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.