# 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} }

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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We say that a topological $n$-manifold $N$ is a cubical $n$-manifold if it is contained in the $n$-skeleton of the canonical cubulation $\mathcal{C}$ of ${\mathbb{R}}^{n+k}$ ($k\geq1$). In this…

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In this paper, we prove that given two cubical links of dimension two in [Formula: see text], they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated…

### Algorithms for Computing Some Invariants for Discrete Knots

- Mathematics, Computer Science
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### Smoothing closed gridded surfaces embedded in ℝ4

- MathematicsJournal of Knot Theory and Its Ramifications
- 2018

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…

### Topological surfaces as gridded surfaces in geometrical spaces

- MathematicsBoletín de la Sociedad Matemática Mexicana
- 2021

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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