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PIN(2)-monopole Floer homology and the Rokhlin invariant
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 12 / December 2018
- Published online by Cambridge University Press:
- 08 November 2018, pp. 2681-2700
- Print publication:
- December 2018
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- Article
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We show that the bar version of the
$\text{Pin}(2)$-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 classical results regarding spin structures on Riemann surfaces.
