The warping degree of a knot diagram

2008/09/08 by Shimizu, Ayaka
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0809.1334

Abstract

For an oriented knot diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain the monotone diagram from D in the usual way. We show that d(D) + d(-D) + 1 is less than or equal to the crossing number of D. Moreover the equality holds if and only if D is an alternating diagram.

Related

• The warping degree of a link diagram
• Lower bounds for the warping degree of a knot projection
• Prime alternating knots of minimal warping degree two
• The warping polynomial of a knot diagram
• The warping matrix of a knot diagram