Knot Floer Homology and Khovanov-Rozansky Homology for Singular Links

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 $H_{\ast }(C_F(S))$ is isomorphic to the HOMFLY-PT homology of $S$. Together with a naturality condition on the induced edge maps, this conjecture would prove the 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 this conjecture.

32 pages, 13 figures. Version 2 significantly improves upon Version 1, proving the desired conjecture

References in corpus (1)

• Framed graphs and the non-local ideal in the knot Floer cube of resolutions

Cited by in corpus (1)

• A quantum categorification of the Alexander polynomial