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Algorithms for Computing Some Invariants for Discrete Knots
Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
- 1 Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
- 2 Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
- 3 Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México
Applied Mathematics·Volume 04 (2013)·Pages 1526–1530·Published 15 October 2013·DOI10.4236/am.2013.411206
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Abstract
Given a cubic knot K , there exists a projection of the Euclidean space R 3 onto a suitable plane such that p ( K ) is a knot diagram and it can be described in a discrete way as a cycle permutation. Using this fact, we develop an algorithm for computing some invariants for K : its fundamental group, the genus of its Seifert surface and its Jones polynomial.
KeywordsCubic KnotsDiscrete KnotsAlgorithms
- M. Boege, G. Hinojosa and A. Verjovsky, “Any Smooth Knot Sn R n+2 Is Isotopic to a Cubic Knot Contained in the Canonical Scaffolding of R n+2 ,” Revista Matemática Complutense, Vol. 24, No. 1, 2011, pp. 1-13. http://dx.doi.org/10.1007/s13163-010-0037-4
- G. Hinojosa, A. Verjovsky and C. V. Marcotte, “Cubulated Moves and Discrete Knots,” 2013, pp. 1-40. http://arxiv.org/abs/1302.2133
- D. Rolfsen, “Knots and Links,” AMS Chelsea Publishing, American Mathematical Society, Providence Rhode Island, 2003.
- R. H. Fox, “A Quick Trip through Knot Theory. Topology of 3-Manifolds and Related Topics,” Prentice-Hall, Inc., Upper Saddle River, 1962.
- “The Knot Atlas,” 2013. http://katlas.math.toronto.edu