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Braids
Author

Joe Christy
Organization: Mathematical Sciences Research Institute
Old MathSource #

0202-228
Revision date

2000-02-03
Description

A braid is a collection of strands which weave over and under one another. In Braids.m, a braid is described by a list {{m1, -m2 ..., mc},s} for a braid with s strands; where strand m1 crosses over strand m2, then strand m2 crosses under the m3, ..., and finally strand mc crosses over mc+1. By joining the ends of the braids in a circle they can be used to represent all knots and links. We can also close up the braid in a slightly different form to get a plat.
Subjects

*Mathematica Technology > Programming
*Mathematics > Topology
Keywords

Artin, Braids, Symmetric, Algebra, Geometry, Topology, Graphics, Knots, Links, Gauss, Curves, Strands, Plat, Ribbon, Braid
Downloads Download Wolfram CDF Player

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copyright.txt (1001 B) - Author's copyright notice
Download
BraidGroup.m (12.1 KB) - Does the algebra in Artin's braid group.
Download
Braids.m (23.5 KB) - Mathematica package to draw various pictures of plats and open and closed braids.
Download
BraidsDemo.nb (16.2 KB) - Sample notebook of aesthetically and mathematically interesting braids.
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SymmetricGroup.m (4.6 KB) - Does the algebra for the symmetric group.

Files specific to Mathematica 2.2 version:
Download
BraidsDemo.ma (11.3 KB) - Sample notebook of aesthetically and mathematically interesting braids.