3 papers
math.GT2020
Triple-crossing number, the genus of a knot or link and torus knots
Michal Jablonowski
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…
math.GT2019
Triple-crossing projections, moves on knots and links and their minimal diagrams
Michal Jablonowski, Lukasz Trojanowski
In this paper we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links wit…
math.GT2018
Independence of Yoshikawa eighth move and a minimal generating set of band moves
Michal Jablonowski
Yoshikawa moves were introduced at least quarter-century ago and are still actively used by researchers. For any marked graph diagram we will define its twisted diagram and its mir…