Topological isotopy and Cochran's invariants of links

We show that there exists a 2-component link in the 3-space that is not isotopic (i.e. not homotopic through embeddings) to any smooth (or piecewise linear) link. The proof is unusually visual and is based on Cochran's invariants. The similar question for 1-component links, that is, knots is a well-known problem of Rolfsen (1974) which remains open. We will also discuss what else is known about isotopy and about Cochran's invariants.

The details are available in https://arxiv.org/abs/2011.01409