2025/02/05 by Hajime Kubota, Kubota, Hajime
Computer Science · Mathematics · #57K10 #57K18 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57K10 #msc:57K18
paper · pdf · doi:10.48550/arxiv.2502.02939
v2: accepted version, 27 pages, 18 figures
openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv created 2026/08/03 · arxiv updated 2026/08/04
We partially determine grid homology (combinatorial knot Floer homology) of diagonal knots, which are conjectured to be equivalent to positive braid knots, by exploiting nice grid diagrams. Its next-to-top term detects the number of prime factors, and the top-2 term corresponds to the decompositions of the knot into two non-integer tangles. We compare diagonal knots to various classes of knots, such as positive braids, fibered positive knots, and L-space knots.