The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex to a singular resolution of a knot . Manolescu conjectured that when is in braid position, the homology is isomorphic to the HOMFLY-PT homology of . 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 , a recursion formula for HOMFLY-PT homology and additional –like differentials on , we prove Manolescu’s conjecture. The naturality condition remains open.
"Knot Floer homology and Khovanov–Rozansky homology for singular links." Algebr. Geom. Topol. 18 (7) 3839 - 3885, 2018. https://doi.org/10.2140/agt.2018.18.3839