Prime non-split links with torsion-free Khovanov homology

Determine whether the unknot and the Hopf link are the only prime, non-split links with torsion-free Khovanov homology, thereby proving or refuting the stated conjecture.

Background

The paper proves a refined semidirect-product formula for the projective unoriented monodromy group of a split link when every link piece has torsion-free Khovanov homology. It then applies this formula to split links made from unknots and Hopf links, whose monodromy groups are computed explicitly.

The authors note that a conjecture in the cited literature asserts that, among prime non-split links, torsion-free Khovanov homology occurs only for the unknot and the Hopf link. If true, this would explain why the preceding corollary is expected to have no further applications in the prime non-split setting.