2022/01/01 by Seonmi Choi, Choi, Seonmi, Seongjeong Kim +1
Computer Science · Mathematics · Physics and Astronomy · #57K12 #57K14 #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #Topological and Geometric Data Analysis #math.GT #msc:57K12 #msc:57K14
paper · pdf · doi:10.48550/arxiv.2201.00082
23 pages, 27 figures
openalex publication_date 2022/01/01 · arxiv created 2022/01/27 · arxiv updated 2022/01/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
M. Niebrzydowski and J. H. Przytycki defined a Kauffman bracket magma and constructed the invariant P of framed links in 3-space. The invariant is closely related to the Kauffman bracket polynomial. The normalized bracket polynomial is obtained from the Kauffman bracket polynomial by the multiplication of indeterminate and it is an ambient isotopy invariant for links. In this paper, we reformulate the multiplication by using a map from the set of framed links to a Kauffman bracket magma in order that P is invariant for links in 3-space. We define a generalization of a Kauffman bracket magma, which is called a marked Kauffman bracket magma. We find the conditions to be invariant under Yoshikawa moves except the first one and use a map from the set of admissible marked graph diagrams to a marked Kauffman bracket magma to obtain the invariant for surface-links in 4-space.