A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology

Let $E_{ k}^{ F}(D)$ be the spectral sequence induced by the oriented cube of resolutions on knot Floer homology. We prove that $E_{ 2}^{ F}(D)$ is a triply graded link invariant whose graded Euler characteristic is the HOMFLY-PT polynomial and that the higher pages are link invariants. By construction, the spectral sequence converges to knot Floer homology. We show that the rank of the torsion-free part of $E_{ 2}^{ F}(D)$ is the rank of HOMFLY-PT homology.

Categories: math.GT