Torsion in Khovanov homology of homologically thin knots

Abstract

We prove that every ${\mathbb{Z}}_2$H-thin link has no $2^k$-torsion for $k>1$ in its Khovanov homology. Together with previous results by Eun Soo Lee and the author, this implies that integer Khovanov homology of non-split alternating links is completely determined by the Jones polynomial and signature. Our proof is based on establishing an algebraic relation between Bockstein and Turner differentials on Khovanov homology over ${\mathbb{Z}}_2$. We conjecture that a similar relation exists between the corresponding spectral sequences.

arXiv comment12 pages, 5 figures