# Cubulated moves and discrete knots

@article{Hinojosa2013CubulatedMA,
title={Cubulated moves and discrete knots},
author={Gabriela Hinojosa and Alberto Verjosvky and Cynthia Verjovsky Marcotte},
journal={arXiv: Geometric Topology},
year={2013}
}
• Published 8 February 2013
• Mathematics
• arXiv: Geometric Topology
In this paper, we prove than given two cubic knots $K_1$, $K_2$ in $\mathbb{R}^3$, they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister moves for classical tame knots. We use the fact that a cubic knot is determined by a cyclic permutation of contiguous vertices of the $\mathbb{Z}^3$-lattice (with some restrictions), to describe some of the classic invariants and properties of the knots in…
6 Citations
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• Mathematics, Computer Science
• 2013
An algorithm is developed for computing some invariants for K: its fundamental group, the genus of its Seifert surface and its Jones polynomial.
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We say that a topological [Formula: see text]-manifold [Formula: see text] is a cubical [Formula: see text]-manifold if it is contained in the [Formula: see text]-skeleton of the canonical cubulation
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Boletín de la Sociedad Matemática Mexicana
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In this paper, we study topological surfaces as discrete models by means of gridded surfaces in the two-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.

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