Lattice homology and Seiberg-Witten-Floer spectra

Using lattice homology, we give an explicit combinatorial description of the Seiberg-Witten-Floer spectrum $SWF(Y)$ 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.