Knot Floer homology and Khovanov–Rozansky homology for singular links

Dowlin, Nathan

doi:10.2140/agt.2018.18.3839

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Knot Floer homology and Khovanov–Rozansky homology for singular links

Nathan Dowlin

Algebraic & Geometric Topology 18 (2018) 3839–3885

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.

Keywords

knot theory, knot Floer, Khovanov–Rozansky, HOMFLY-PT, homology

Mathematical Subject Classification 2010

Primary: 57M27

References

Publication

Received: 29 June 2017

Revised: 14 April 2018

Accepted: 23 April 2018

Published: 11 December 2018

Authors

Nathan Dowlin
Department of Mathematics Columbia University New York, NY United States

Volume 18, issue 7 (2018)