Symplectic reduction

Steven Sivek.

Suppose we have a circle acting nontrivially on a symplectic manifold M. No matter how nice the action is, the quotient M/S^1 can’t possibly still have a symplectic structure because its dimension is odd. We will discuss how symplectic reduction gives us a way to make sense of quotients of symplectic manifolds, by using nice (Hamiltonian) group actions on symplectic manifolds to produce natural symplectic structures on lower-dimensional manifolds.

There are some notes from previous years.