A spectral sequence from Khovanov homology to knot Floer homology

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.

arXiv comment44 pages

Cited by in corpus (6)

• Khovanov homology and the cinquefoil
• Ozsvath-Szabo bordered algebras and subquotients of category O
• Extremal Khovanov homology of Turaev genus one links
• Rank Bounds in Link Floer Homology and Detection Results
• Skein relations for tangle Floer homology
• An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2