Hyperbolic Knots and Torsion in Khovanov Homology

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.

10 pages, 8 figures. Comments welcome. v2-typo corrected in ArXiv metadata. No change to paper