Group generators and relations, and making balls of triangles

• Richard Parker
• Monday 02 February 2009, 16:00-17:00
• MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.

Generators and relations for a group can always be put into the form where all relations are of length three. Any word that is the identity in the group must then be the boundary of a region filled in with triangles. It is therefore critical to understand what a region can look like that has a lot of triangles and a short boundary. Of course in that case the remainder of the sphere can be filled in with a few more triangles, so the real question is to understand something about balls made of triangles.

For example, one can define the curvature of a vertex to be 6 – <number of triangles meeting at that vertex>. Can one then make the ball one vertex at a time, remaining connected and having positive total curvature?

I feel there is a whole new subject here!

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.