A Rasmussen invariant for links in $\mathbb{RP}^3$

Asaeda-Przytycki-Sikora, Manturov, and Gabrov\v{s}ek extended Khovanov homology to links in $\mathbb{RP}^3$. We construct a Lee-type deformation of their theory, and use it to define an analogue of Rasmussen's s-invariant in this setting. We show that the s-invariant gives constraints on the genera of link cobordisms in the cylinder $I \times \mathbb{RP}^3$. As an application, we give examples of freely 2-periodic knots in $S^3$ that are concordant but not standardly equivariantly concordant.