CUBULATED MOVES AND DISCRETE KNOTS-Reference-Cited by-同舟云学术

CUBULATED MOVES AND DISCRETE KNOTS

Published:2013-12 Issue:14 Volume:22 Page:1350079
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

HINOJOSA GABRIELA¹,VERJOVSKY ALBERTO²,VERJOVSKY MARCOTTE CYNTHIA³

Affiliation:

1. Facultad de Ciencias. Universidad, Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa. Cuernavaca, Morelos 62209, Mexico

2. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Av. Universidad s/n, Col. Lomas de Chamilpa. Cuernavaca, Morelos 62209, Mexico

3. Mathematics Department, St. Edward's University, 3001 South Congress Avenue, Austin, TX 78704, USA

Abstract

In this paper, we prove that two cubic knots K1, K2 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 this fact to describe a cubic knot in a discrete way, as a cyclic permutation of contiguous vertices of the ℤ3-lattice (with some restrictions); moreover, we describe a regular diagram of a cubic knot in terms of such cyclic permutations.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821651350079X

Reference11 articles.

1. CUBE DIAGRAMS AND 3-DIMENSIONAL REIDEMEISTER-LIKE MOVES FOR KNOTS

2. Wild knots in higher dimensions as limit sets of Kleinian groups

3. Any smooth knot $\mathbb{S}^{n}\hookrightarrow\mathbb{R}^{n+2}$ is isotopic to a cubic knot contained in the canonical scaffolding of ℝ n+2

4. A. Douady, 1961/1962 Séminaire Henri Cartan (Secrétariat mathématique, Paris, 1962) p. 25.

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