Triple-crossing projections, moves on knots and links and their minimal diagrams

Michal Jablonowski; Lukasz Trojanowski

doi:10.1142/s0218216520500157

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arXiv · 1908.11751

Triple-crossing projections, moves on knots and links and their minimal diagrams

Michal Jablonowski·Lukasz Trojanowski

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Abstract

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 with triple-crossing number at most four. We also extend the table of known knots and links with triple-crossing number equal to five. By introducing a new type of diagrammatic move, we reduce the number of generating moves on triple-crossing diagrams, and derive a minimal generating set of moves connecting triple-crossing diagrams of the same knot.

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BibTeX RIS

Michal Jablonowski, Lukasz Trojanowski. 2019-08-30. Triple-crossing projections, moves on knots and links and their minimal diagrams. https://doi.org/10.1142/s0218216520500157

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