Is every knot isotopic to the unknot?

50 years ago D. Rolfsen asked two questions: (A) Is every knot in the 3-sphere isotopic (=homotopic through embeddings) to a PL knot (or, equivalently, to the unknot)? In particular, is the Bing sling isotopic to a PL (=piecewise linear) knot? (B) If two PL links in the 3-sphere are isotopic, are they PL isotopic?
We show that the answer to (B) is positive if finite type invariants separate links in the 3-sphere, [arXiv:2406.09331].
Regarding (A), it was previously shown by the author that not every link in the 3-sphere is isotopic to a PL, link [arXiv:2011.01409]. Now we show that the Bing sling is not isotopic to any PL knot by an isotopy which extends to an isotopy of 2-component links with linking number 1. Moreover, the additional component may be allowed to self-intersect, and even to get replaced by a new one as long as it represents the same conjugacy class in $G/[G',G'']$, where $G$ is the fundamental group of the complement to the original component, [arXiv:2406.09365].
The proofs are based in part on a formula explaining the geometric meaning of the formal analogues of Cochran's derived invariants for PL links of linking number 1. These formal analogues are defined by using the 2-variable Conway polynomial, [arXiv:math/0312007].