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Thom's transversality theorem

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Context

Manifolds and cobordisms

manifolds and cobordisms

Definitions

Genera and invariants

Theorem

Contents

Statement

Theorem

Let P be a smooth manifold and let i:M↪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 i 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)
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