Lie Groups

LIE GROUPS
Vector fields, flow
Distributions, Involutive Distributions, Frobenius Theorem
Lie Groups examples
Covering of Lie groups and their fundamental Groups
Lie algebras
Invariant fields
Lie groups Theorems, correspondences between Algebras and Lie Groups
Adjoint representations, exponential maps
Classification of abelian Lie Groups.

LIE GROUPS ACTIONS
Actions, proper actions, Actions of compact Lie Groups
Haar Measure, unimodular groups
The Slice Theorem
Classifications of orbits types, coadjoint action,
Symplectic manifolds, Hamiltonian actions, moment map.
Delzant conjecture. Toric manifolds.


· Azioni di gruppi compatti. Gruppi unimodulari. Esistenza di Misure di Haar;
· Il teorema della Slice e idee della dimostrazione;
· Classificazione delle orbite;
· Variet`a simplettiche, richiami su fibrati principali e fibrati associati;
· Azioni Hamiltoniane, mappa momento;
· Riduzioni simplettiche, Teorema di Marsden-Weintein;
· Variet`a Simplettiche Toriche, Teorema di Delzant.