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.
Lattice homology, formality, and plumbed L-space links
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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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Colored knot Floer homology: structures and examples
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.