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arXiv · 1703.01401

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

Nathan Dowlin
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Abstract

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.

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Nathan Dowlin. 2017-03-04. A Categorification of the HOMFLY-PT Polynomial with a Spectral Sequence to Knot Floer Homology. https://arxiv.org/abs/1703.01401

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