Invariants of Foliations

  • Igor Nikolaev
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 41)

Abstract

We do not distinguish between two foliations if they are topologically equivalent. Such an equivalence relation splits the space of foliations into the equivalence classes which we are going to study in this chapter. This objective requires the following tasks:
  1. (i)

    Find a constructive invariant which takes the same values on topologically equivalent foliations.

     
  2. (ii)

    To describe all topological invariants which are admissible, i.e., which may be realized in the chosen class of foliations.

     
  3. (iii)

    Find a standard representative in each equivalence class, i.e., for a given admissible invariant to construct a flow whose invariant “coincides” with the admissible invariant.

     

Keywords

Manifold Stratification Librium 

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References

  1. D. V. Anosov, On an additive functional homology equation connected an ergodic rotation on the circle, Math. of USSR, Izvestia, 1973, 7 (6), 1257 - 1271.CrossRefGoogle Scholar
  2. V. I. Arnold, Small denominators I. Mapping of the circle onto itself, Translations of AMS (series 2 ), 46, 1965, 213 - 284.Google Scholar
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  4. G. R. Belitsky, Equivalence and normal forms of germs of smooth mappings, Russian Math. Survey, 31, 1978, 1, 107 - 177.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Igor Nikolaev
    • 1
  1. 1.The Fields Institute for Research in Mathematical SciencesTorontoCanada

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