Algorithms for Computing Some Invariants for Discrete Knots

DOI: 10.4236/am.2013.411206   PDF   HTML     2,891 Downloads   4,234 Views  


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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.


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[2] G. Hinojosa, A. Verjovsky and C. V. Marcotte, “Cubulated Moves and Discrete Knots,” 2013, pp. 1-40.
[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.

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