### arXiv:1806.05168 [math.GT]AbstractReferencesReviewsResources

#### Torsion in Khovanov homology of homologically thin knots

Published 2018-06-13Version 1

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.

**Comments:**12 pages, 5 figures

The Jones polynomial of ribbon links

arXiv:1707.05443 [math.GT] (Published 2017-07-18)

The Jones polynomial of an almost alternating link

A determinant formula for the Jones polynomial of pretzel knots