The course will introduce the idea of Topological Quantum Field Theory in an axiomatic way. It will proceed by discussing commutative Frobenius algebras. The main result will be to show that two dimensional TQFT's are equivalent with commutative Frobenius algebras. Frobenius's original example of a Frobenius algebra, the center of the group algebra of a finite group will be discussed in detail.
• Lecture: Tuesday/Thursday, 1:30-2:45pm
• Recitation: Thursday, 4:50-5:40 pm
Mondi 2 (except May 18, when Recitation will be in Meeting room 1st floor / Lab Bldg West)
The course will build on basic notions of differentiable manifolds, such as atlases, smooth mappings and orientation. Otherwise we will strive to be self-contained as much as possible.
We will more or less follow: Joachim Kock: Frobenius Algebras and 2D topological Quantum Field Theories, short version + the library has three copies, one for reference two to check-out
We may use parts of: Dan Freed: Bordism: Old and New
For finite groups: Jean-Pierre Serre: Linear Representations of Finite Groups
For differential topology: Hirsch: Differential topology
The final grade will be decided on the combination of work on the exercises in the regular example sheets and a presentation of a talk related to the ideas in the course, whose subject could be chosen with the help of the lecturer or TA. There will be no exam.