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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… Click to show full abstract
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.
Keywords:
triple crossing;
torus knots;
genus;
crossing number;
knot
Journal Title: Topology and its Applications
Year Published: 2020
Link to full text (if available)
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Journal Title: Topology and its Applications
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!