Special topics in geometry: Group actions on manifolds

Special topics in Geometry: Group actions on Manifolds

Fall 2005, Courant Institute

Announcement: December 13 special class will be held at WWH 613, 15:00--19:00 (notice the change in starting time)

Meetings: Mondays 9:30--11:20 WWH 813

Credit: Seminar representations

Required background: Fundamental Concepts in Topology and Differential Geometry.

Text: Symplectic techniques in physics, V. Guillemin & S. Sternberg, Cambridge University Press, 1984

Recommended texts:

Lectures on Symplectic Geometry, A. C. da Silva, Lecture Notes in Mathematics, Springer-Verlag, 2001
Torus actions on symplectic manifolds, M. Audin, Birkhauser, 2004
Introduction to Symplectic Topology, D. McDuff and D. Salamon, Oxford University Press, 1998
Morse Theory, J. W. Milnor, Princeton University Press, 1963

We will define group actions on manifolds, and discuss the basic concepts and examples. We will then restrict our attention to group actions on symplectic manifolds (a short introduction to symplectic manifolds will be given). We will define and study Hamiltonian torus actions, and prove the convexity theorem; for the proof we will learn some Morse Theory. We will also discuss Delzant's classification.

Special topics in Geometry: Group actions on Manifolds

Lecture notes