Tangle Braid

This section will breifly describe another apporach to the tangle embedding problem, provide links to Maple programs to perform calculation of the quandle cocycle invariants, and gives links to the values of various cases of quandle cocycle tangle invariants that were calculated with Maple.

Each section will explain the notation used as well as the idea behind the particular case. The calculations performed with Maple are clearly limited. Most of the programs ran for knots with 8 or fewer crossing; however, some of them ran for knots with 9 or fewer crossings. Also, only small quandles were used (6 elements or less). In some examples we were able to use larger quandles with about 25 elements or so.

We used polynomial type cocycles given by Mochizuki, and also studied by Kheira Ameur in her dissertation (USF, 2006).

Quandle cocycle knot invariants calculated with Maple for the following cases: