Introduction to Cartan Geometry - 2023

Le polycopié sera actualisé chaque semaine.

---

cours 10/01 : Introduction, Frobenius theorem, Differential ideals.

cours 13/01 : Differential ideals, the equivalence problem.

cours 17/01 : Pfaff problem, Darboux's theorem. Some global results: Godbillon-Vey invariant, Gray's rigidity theorem.

cours 20/01 : Lie groups and Lie algebras. The automorphism group of the Heisenberg group.

cours 24/01 : Maurer-Cartan forms. The adjoint representation.

cours 27/01 : Homogeneous spaces, principal bundles, frame and coframe bundles.

cours 03/02 : Tautological forms, Cartan connections.

cours 07/02 : Examples: Riemannian Geometry and Web geometry.

cours 10/02 : Example: Path structures.

cours 14/02 : Dynamics: Poincaré's recurrence theorem.

cours 17/02 : Uniformization of strict path structures with large automorphism group.

---

TD1

TD2

TD3

TD4

TD5