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Thom's transversality theorem

Contents

Contents

Statement

Theorem

Let PP be a smooth manifold and let i:MEi \colon M \hookrightarrow E be a smooth submanifold. Then the topological subspace

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

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

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

Relate entries

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.