Contact Topology VIGRE Group

Gordana Matic

I will again be running a VIGRE group on contact topology/geometry this semester. Last semester we had a VIGRE group on the same topic, where we worked out an algorithm to find all contact structures - plane fields satisfying a certain everywhere twisting property - on a handlebody of genus 2 (for those who do not know, a handlebody is something like a pretzel, and a genus two handlebody is like a donut with two holes). A computer program was produced that will now take in data describing the contact structure on the boundary and give you the number of contact structures (as well as a description of each one).

We will start by explaining the geometry that goes into the problem. To really understand this one might need to eventually take a course in contact geometry, but with an imperfect understanding you can still work on the project and make a major contribution. We will then give the combinatorial description of the project and present the algorithm developed so far (accessible to smart undergraduates). The goal is to generalize the algorithm to higher genus (more holes in the donut) and to improve its speed and interface. We would like to add graphic presentation and possibly a way to graphically input data. We would like in the end be able to put it on the web as a tool for contact geometers everywhere.

I will give an introductory talk in the topology seminar on Monday, Aug 25 at 2.30.