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Lattice homology, formality, and plumbed L-space links

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arxiv 2210.15792 v2 pith:QV6PUKO6 submitted 2022-10-27 math.GT math.AG

Maciej Borodzik , Beibei Liu , Ian Zemke This is my paper · ORCID
classification math.GTmath.AG
keywords linklinksplumbedcomplexfloerhomologyl-spacelattice
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abstract

We define a link lattice complex for plumbed links, generalizing constructions of Ozsv\'ath, Stipsicz and Szab\'o, and of Gorsky and N\'emethi. We prove that for all plumbed links in rational homology 3-spheres, the link lattice complex is homotopy equivalent to the link Floer complex as an $A_\infty$-module. Additionally, we prove that the link Floer complex of a plumbed L-space link is a free resolution of its homology. As a consequence, we give an algorithm to compute the link Floer complexes of plumbed L-space links, in particular of algebraic links, from their multivariable Alexander polynomial.

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  1. Colored knot Floer homology: structures and examples

    math.GT 2025-08 conditional novelty 7.0 of 10

    The authors construct an n-colored knot Floer homology as a colimit over cable links with increasing full twists and equip it with a module structure over an explicit algebra.

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