2017/04/28 by Mizuki Fukuda, Fukuda, Mizuki
Biochemistry, Genetics and Molecular Biology · Mathematics · #57M27 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Primary 57Q45 #Secondary 57M60
paper · pdf · doi:10.48550/arxiv.1704.08923
openalex publication_date 2017/04/28 · openalex created_date 2018/06/01 · openalex updated_date 2026/07/28
An (m,n)-branched twist spin is a fibered 2-knot in S4 which is determined by a 1-knot K and coprime integers m and n. For a 1-knot, Lin proved that the number of irreducible SL(2,ℂ)-metabelian representations of the knot group of a 1-knot up to conjugation is determined by the knot determinant of the 1-knot. In this paper, we prove that the number of irreducible SL(2,ℂ)-metabelian representations of the knot group of an (m,n)-branched twist spin up to conjugation is determined by the determinant of a 1-knot in the orbit space by comparing a presentation of the knot group of the branched twist spin with the Lin's presentation of the knot group of the 1-knot.