in KnotViewer make it visible whether it's over/under crossing or only touching (z-buffer), and indicate orientation (direction)
perhaps interactive Reidemeister moving lines around
discrete Reidemeister movements build a finite group, figure out a construction for this
implement the finishing parts for the knot treatment on graphs with boundary
dichromatic polynomial and connections to graph coloring
symmetry group of a link (see references Z(2) × A(5) and others)
what happens when we take those polynomials seriously and let the variable having values (in some field)
the running time and space requirements for the used Jones polynomial computing algorithm are in what class? O(n sqrt(n)) or s.th. like that (n denoting the number of crossings)?
formula for Jones polynomial of (p,q) torus knot can be retrieved using algebras; well, so there is hope that our computational approach can serve as a starting point for general guesses and theorems (avoiding the skein tree at all and just using general formula in case the above conjecture (about no crossings needed) holds)
classify Chess piece movements (multiple pieces trying to kill the kings, resulting in a periodical behavior of some kind, the paths having over/under-crossings in time) in the context of links
use MathML™ and special fonts designed for knot diagrams