nLab Thom's transversality 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


The result is due to (Theorem I.5?)

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 1, 2021 at 04:03:38. See the history of this page for a list of all contributions to it.