Hyperbolic Knots and Torsion in Khovanov Homology

Micah Chrisman; Sujoy Mukherjee

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arXiv · 2205.07747

Hyperbolic Knots and Torsion in Khovanov Homology

Micah Chrisman·Sujoy Mukherjee

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Abstract

In this note, we show that if there is a knot in $S^3$ having $\mathbb{Z}_m$ torsion in its Khovanov homology, then there are infinitely many hyperbolic knots and infinitely many prime satellite knots having $\mathbb{Z}_m$ torsion in their Khovanov homology. As an application, we give the first known examples of hyperbolic knots and links with odd (and other non-$\mathbb{Z}_2$ torsion) in their Khovanov homology.

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Micah Chrisman, Sujoy Mukherjee. 2022-05-16. Hyperbolic Knots and Torsion in Khovanov Homology. https://arxiv.org/abs/2205.07747

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