The rank of a warping matrix

2015/08/25 by Taira Akiyama, Akiyama, Taira, Ayaka Shimizu +3
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1508.06065

13 pages, 4 figures

arxiv created 2015/08/25 · arxiv updated 2015/08/26

Abstract

The warping matrix has been defined for knot projections and knot diagrams by using warping degrees. In particular, the warping matrix of a knot diagram represents the knot diagram uniquely. In this paper we show that the rank of the warping matrix is one greater than the crossing number. We also discuss the linearly independence of knot diagrams by considering the warping incidence matrix.

Related

• The warping matrix of a knot diagram
• Lower bounds for the warping degree of a knot projection
• The warping degree of a knot diagram
• The warping polynomial of a knot diagram
• The warping degree of a link diagram