Sorry for the somewhat qualitative question but what are the essential prerequisites for someone wanting to learn topological field theory from say the more physical side of things? The math side also sounds interesting but it may be a bit heavy going for my current background. I know quantum mechanics, some algebraic topology and some basic manifold theory. Here is the impression of what I have so far:
- Path integral formulation of QFT
- Differential Geometry including differential forms, bundles, cohomology theory etc
- Yang-Mills/Chern-Simons gauge theories
- Knot Theory and the Jones Polynomial
And for a more mathematical view:
- Category Theory.
Baez's book "Gauge Fields, Knots and Gravity" seems to cover a good amount of these topics.
Am I on the right track or should I add/remove any topics from these? Thanks.