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Lattice homology and Seiberg-Witten Floer spectra

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arxiv 2309.01253 v2 pith:NQJMFLXF submitted 2023-09-03 math.GT

Irving Dai , Hirofumi Sasahira , Matthew Stoffregen This is my paper · ORCID
classification math.GT
keywords homologylatticealmost-rationalbasecalculationcertainclasscombinatorial
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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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  1. Naturality in real Heegaard Floer theory

    math.GT 2026-07 conditional novelty 7.0 of 10

    Real Heegaard Floer homology becomes a natural functor on based real 3-manifolds, with an equivariant mapping class group action and a new involutive variant.

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