Algorithms for Computing Some Invariants for Discrete Knots

Gabriela Hinojosa, David Torres, Rogelio Valdez

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Cuernavaca, México.

DOI: 10.4236/am.2013.411206                

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.

Keywords

Cubic Knots; Discrete Knots; Algorithms

Conflicts of Interest

The authors declare no conflicts of interest.

References

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