying space becomes singular. This book discusses their explorations within the framework of the obstruction theory and the Chern-Weil theory.

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