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Haefliger theorem

Contents

Idea

On the classification of foliations:

Statement

Theorem

If XX is an open manifold, then there is a bijection between

  1. codimension q foliations on XX up to integral homotopy;

  2. homotopy classes of fiberwise surjective vector bundle maps TXNΓ qT X \to N \Gamma_q,

where Γ q\Gamma_q is the topological groupoid of germs of local diffeomorphisms of q\mathbb{R}^q.

References

  • John Francis, notes by M. Hoyois, Haefliger’s theorem classifying foliations over open manifold (pdf)

Last revised on May 13, 2013 at 03:57:12. See the history of this page for a list of all contributions to it.