This is a page for the course on TFTs and character varieties. For now just a temptative plan and a list of references that I will be relying on during the lectures. This page will be updated regularly during the week.

Plan

  1. Outline
  2. Classical character varieties
    1. Definition
    2. Combinatorial description
    3. Topological description
    4. Classical skein categories and character stacks
  3. Poisson structure
    1. The Fock-Rosly construction
    2. The Goldman bracket
  4. Quantization
    1. Moduli algebras
    2. Skein quantization
  5. Categorified linear algebra
    1. Locally presentable categories
    2. Modules over monoidal categories
    3. Reconstruction theorems
  6. Quantum character varieties as a TFT
    1. Factorization homology (and skein categories)
    2. Main theorem for punctured surfaces
    3. Main theorem for closed surfaces
    4. Odds and ends

References