Connected Heegaard Floer homology of sums of Seifert fibrations

Irving Dai

doi:10.2140/agt.2019.19.2535

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arXiv · 1804.06058

Connected Heegaard Floer homology of sums of Seifert fibrations

Irving Dai

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Abstract

We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3-manifolds, including all linear combinations of Seifert fibered homology spheres. We show that for such manifolds, the connected Floer homology completely determines the local equivalence class of the associated $\iota$-complex. Some identities relating the rank of the connected Floer homology to the Rokhlin invariant and the Neumann-Siebenmann invariant are also derived. Our computations are based on combinatorial models inspired by the work of N\'emethi on lattice homology.

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Irving Dai. 2018-04-17. Connected Heegaard Floer homology of sums of Seifert fibrations. https://doi.org/10.2140/agt.2019.19.2535

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