2023/11/30 by Neetal Neel, Neel, Neetal
Computer Science · Mathematics · #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2312.00208
openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kakimizu complexes have been found for several classes of links. O.Kakimizu found the Kakimizu complexes of knots with crossing number less than or equal to 10. Hatcher and Thurston found the 0-skeleton of the Kakimizu complex of 2-bridge links. Sakuma later generalized the result for special arborescent links and found the Kakimizu complexes for the same. Jessica Banks gave a complete proof of results announced by Hirasawa and Sakuma, describing explicitly the Kakimizu complexes of non-split, prime special alternating links. The Kakimizu complexes of prime, non-split alternating links have finite number of vertices. In this paper we compute the Kakimizu complexes for all 11 crossing prime, alternating knots, explicitly describing each of them. For most knots and links we use known algorithms. The rest of the Kakimizu complexes were found by using Murasugi sums and sutured manifold theory developed by Gabai, Scharlemann, Kakimizu and others.