Dunfield–Gukov–Rasmussen spectral sequence conjecture

Let $K$ be a knot. Its HOMFLY-PT homology and knot Floer homology are homological invariants associated to $K$.

Dunfield–Gukov–Rasmussen conjecture. There is a spectral sequence from HOMFLY-PT homology to knot Floer homology.

This conjecture proposes a direct relationship between two knot homology theories. The paper develops such a relationship using the oriented cube of resolutions and proves results supporting the existence of a spectral sequence whose higher pages are link invariants and which converges to knot Floer homology.