Torsion in Khovanov homology of homologically thin knots

Alexander N. Shumakovitch

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arXiv · 1806.05168

Torsion in Khovanov homology of homologically thin knots

Alexander N. Shumakovitch

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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.

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BibTeX RIS

Alexander N. Shumakovitch. 2018-06-13. Torsion in Khovanov homology of homologically thin knots. https://arxiv.org/abs/1806.05168

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