Prime alternating knots of minimal warping degree two

2020/04/30 by Ayaka Shimizu, Shimizu, Ayaka
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2004.14520

openalex publication_date 2020/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The warping degree of an oriented knot diagram is the minimal number of crossing changes which are required to obtain a monotone knot diagram from the diagram. The minimal warping degree of a knot is the minimal value of the warping degree for all oriented minimal diagrams of the knot. In this paper, all prime alternating knots with minimal warping degree two are determined.

Related

• The warping degree of a knot diagram
• Lower bounds for the warping degree of a knot projection
• The warping polynomial of a knot diagram
• On the warping sum of knots
• Minimal Grid Diagrams of the Prime Alternating Knots with 12 Crossings