2011-09-09

Non-Hamiltonian symplectic circle actions

Susan Tolman, University of Illinois at Urbana-Champaign

Let a circle act symplectically on a compact symplectic manifold. If the action is Hamiltonian, then we can reduce the number of degrees of freedom by considering the symplectic quotient. Moreover, the moment map is a Morse-Bott function whose critical set is the fixed set, and so the fixed set determines a great deal of information about the manifold. For this reason, it is interesting to ask the following question: What conditions guarentee that a symplectic action to be Hamiltonian? In this talk, I will discuss recent research that showing that cetain symplectic actions with "few" fixed points must be Hamiltonian.