Quantum Gravity Seminar - Winter 2005

Gauge Theory and Topology

John Baez and Derek Wise

In the 2004-2005 academic year, our seminar is about gauge theory and topology. In the Fall we showed how to construct 2d topological quantum field theories (or TQFTs) from semisimple algebras. In the Winter, we categorified all this and saw how to construct 3d TQFTs from "semisimple 2-algebras". The fun part was seeing how categorification - the process of replacing equations by isomorphisms - naturally boosts the dimension by one! Then we turned to examples: the "Dijkgraaf-Witten models", which are gauge theories with finite gauge group. We discussed how these models could be "twisted", and used this as an excuse to learn about the cohomology of groups.

A bunch of this material will eventually be incorporated in this paper:

You may already enjoy looking at the draft version. You may also want to review some definitions leading up to the concept of "topological quantum field theory":

As usual, Derek Wise is writing notes for the seminar:

To dig deeper, try the Spring notes.

To learn more about the Dijkgraaf-Witten models, try their original paper, especially starting on page 42:

If you discover any errors in the course notes please email me, and we'll try to correct them. We'll keep a list of errors that haven't been fixed yet.

You can also download the LaTeX, encapsulated PostScript and xfig files if for some bizarre reason you want them. However, I reserve all rights to this work.

© 2005 John Baez and Derek Wise