Quantum Gravity Seminar - Spring 2002

John Baez

This is the continuation of my lectures on categorified gauge theory, which I began in Winter 2002. This quarter's lectures explain the classification of bundles using Cech cohomology in a way that is easy to generalize to "2-bundles". These are a "categorified" version of bundles in which the fiber is not a set but a category, transition functions are replaced by transition functors, and the usual equation satisifed by the transition functions now holds only up to a specified natural isomorphism, which satisfies an equation of of its own.

If you're the sort of mathematician who is fond of "stacks", you'll be pleased to know that just as an ordinary bundle has a sheaf of sections, a 2-bundle has a stack of sections.

If you're more interested in physics, you should think of 2-bundles as permitting a generalization of gauge theory that describes not the parallel transport of point particles but of 1-dimensional extended objects - open strings, or spin network edges. The most familiar example is 2-form electromagnetism, which I explained in detail in the Winter 2002 notes.

To get a general overview of these ideas, you should start by peeking at the slides of this talk:

There are also a lot of links to papers here.

The course notes below were taken by Alissa Crans, who has kindly scanned them in and made PDF files out of them:

Eventually I will try to give descriptive titles for the notes from each class, but right now I only have them listed by date.


© 2002 John Baez and Alissa Crans