Invariants of Foliations

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:

• (i) Find a constructive invariant which takes the same values on topologically equivalent foliations.

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

• (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.