A knot to me is the image of a smooth (pl locally flat) embedding $S^n \to S^m$ under the equivalence of smooth (ambient pl) isotopies. And more generally embeddings of closed manifolds $N \to M$.

These (pl vs smooth) objects are different in codimension $>2$: Haefliger knots are non-trivial while any pl-knot is trivial in this codimension. What about the case of $m-n=2$?

Triangulating smooth knots and isotopies seems to be doable, but can we smooth out pl knots and isotopies at least for $m=4, n=2$? Is there a reference?


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