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

We study the instanton Floer homology for links in ${\mathbb{R}\mathbb{P}}^3$ 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 ${\mathbb{R}\mathbb{P}}^3$.