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… 

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