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

Abstract

Asaeda-Przytycki-Sikora, Manturov, and Gabrovšek 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.

36 pages; Section 4.4 re-written; final version, to appear in Transactions AMS