We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.
"A refinement of Khovanov homology." Geom. Topol. 25 (4) 1861 - 1917, 2021. https://doi.org/10.2140/gt.2021.25.1861