Khovanov homology

Torsion in Thin Regions of Khovanov Homology

In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links--links whose Khovanov homology is supported on two adjacent diagonals--are known to only contain torsion of order 2. In this paper, we prove a local version of this result. If the Khovanov homology of a link is supported in two adjacent diagonals over a range of homological gradings and the Khovanov homology satisfies some other mild restrictions, then the Khovanov homology of that link has only torsion of order 2 over that range of homological gradings. These conditions are then shown to be met by an infinite family of 3-braids, strictly containing all 3-strand torus links, thus giving a partial answer to Sazdanovic and Przytycki's conjecture that 3-braids have only torsion of order 2 in Khovanov homology. We also give explicit computations of integral Khovanov homology for all links in this family.