Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.00878 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In 2005 Dunfield, Gukov and Rasmussen conjectured an existence of the spectral sequence from the reduced triply graded Khovanov-Rozansky homology of a knot to its knot Floer homology defined by Ozsváth and Szabó. The main result of this paper is a proof of this conjecture. For this purpose, we construct a bigraded spectral sequence from the $\mathfrak{gl}_0$ homology constructed by the last two authors to the knot Floer homology. Using the fact that the $\mathfrak{gl}_0$ homology comes equipped with a spectral sequence from the reduced triply graded homology, we obtain our main result. The first spectral sequence is of Bockstein type and comes from a subtle manipulation of coefficients. The main tools are quantum traces of foams and of singular Soergel bimodules and a $\mathbb Z$-valued cube of resolutions model for knot Floer homology originally constructed by Ozsváth and Szabó over the field of two elements. As an application, we deduce that the $\mathfrak{gl}_0$ homology as well as the reduced triply graded Khovanov-Rozansky one detect the unknot, the two trefoils, the figure eight knot and the cinquefoil.