Implementation for representation of 2-knots

[Calvin Godfrey]

First of all, I apologize if this isn't the right place to ask this. I spent ages looking for links on the sage website, and this seemed like the most relevant.

I spent this summer doing an undergraduate research project on 2-knots, based primarily off of the work from https://arxiv.org/abs/1507.08370. In particular, we have a way to represent 2-knots as a triplet of braid words, and we're able to calculate the Alexander Invariant (an ideal over the ring of Laurent polynomials) for an arbitrary 2-knot with this representation.

Would this be something worth fleshing out to add to sage? I looked through the developer's guide, and it looked like there were a lot of steps to do everything properly. I just want to make sure this would be fruitful work before I get started downloading and compiling from source.

If not the full implementation, there are some smaller parts that I think could be useful to have in sage. In particular, an alternative closure of a braid on 2n strands. Instead of joining the top and bottom of each strand, we join together the top and bottom of adjacent strands, like in this crudely made diagram.

I would appreciate any feedback!

[John H Palmieri]

I think that more math of almost any sort would be great to add to Sage. Improving the knot and link capabilities would be great!

  John