Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 7 (2018), 3839-3885.
Knot Floer homology and Khovanov–Rozansky homology for singular links
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.
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3839-3885.
Received: 29 June 2017
Revised: 14 April 2018
Accepted: 23 April 2018
First available in Project Euclid: 18 December 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M27: Invariants of knots and 3-manifolds
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