Lattice homology and Seiberg–Witten Floer spectra

Using lattice homology, we give an explicit combinatorial description of the Seiberg–Witten Floer spectrum \mathit{SWF}(Y) for Y an almost-rational plumbed homology sphere. This class of manifolds includes all Seifert fibered rational homology spheres with base orbifold S^{2} . Using our computations, we provide a calculation of Manolescu’s \kappa -invariant for certain connected sums of these spaces.