2020/03/31 by Sung‐Mo Kang, Kang, Sungmo · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Primary 57M25
paper · pdf · doi:10.48550/arxiv.2003.13972
openalex publication_date 2020/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simple closed curve α in the boundary of a genus two handlebody H is primitive if adding a 2-handle to H along α yields a solid torus. If adding a 2-handle to H along α yields a Seifert-fibered space and not a solid torus, the curve is called Seifert. If α is disjoint from an essential separating disk in H, does not bound a disk in H, and is not primitive in H, then it is said to be proper power. As one of the background papers of the classification project of hyperbolic primitive/Seifert knots in S3 whose complete list is given in [BK20], this paper classifies in terms of R-R diagrams primitive, proper power, and Seifert curves. In other words, we provide up to equivalence all possible R-R diagrams of such curves. Furthermore, we further classify all possible R-R diagrams of proper power curves with respect to an arbitrary complete set of cutting disks of a genus two handlebody.