Algebraic & Geometric Topology

Knot Floer homology and Khovanov–Rozansky homology for singular links

Nathan Dowlin

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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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

knot theory knot Floer Khovanov–Rozansky HOMFLY-PT homology


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.

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