Skein exact triangles in knot Floer homology

2025/09/10 by Eaman Eftekhary, Eftekhary, Eaman
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2509.08317

openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a new family of skein exact triangles for link Floer homology. The skein triples are described by a triple of rational tangles (R₀,R₁,R_2n+1), where R₀ is the trivial tangle and R_k is obtained from it by applying k positive half-twists. We also set up an appropriate framework for potential construction of further skein exact triangles corresponding to arbitrary triples of rational tangles.

Citations

• Tangle replacements and knot Floer homology torsions
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• Heegaard Floer homology and Morse surgery
• Link Floer homology and the Thurston norm
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds
• Holomorphic disks and topological invariants for closed three-manifolds

Related

• On the skein exact squence for knot Floer homology
• An unoriented skein exact triangle in unoriented link Floer homology
• An unoriented skein relation via bordered-sutured Floer homology
• Real Monopole Floer Homology and Skein Exact Triangles
• Spectral sequences in unoriented link Floer homology