# Contents

## Idea

On the classification of foliations:

## Statement

###### Theorem

If $X$ is an open manifold, then there is a bijection between

1. codimension q foliations on $X$ up to integral homotopy;

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

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

## 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.