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The equivalence of two Pin(2)-equivariant Seiberg-Witten Floer homologies (2503.03063v1)
Published 4 Mar 2025 in math.GT
Abstract: We show that for a rational homology 3-sphere $Y$ equipped with a self-conjugate spin$c$-structure $\mathfrak s$, the $\operatorname{Pin}(2)$-equivariant monopole Floer homology of $(Y,\mathfrak s)$, as defined by Lin, is isomorphic to the $\operatorname{Pin}(2)$-equivariant Seiberg-Witten Floer homology of $(Y,\mathfrak s)$ defined by Manolescu.