Khovanov and knot Floer homology of fibered positive links

Abstract

For fibered positive links, we compute the reduced and unreduced Khovanov homology in homological grading two over both $\mathbb{Z}$ and ${\mathbb{F}}_2$, and the knot Floer homology in the penultimate Alexander grading. Our Khovanov calculations, combined with the result of Przytycki-Sazdanović, prove that every nontrivial semi-adequate knot has 2-torsion in its unreduced Khovanov homology. This establishes Shumakovitch's conjecture for semi-adequate knots, which include all nontrivial positive knots. The proofs involve induction using the skein exact sequences, with the Hopf link as the base case.

arXiv commentv2: Added Khovanov results and changed the title. 36 pages, 11 figures