Tangle Braid

This section will briefly describe another approach to the tangle embedding problem, provide links to Maple programs that perform calculations of the quandle cocycle invariants for tangle braids, and gives links to the values of various cases of quandle cocycle 2-tangle invariants that were calculated with Maple.

Tangle Braid Calculations

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:

• Polynomial 2-cocycle invariants for Alexander quandles
• Polynomial 3-cocycle invariants for Alexander quandles
• 3-cocycle invariants for dihedral quandles with Mochizuki cocycle
• 2-cocycle invariants for quandles with 3-6 elements
• 3-cocycle invariants for quandles with 3-6 elements

Tangle Braid Worksheet

The Tangle Braid worksheet will calculate the quandle cocycle invariant for partially closed braid words. The features of this worksheet include:

• Coloring braids by a dynamically linked C program
• Procedures for mass calculation and filename generation
• All of the previous procedures are bundled into one package.

One consequence of these new features is that the programs become system dependent. These packages have only been implemented and tested on various distributions of Linux. A link to the source code of the C coloring program will be given to allow you access to the file if you need to compile it for your particular OS. Perhaps if time permits or demand is high, we could compile and implement it for your particular OS and symbolic computation software. The sample worksheet explains more about the use and how the new coloring method works. An html version is included below.

must insert.

Maple 10 sample worksheet TangleBraidDLL.mw.

This worksheet requires the following files:

Maple input file TangleBraidquancocDLLpkg.m containing procedures for worksheet.

Maple input file alexQuanpkg.m containing procedures to generate Alexander quandles.

shared object file (DLL) to be linked to Maple for coloring the tangle braids.

Code for the procedures:

Maple worksheet containing code for the tangle braid Maple procedures.

HTML version of Maple code. MUST INSERT

C source code for the coloring program.