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I've been studying a lot of differential topology recently, and I like it a lot so far. Out of curiosity, I've tried looking online to see what some applications of differential topology are to things like physics, economics, etc., but most of what I have found is for differential geometry instead.

My question is: what are some applications of differential topology currently, both in the "mathematical world" and elsewhere? It seems that differential geometry is very applicable to other subject areas, but can the same be said for differential topology as well?

Nicholas James
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    Mathematical economics of about 40 years ago was full of transversality theory. Same with catastrophe theory. Degree theory and intersection theory are all over characteristic classes, geometric topology, and algebraic geometry. – Ted Shifrin Jan 16 '23 at 23:02

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