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Splitting maps in link Floer homology and integer points in permutahedra

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arxiv 2307.07741 v1 pith:WIZTAEMB submitted 2023-07-15 math.GT

Akram Alishahi , Eugene Gorsky , Beibei Liu This is my paper · ORCID
classification math.GT
keywords exacthomologylinksplittingfloermapsskeininteger
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abstract

In this paper, we study the skein exact sequence for links via the exact surgery triangle of link Floer homology and compare it with other skein exact sequences given by Ozsv\'ath and Szab\'o. As an application, we use the skein exact sequence to study the splitting number and splitting maps for links. In particular, we associate the splitting maps for the torus link $T(n, n)$ to integer points in the $(n-1)$-dimensional permutahedron, and obtain the link Floer homology of an $n$-component homology nontrivial unlink in $S^{1}\times S^{2}$.

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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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