Algorithms for Computing Some Invariants for Discrete Knots - Applied Mathematics

AM > Vol.4 No.11, November 2013

Applied Mathematics

Volume 4, Issue 11 (November 2013)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

Algorithms for Computing Some Invariants for Discrete Knots ()

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DOI: 10.4236/am.2013.411206 3,236 Downloads 4,955 Views Citations

Author(s)

Gabriela Hinojosa, David Torres, Rogelio Valdez

Affiliation(s)

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

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

Share and Cite:

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.

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