Lattice Diagrams of Knots and Diagrams of Lattice Stick Knots

Margaret Allardice; Ethan D. Bloch

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arXiv · 1803.03685

Lattice Diagrams of Knots and Diagrams of Lattice Stick Knots

Margaret Allardice·Ethan D. Bloch

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Abstract

We give a simple example showing that a knot or link diagram that lies in the ${\mathbb{Z}}^2$ lattice is not necessarily the projection of a lattice stick knot or link in the ${\mathbb{Z}}^3$ lattice, and we give a necessary and sufficient condition for when a knot or link diagram that lies in the ${\mathbb{Z}}^2$ lattice is in fact the projection of a lattice stick knot or link.

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BibTeX RIS

Margaret Allardice, Ethan D. Bloch. 2018-03-09. Lattice Diagrams of Knots and Diagrams of Lattice Stick Knots. https://arxiv.org/abs/1803.03685

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