We study the conjugation involution in Seiberg-Witten theory in the context of the Ozsváth-Szabó and Bloom's spectral sequence for the branched double cover of a link L in S3. We prove that there exists a spectral sequence of F[Q]/Q2-modules (where Q
Nearby in the stack
has degree
−1
) which converges to
HMI∗(Σ(L))
, an involutive version of the monopole Floer homology of the branched double cover, and whose
E2
-page is a version of Bar Natan's characteristic two Khovanov homology of the mirror of
L
. We conjecture that an analogous result holds in the setting of