English

Hyperbolic Knots and Torsion in Khovanov Homology

Geometric Topology 2022-05-18 v2

Abstract

In this note, we show that if there is a knot in S3S^3 having Zm\mathbb{Z}_m torsion in its Khovanov homology, then there are infinitely many hyperbolic knots and infinitely many prime satellite knots having Zm\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-Z2\mathbb{Z}_2 torsion) in their Khovanov homology.

Keywords

Cite

@article{arxiv.2205.07747,
  title  = {Hyperbolic Knots and Torsion in Khovanov Homology},
  author = {Micah Chrisman and Sujoy Mukherjee},
  journal= {arXiv preprint arXiv:2205.07747},
  year   = {2022}
}

Comments

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