AM  Vol.4 No.11 , November 2013
Algorithms for Computing Some Invariants for Discrete Knots
ABSTRACT
Given a cubic knot K, there exists a projection  of the Euclidean space R3 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.

Cite this paper
Hinojosa, G. , Torres, D. and Valdez, R. (2013) Algorithms for Computing Some Invariants for Discrete Knots. Applied Mathematics, 4, 1526-1530. doi: 10.4236/am.2013.411206.
References
[1]   M. Boege, G. Hinojosa and A. Verjovsky, “Any Smooth Knot Sn Rn+2 Is Isotopic to a Cubic Knot Contained in the Canonical Scaffolding of Rn+2,” Revista Matemática Complutense, Vol. 24, No. 1, 2011, pp. 1-13.
http://dx.doi.org/10.1007/s13163-010-0037-4

[2]   G. Hinojosa, A. Verjovsky and C. V. Marcotte, “Cubulated Moves and Discrete Knots,” 2013, pp. 1-40.
http://arxiv.org/abs/1302.2133

[3]   D. Rolfsen, “Knots and Links,” AMS Chelsea Publishing, American Mathematical Society, Providence Rhode Island, 2003.

[4]   R. H. Fox, “A Quick Trip through Knot Theory. Topology of 3-Manifolds and Related Topics,” Prentice-Hall, Inc., Upper Saddle River, 1962.

[5]   “The Knot Atlas,” 2013. http://katlas.math.toronto.edu

 
 
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