Arbitrarily large torsion in Khovanov cohomology

TL;DR

This paper constructs links with arbitrarily large torsion in their Khovanov cohomology, demonstrating the existence of complex torsion structures in link invariants.

Contribution

It introduces a method to explicitly construct links with large torsion summands in Khovanov cohomology for primes 3, 5, and 7.

Findings

Existence of links with $ ext{Z}/p^k ext{Z}$ torsion in Khovanov cohomology for specified primes.

Explicit constructions for links with arbitrarily large torsion summands.

Demonstrates the richness of torsion phenomena in Khovanov cohomology.

Abstract

For any positive integer $k$ and $p\in \{3,5,7\}$ we construct a link which has a direct summand $\mathbb{Z}/p^k\mathbb{Z}$ in its Khovanov cohomology.