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Given a link in the thickened annulus, its annular Khovanov homology carriesan action of the Lie algebra $\mathfrak{sl}_2$, which is natural with respectto annular link cobordisms. We consider the problem of lifting this action tothe stable homotopy refinement of the annular homology. As part of thisprogram, the actions of the standard generators of $\mathfrak{sl}_2$ are liftedto maps of spectra. In particular, it follows that the $\mathfrak{sl}_2$ actionon homology commutes with the action of the Steenrod algebra. The main newtechnical ingredients developed in this paper, which may be of independentinterest, concern certain types of cancellations in the cube of resolutions andthe resulting more intricate structure of the moduli spaces in the framed flowcategory.

Towards an $\mathfrak{sl}_2$ action on the annular Khovanov spectrum