Seifert rational homology 3-spheres fibering over RP² are L-spaces whose Floer homotopy type is a suspension of S^0, with d-invariants computed via eta invariants of spin^c-Dirac operators and orbifold pin^c-connections.
Manolescu, Seiberg–Witten–Floer stable homotopy type of three-manifolds withb 1 = 0
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Floer homotopy type and eta invariants of Seifert $3$-manifolds fibering over $\mathbb{RP}^2$
Seifert rational homology 3-spheres fibering over RP² are L-spaces whose Floer homotopy type is a suspension of S^0, with d-invariants computed via eta invariants of spin^c-Dirac operators and orbifold pin^c-connections.