# Hamiltonian S^1 Actions with Isolated Fixed Points on 6-Dimensional Symplectic Manifolds

# Hamiltonian S^1 Actions with Isolated Fixed Points on 6-Dimensional Symplectic Manifolds

The question of what conditions guarantee that a symplectic circle action is Hamiltonian has been studied for many years. In 1998, Sue Tolman and Jonathon Weitsman proved that if the action is semifree and has a non-empty set of isolated fixed points then the action is Hamiltonian. In 2010, Cho, Hwang, and Suh proved in the 6-dimensional case that if we have b_2^+=1 at a reduced space at a regular level \lambda of the circle valued moment map, then the action is Hamiltonian. In this talk, we will discuss using their result to prove that certain 6-dimensional symplectic actions which are not semifree and have a non-empty set of isolated fixed points are Hamiltonian. In this case, the reduced spaces are 4-dimensional symplectic orbifolds, and we will discuss resolving the orbifold singularities and using J-holomorphic curve techniques on the resolutions.