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Thom's transversality theorem

Contents

Statement

Theorem

Let PP be a smooth manifold and let i:MEi : M \hookrightarrow E be a smooth submanifold. The 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).

References

The result is due to

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

A review is in

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

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

Created on December 21, 2010 09:30:06 by Urs Schreiber (131.211.232.166)