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arXiv:1806.05168 [math.GT]AbstractReferencesReviewsResources

Torsion in Khovanov homology of homologically thin knots

Alexander N. Shumakovitch

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
Categories: math.GT, math.AT
Subjects: 57M25, 57M27
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