Search for torsion in Khovanov homology

Sujoy Mukherjee, Józef H. Przytycki, Marithania Silvero, Xiao Wang, Seung Yeop Yang

Published 2017-01-18Version 1

In the Khovanov homology of links, presence of $\mathbb{Z}_2$-torsion is a very common phenomenon. Finite number of examples of knots with $\mathbb{Z}_n$-torsion for $n>2$ were also known, none for $n>8$. In this paper, we prove that there are infinite families of links whose Khovanov homology contains $\mathbb{Z}_n$-torsion for $2 < n < 9$ and $\mathbb{Z}_{2^s}$-torsion for $s < 24$. We also introduce $4$-braid links with $\mathbb{Z}_3$-torsion which are counterexamples to the PS braid conjecture. We also provide an infinite family of knots with $\mathbb{Z}_5$-torsion in reduced Khovanov homology and $\mathbb{Z}_3$-torsion in odd Khovanov homology.