Base-Tangle Decompositions of $n$-String Tangles with $1
Ochiai, Mitsuyuki ; Morimura, Noriko
Experiment. Math., Tome 17 (2008) no. 1, p. 1-8 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
This study describes the program bTd, which was developed for the decomposition of any $n$-tangle with $1 < n < 10$} into base {\small$n$}-tangles using the Skein relation. The program enables us to compute HOMFLY polynomials of knots and links with a large number of crossing points within a matter of hours (see Examples 4.4 and 4.5). This contrasts with the results of attempting computations using Hecke algebras $H(q,n)$} with $18 \ge n$. Such a computation did not complete even after a period of thirty days in a recent examination by the first author and F. Kako [Imafuji and Ochiai 02, Murakami 89, Ochiai and Murakami 94, Ochiai and Kako 95]. In this paper, we first introduce two new concepts: an oriented ordered tangle and a subdivision of a tangle. We then present some examples of base-tangle decompositions achieved using the present program along with the corresponding computational times.
Publié le : 2008-05-15
Classification:  Knot,  tangle decomposition,  polynomial invariant,  mutation,  57N10,  57M25 
@article{1227031893,
     author = {Ochiai, Mitsuyuki and Morimura, Noriko},
     title = {Base-Tangle Decompositions of $n$-String Tangles with
 $1<n<10$},
     journal = {Experiment. Math.},
     volume = {17},
     number = {1},
     year = {2008},
     pages = { 1-8},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227031893}
}

Ochiai, Mitsuyuki; Morimura, Noriko. Base-Tangle Decompositions of $n$-String Tangles with
 $1