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The equivalence of lattice and Heegaard Floer homology

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arxiv 2111.14962 v4 pith:SZYH4D7C submitted 2021-11-29 math.GT

Ian Zemke This is my paper · ORCID
classification math.GT
keywords homologyfloerheegaardlatticeactionboundarybundlescoincides
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abstract

We prove N\'{e}methi's conjecture: if $Y$ is a 3-manifold which is the boundary of a plumbing of a tree of disk bundles over $S^2$, then the lattice homology of $Y$ coincides with the Heegaard Floer homology of $Y$. We also give a conjectural description of the $H_1(Y)/\mathrm{Tors}$ action when $b_1(Y)>0$.

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  1. On $h$-cobordisms of complexity $2$

    math.GT 2025-01 conditional novelty 7.0 of 10

    Computes the monopole Floer homology and twisting involution of the complexity-2 protocork boundary, and constructs h-cobordisms of arbitrarily large Morgan-Szabó complexity between exotic pairs of closed 1-connected ...

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