Vector fields on Singular Varieties

  • Jean-Paul Brasselet
  • José Seade
  • Tatsuo Suwa

Part of the Lecture Notes in Mathematics book series (LNM, volume 1987)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 1-29
  3. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 31-41
  4. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 43-69
  5. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 71-83
  6. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 85-96
  7. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 97-113
  8. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 115-128
  9. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 129-141
  10. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 143-166
  11. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 167-184
  12. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 185-192
  13. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 193-200
  14. Jean-Paul Brasselet, José Seade, Tatsuo Suwa
    Pages 201-213
  15. Back Matter
    Pages 215-231

About this book

Introduction

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.

Keywords

Chern classes Indices of vector fields Poincaré-Hopf Theorem Singular foliations Singular varieties Vector field manifold

Authors and affiliations

  • Jean-Paul Brasselet
    • 1
  • José Seade
    • 2
  • Tatsuo Suwa
    • 3
  1. 1.Inst. de Mathématiques de Luminy (IML)CNRS Marseille Cedex 9France
  2. 2.Instituto de MatématicasUniversidad Nacional AutónomiaCuernavaca, MorelosMexico
  3. 3.Dept. MathematicsHokkaido UniversitySapporo, HokkaidoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-05205-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-05204-0
  • Online ISBN 978-3-642-05205-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book