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2018 Knot Floer homology and Khovanov–Rozansky homology for singular links
Nathan Dowlin
Algebr. Geom. Topol. 18(7): 3839-3885 (2018). DOI: 10.2140/agt.2018.18.3839

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.

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Nathan Dowlin. "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

Information

Received: 29 June 2017; Revised: 14 April 2018; Accepted: 23 April 2018; Published: 2018
First available in Project Euclid: 18 December 2018

zbMATH: 07006379
MathSciNet: MR3892233
Digital Object Identifier: 10.2140/agt.2018.18.3839

Subjects:
Primary: 57M27

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 7 • 2018
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