Lattice homology and Seiberg-Witten Floer spectra

Irving Dai; Hirofumi Sasahira; Matthew Stoffregen

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arXiv · 2309.01253

Lattice homology and Seiberg-Witten Floer spectra

Irving Dai·Hirofumi Sasahira·Matthew Stoffregen

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Abstract

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.

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Irving Dai, Hirofumi Sasahira, Matthew Stoffregen. 2023-09-03. Lattice homology and Seiberg-Witten Floer spectra. https://arxiv.org/abs/2309.01253

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