$\mathrm{Pin}(2)$-Monopole Floer homology and the Rokhlin invariant

Francesco Lin

doi:10.1112/s0010437x18007510

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arXiv · 1708.07879

$\mathrm{Pin}(2)$-Monopole Floer homology and the Rokhlin invariant

Francesco Lin

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Abstract

We show that the bar version of the $\mathrm{Pin}(2)$-monopole Floer homology of a three-manifold $Y$ equipped with a self-conjugate spin$^c$ structure $\mathfrak{s}$ is determined by the triple cup product of $Y$ together with the Rokhlin invariants of the spin structures inducing $\mathfrak{s}$. This is a manifestation of mod $2$ index theory, and can be interpreted as a three-dimensional counterpart of Atiyah's classic results regarding spin structures on Riemann surfaces.

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Francesco Lin. 2017-08-25. $\mathrm{Pin}(2)$-Monopole Floer homology and the Rokhlin invariant. https://doi.org/10.1112/s0010437x18007510

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