Hamiltonian Circle Actions with Isolated Fixed Points on 6-Dimensional Symplectic Manifolds

Geometry Topology Seminar
Monday, February 17, 2014 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Morehouse College
The question of what conditions guarantee that a symplectic$S^1$ action is Hamiltonian has been studied for many years.  Sue Tolmanand Jonathon Weitsman proved that if the action is semifree and has anon-empty set of isolated fixed points then the action is Hamiltonian.Furthermore, Cho, Hwang, and Suh proved in the 6-dimensional case that ifwe have $b_2^+=1$ at a reduced space at a regular level $\lambda$ of thecircle valued moment map, then the action is Hamiltonian. In this paper, wewill use this to prove that certain 6-dimensional symplectic actions whichare not semifree and have a non-empty set of isolated fixed points areHamiltonian. In this case, the reduced spaces are 4-dimensional symplecticorbifolds, and we will resolve the orbifold singularities and useJ-holomorphic curve techniques on the resolutions.