2010/01/06 by Kim, Jungsoo
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #57M27 #57M50 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Orthopedic Surgery and Rehabilitation
paper · pdf · doi:10.48550/arxiv.1001.0874
openalex publication_date 2010/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to construct a manifold decomposition of double branched cover of (S3, k) from a thin position of k. In this article, we will prove that if a thin position of k induces a thin decomposition of double branched cover of (S3,k) by Howards and Schultens' method, then the thin position is the sum of prime summands by stacking a thin position of one of prime summands of k on top of a thin position of another prime summand, and so on. Therefore, k holds the nearly additivity of knot width (i.e. for k = k1#k2, w(k) = w(k1)#w(k2) - 2) in this case. Moreover, we will generalize the hypothesis to the property a thin position induces a manifold decomposition whose thick surfaces consists of strongly irreducible or critical surfaces (so topologically minimal.)