Symplectic Circle Actions

Friday, 14 April 2017 - 3:00pm
Dr. Susan Tolman, Univ. of Illinois - Urbana
LD 229

   Let the circle act on a closed manifold M, preserving a symplectic form ω. We say that the action is Hamiltonian if there exists a moment map, that is, a map Ψ: M ® R such that ιc ω = -dΨ, where c is the vector field that generates the action.  In this case, a great deal of information about the manifold is determined by the fixed set.  Therefore, it is very important to determine when symplectic actions are Hamiltonian.

  There has been a great deal of research on this question, but it left the  following question, usually called the “McDuff conjecture”: Does there exists a non-Hamiltonian symplectic circle action with isolated fixed points on a closed, connected symplectic manifold?  I will answer this question by constructing such an example