Real monopoles and a spectral sequence from Khovanov homology

Abstract

Given a based link $(K,p)$, we define a "tilde"-version $\tilde{HMR}(K,p)$ of real monopole Floer homology and prove an unoriented skein exact triangle. We show the Euler characteristic of $\tilde{HMR}(K,p)$ is equal to Miyazawa's invariant $|deg(K)|$ arXiv:2312.02041 and examine some examples. Further, we construct a spectral sequence over $\mathbb{F}_2$ abutting to $\tilde{HMR}(K,p)$, whose $E_2$ page is the reduced Khovanov homology $Khr(\overline{K})$ of the mirror link $\overline{K}$.