Volume 18, issue 7 (2018)

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Knot Floer homology and Khovanov–Rozansky homology for singular links

Nathan Dowlin

Algebraic & Geometric Topology 18 (2018) 3839–3885

The (untwisted) oriented cube of resolutions for knot Floer homology assigns a complex CF(S) to a singular resolution S of a knot K. Manolescu conjectured that when S is in braid position, the homology H(CF(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 CF(S), a recursion formula for homfly-pt homology and additional sln–like differentials on CF(S), we prove Manolescu’s conjecture. The naturality condition remains open.

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knot theory, knot Floer, Khovanov–Rozansky, HOMFLY-PT, homology
Mathematical Subject Classification 2010
Primary: 57M27
Received: 29 June 2017
Revised: 14 April 2018
Accepted: 23 April 2018
Published: 11 December 2018
Nathan Dowlin
Department of Mathematics
Columbia University
New York, NY
United States