Geodesic
Knot Floer homology and Khovanov–Rozansky homology for singular links
Dowlin, Nathan1
1 Department of Mathematics, Columbia University, New York, NY, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3839-3885

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2018.18.3839
Classification : 57M27
Keywords: knot theory, knot Floer, Khovanov–Rozansky, HOMFLY-PT, homology

Dowlin, Nathan 1

1 Department of Mathematics, Columbia University, New York, NY, United States 
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Dowlin, Nathan. Knot Floer homology and Khovanov–Rozansky homology for singular links. Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3839-3885. doi: 10.2140/agt.2018.18.3839

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