A Spectral Sequence from Khovanov Homology to Knot Floer Homology

Dowlin, Nathan

doi:10.1090/jams/1039

A Spectral Sequence from Khovanov Homology to Knot Floer Homology
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by Nathan Dowlin;

J. Amer. Math. Soc. 37 (2024), 951-1010

DOI: https://doi.org/10.1090/jams/1039

Published electronically: January 19, 2024

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Abstract:

A well-known conjecture of Rasmussen states that for any knot $K$ in $S^{3}$, the rank of the reduced Khovanov homology of $K$ is greater than or equal to the rank of the reduced knot Floer homology of $K$. This rank inequality is supposed to arise as the result of a spectral sequence from Khovanov homology to knot Floer homology. Using an oriented cube of resolutions construction for a homology theory related to knot Floer homology, we prove this conjecture.

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