Jin–Rolfsen conjecture on Alexander polynomials of rotant links

Let $L$ be an oriented link, and let $r(L)$ denote the link obtained from $L$ by rotation of its rotor. The Jin–Rolfsen conjecture. The Alexander polynomials of $L$ and $r(L)$ are equal.

The conjecture is motivated by the invariance of the determinant $|\Delta_L(-1)|$ under rotation and by computations confirming Alexander-polynomial invariance in many examples. It was disproved by a counterexample using a 6-rotor; a restricted version for $n$-rotors with alternating inputs and outputs was proved by P. Traczyk.