## Algebraic & Geometric Topology

### Knot Floer homology and Khovanov–Rozansky homology for singular links

Nathan Dowlin

#### Abstract

The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex $C F ( S )$ to a singular resolution $S$ of a knot $K$. Manolescu conjectured that when $S$ is in braid position, the homology $H ∗ ( C F ( S ) )$ is isomorphic to the HOMFLY-PT homology of $S$. Together with a naturality condition on the induced edge maps, this conjecture would prove the existence of a spectral sequence from HOMFLY-PT homology to knot Floer homology. Using a basepoint filtration on $C F ( S )$, a recursion formula for HOMFLY-PT homology and additional $s l n$–like differentials on $C F ( S )$, we prove Manolescu’s conjecture. The naturality condition remains open.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3839-3885.

Dates
Revised: 14 April 2018
Accepted: 23 April 2018
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.agt/1545102056

Digital Object Identifier
doi:10.2140/agt.2018.18.3839

Mathematical Reviews number (MathSciNet)
MR3892233

Zentralblatt MATH identifier
07006379

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds

#### Citation

Dowlin, Nathan. Knot Floer homology and Khovanov–Rozansky homology for singular links. Algebr. Geom. Topol. 18 (2018), no. 7, 3839--3885. doi:10.2140/agt.2018.18.3839. https://projecteuclid.org/euclid.agt/1545102056

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