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
- Outline
- Classical character varieties
- Definition
- Combinatorial description
- Topological description
- Classical skein categories and character stacks
- Poisson structure
- The Fock-Rosly construction
- The Goldman bracket
- Quantization
- Moduli algebras
- Skein quantization
- Categorified linear algebra
- Locally presentable categories
- Modules over monoidal categories
- Reconstruction theorems
- Quantum character varieties as a TFT
- Factorization homology (and skein categories)
- Main theorem for punctured surfaces
- Main theorem for closed surfaces
- Odds and ends
References
- [AB] M. Atiyah, R. Bott, The Yang-Mills Equations over Riemann Surfaces
- [AF] D. Ayala, J. Francis, Factorization homology of topological manifolds
- [AGS] A. Alekseev, H. Grosse, V. Schomerus, Combinatorial quantization of the Hamiltonian Chern-Simons theory I
- [AKS] A. Alekseev, Y. Kosmann-Schwarzbach, Manin pairs and moment maps
- [AMM] A. Alekseev, A. Malkin, E. Meinrenken, Lie Group Valued Moment Maps
- [Au] M. Audin, Lectures on gauge theory and integrable systems
- [BBJ1] D. Ben-Zvi, A. Brochier, D. Jordan, Integrating quantum groups over surfaces
- [BBJ2] D. Ben-Zvi, A. Brochier, D. Jordan, Quantum character varieties and braided module categories
- |BCJ] M. Brandenburg, A. Chirvasitu, T. Johnson-Freyd, Reflexivity and dualizability in categorified linear algebra
- [BJS] A. Brochier, D. Jordan, N. Snyder On dualizability of braided tensor categories
- [Co] J. Cooke, Excision of Skein Categories and Factorisation Homology
- [CP] V. Chari, A. Presley, A guide to quantum groups
- [DKM] J. Donin, P. Kulish, A. Mudrov, On universal solution to reflection equation
- [FR] V. Fock, A. Rosly, Poisson structure on moduli of flat connections on Riemann surfaces and r-matrix
- [Fra] I. L. Franco, Tensor products of finitely cocomplete and abelian categories
- [Go] W. Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations
- [LBS] D. Li-Bland, P. Severa, Symplectic and Poisson geometry of the moduli spaces of flat connections over quilted surfaces
- [LM] A. Lubotzky, A. Magid, Varieties of Representations of Finitely Generated Groups
- [Lu] J. Lurie, On the Classification of Topological Field Theories
- [Sa] P. Safronov, Quasi-Hamiltonian reduction via classical Chern-Simons theory
- [Si] A. Sikora, Sl_n-character varieties as spaces of graphs
- [STS] M. Semenov-Tian-Shansky, Poisson-Lie groups. the quantum duality principle and the twisted quantum double
- [Ti] P. Tingley, A minus sign that used to annoy me but now I know why it is there
- [Wa] K. Walker, Notes on TQFTs