arXiv:2611.14806v1 Announce Type: new Abstract: We prove that the Euler characteristic of the framed real monopole Floer homology of the double branched cover of a link is given by the Alexander polynomial evaluated at $\sqrt{-1}$. For knots $K$ with determinant one, this formula shows that Miyazawa's degree invariant of $K$ can be computed in terms of the Alexander polynomial of $K$. The proof involves a new connected-sum formula and oriented skein exact triangles for some new variants of real monopole Floer homology, called the diagonal and cone real monopole Floer homology, which admit mod-two gradings. This is the monopole counterpart of Srivastava's Euler characteristic formula in real Heegaard Floer homology.
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