# Symplectic Geometry 1

## WS2016/17

### General Information

The Lectures will take place Tuesday and Thursday 12-14 in A27. The Exercise Classes take place Wednesday 12-14 in B132.

### Outline

This course is intended as an introduction to symplectic geometry. After covering the basic material and constructions there will be a discussion of further topics which may inlcude: Hamiltonian group actions, symplectic quotients, toric manifolds, symplectic dynamics, Gompf's Theorem on realising groups as fundamental groups of symplectic manifolds, generating functions and applications.

Some knowledge of differentiable manifolds, vector bundles and differential forms will be assumed, as covered for example in the Bachelor or Master course Differential Geometry.

### References

- A. Cannas da Silva, Lectures on symplectic geometry, Lecture Notes in Mathematics, 1764, Springer-Verlag, Berlin, 2001 and 2008.

- Kai Cieliebak`s Lecture Notes (.ps format).
- D. McDuff, D. Salamon: Introduction to symplectic topology (Oxford Math. Monographs)

- M. Audin: The topology of torus actions on symplectic manifolds (Birkhäuser)

- J. Moser, E. Zehnder: Notes on dynamical systems (Courant Lect. Notes in Math.)

### Exercise sheets

Sheet 1 Solution to Problem 3

Sheet 2

Sheet 3

Sheet 4

Sheet 5

Sheet 6

Sheet 7

Sheet 8 (Corrected Version)

Sheet 9

Sheet 10

Sheet 11

Sheet 12