Splitting maps in link Floer homology and integer points in permutahedra

2023/07/15 by Akram Alishahi, Eugene Gorsky, Alishahi, Akram +3 · 1 citation
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.07741

openalex publication_date 2023/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 Ozsváth and Szabó. 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 S¹× S².

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