On Variations of s-invariants from sl(3)-link homology

Abstract

We use the Mackaay-Vaz universal $sl(3)$-link homology to deepen the study of $s$-invariants on Khovanov's link homology associated to $sl(3)$. Such $s$-invariants have already been studied by Lobb and Wu in characteristic 0 and we show how to extend this to other characteristics, particularly to $p=3$. We also use Bar-Natan's scanning algorithm for efficient calculations of these invariants, and exhibit more examples of unusual behaviour that has been previously observed by Lewark-Lobb.