2021/02/15 by Zhenkun Li, L. Yi, Li, Zhenkun +1
Mathematics · Medicine · #Algebraic Topology (math.AT) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2102.07300
openalex publication_date 2021/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper, the first author and his collaborator developed a method to compute an upper bound of the dimension of instanton Floer homology via Heegaard Diagrams of 3-manifolds. For a knot inside S3, we further develop an algorithm that can compute an upper bound of the dimension of instanton knot homology from knot diagrams. We test the effectiveness of the algorithm and found that for all knots up to seven crossings, the algorithm provides sharp bounds. In the second half of the paper, we show that, if the instanton knot Floer homology of a knot has a specified form, then the knot must an instanton L-space knot.