Triple-crossing number, the genus of a knot or link and torus knots

Abstract

We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we show that this bound is strong enough to obtain the triple-crossing numbers of all torus knots, and of many more knots and their connected sums.

Cited by in corpus (3)

• Strict Inequalities for the $n$-crossing Number
• Upper and lower bound on delta-crossing number and tabulation of knots
• Tabulation of knots up to five triple-crossings and moves between oriented diagrams