I am looking for applications of the strong Whitney's embedding theorem that have an advantage over weak theorems. That is, applications where it's important that the dimension of the Euclidian space be minimal.
2026-03-25 17:19:23.1774459163
Applications of Strong Whitney Embedding
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I cannot think on the top of my head of an important application of the strong Whitney embedding theorem. However, the proof of this theorem is extremely instructive and useful in topology.
To upgrade the weak Whitey embedding theorem to its strong version, one needs to get rid of self-transverse intersections. For that purpose, one uses the so-called Whitney trick, which has, for example, later been successfully used to show the $h$-cobordism theorem.