2
votes
1answer
185 views

Min Bend Orthogonal Knots

I am seeking literature on 3D orthogonal drawings of knots, especially minimum bend drawings. An orthogonal drawing employs segments parallel to the axes of a Cartesian coordinate system. A bend is a ...
26
votes
1answer
1k views

Does this knot invariant distinguish trefoil chiralities?

Let $C_N$ denote the labelled configuration of $N^{th}$ roots of unity with $p_J = e^{\frac{2\pi iJ}{N}}$ for $J = 1\ldots N$. As a corollary of something else I was playing around with, I recently ...
17
votes
7answers
2k views

Is there a “knot theory” for graphs?

I think knot theory has been studied for quite a while (like a century or so), so I'm just wondering whether there is a "knot theory" for graphs, i.e. the study of (topological properties of) ...
1
vote
2answers
338 views

Untangling a graph

Assume you have a 4-valent graph (i.e., a knot universe, i.e. a collection of self-intersecting curves). Your allowed moves are the equivalents of Reidemeister 1, 2, 3, just with 4-nodes instead of ...
0
votes
1answer
230 views

“Skein” equations sets that can reduce any graph

Consider for example the approach to the Kuperberg G2 or the Yamada polynomial. I don't know whether relations of graph (in contrast to knot) theory are also usually called "skein" but I simply carry ...
2
votes
2answers
997 views

How many lanes has a freeway? (Crossing free Kuperberg G2, that is.) EDITED

For referencing, I keep the original title and post and ask only about the simplest case (and forget the freeway with crossings for now). Consider a trivalent graph, e.g. the dodecahedron or cube ...
3
votes
0answers
286 views

Computing Quantum Dimensions

Hi, in "Jaeger’s Higman-Sims state model and the B2 spider" by Greg Kuperberg (arxiv:math9601221v1, 1996) there are some quantum dimensions listed in the "Discussion" part. Evidently quantum groups ...