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Lecture Notes in Mathematics

Vector fields on Singular Varieties

Authors: Brasselet, Jean-Paul, Seade, José, Suwa, Tatsuo

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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.

Reviews

From the reviews:

“This book is dedicated to the study of indices of vector fields and flows around an isolated singularity, or stationary point, in the cases where the underlying space is either a manifold or a singular variety. … The book gives a thorough presentation of the results, old and new, related to indices of vector fields on singular varieties and is a valuable reference for both the specialist and the non-specialist.” (M. G. Soares, Mathematical Reviews, Issue 2011 d)

Table of contents (3 chapters)

  • The Schwartz Index

    Jean-Paul Brasselet, José Seade, Tatsuo Suwa

    Pages 31-41

  • The Virtual Index

    Jean-Paul Brasselet, José Seade, Tatsuo Suwa

    Pages 85-96

  • Characteristic Classes of Coherent Sheaves on Singular Varieties

    Jean-Paul Brasselet, José Seade, Tatsuo Suwa

    Pages 201-213

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-05205-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-05204-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Vector fields on Singular Varieties
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1987
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-05205-7
DOI
10.1007/978-3-642-05205-7
Softcover ISBN
978-3-642-05204-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XX, 232
Topics