A note on the unknotting number and the region unknotting number of weaving knots

2024/08/27 by Shimizu, Ayaka, Gill, Amrendra, Joshi, Sahil · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2408.14938

Abstract

A weaving knot is an alternating knot whose minimal diagram is a closed braid of a lattice-like pattern. In this paper, the warping degree of a braid diagram is defined, and upper bounds of the unknotting number and the region unknotting number for some families of weaving knots are given by diagrammatical and combinatorial examination of the warping degree of weaving knot diagrams.

Cited by

• The CN matrix of a pure braid projection

Related

• The warping polynomial of a knot diagram
• Lower bounds for the warping degree of a knot projection
• The warping degree of a knot diagram
• Prime alternating knots of minimal warping degree two
• On closed 3-braids with unknotting number one