Instantons and Khovanov homology in $\mathbb{RP}^3$

Abstract

We study the instanton Floer homology for links in $\mathbb{RP}^3$ and compute the second page of Kronheimer--Mrowka's spectral sequence. As an application, we show that Khovanov homology detects the unknot and the projective unknot in $\mathbb{RP}^3$.