Intrinsic Khovanov homology in $\mathbb{RP}^3$

Abstract

We prove that Khovanov homology is an invariant of links in unparametrized $\mathbb{RP}^3$'s, i.e., oriented $3$-manifolds diffeomorphic to $\mathbb{RP}^3$. Along the way, we establish the functoriality of Khovanov homology for link cobordisms in $I\times\mathbb{RP}^3$.