Khovanov spectrum of periodic links admits a homology group action

Abstract: We prove that, given an $m$-periodic link, the Khovanov spectrum constructed by Lipshitz and Sarkar admits a homology group action. The action of Steenrod algebra on the cohomology of the spectrum gives an extra structure of the link. Another consequence of our construction is an alternative proof of the localization formula for Khovanov homology obtained first by Stoffregen and Zhang. We also express Khovanov homology of the quotient link in terms of equivariant Khovanov homology of the original link.