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Group generators and relations, and making balls of triangles

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If you have a question about this talk, please contact Anton Evseev.

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 and Number Theory seminar series.

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