Group actions on Manifolds

Fall 2005, Courant Institute

Lecturer: Liat Kessler

Lecture notes

Lecture 1, September 12 2005.: Lie group. Group action. Orbits and stabilizers. Lia algebra. Exponential map.
Lecture 2, September 19.: Symplectic vector space. Symplectic manifold. The Darboux theorem.
Lecture 3, September 26.: The G-invariant Darboux-Weinstein theorem. Hamiltonian torus actions.
Student talk: Hamiltonian group actions, by Sara Grundel.
Student talk: Morse theory, by Al Momin.
Lecture 4, November 14.: The local convexity theorem. A component of a moment map is Morse-bott.
Lecture 5, November 21.: The set of points with stabilizer group H and its image under a moment map.
The full statement of Theorem 32.3
Lecture 6.: The convexity theorem. Delzant's theorem.
Student talk: The slice theorem, by Yakov Kerzhner.
Student talk: The convexity theorem, by Maria Calle.
Student talk: Algebraic Varieties, by Pedro Antonio Santro Salomao.
Guided Exercise: Linear action of a torus.