Contents

# Contents

## Statement

###### Theorem

Let $P$ be a smooth manifold and let $i \colon M \hookrightarrow E$ be a smooth submanifold. Then the topological subspace

$C^{\infty}_{tr i}(P,E) \subset C^\infty(P,E)$

of smooth functions that are transverse maps to $i$ is a dense subspace.

This is due to Thom 54, see e.g. Kosinski 93, IV (2.5).

## References

The result is due to

• René Thom, Quelques propriétés globales des variétés différentiables Comment. Math. Helv. 28, (1954). 17-86

Textbook account:

Lecture notes

• John Francis, Topology of manifolds course notes (2010) (web)

Lecture 4 Transversality (notes by I. Bobkova) (pdf)

Last revised on February 5, 2019 at 12:28:27. See the history of this page for a list of all contributions to it.