Classifying semi-free Hamiltonian S¹-manifolds

الأصل · EN

In this paper we describe a method to establish when a symplectic manifold M with semi-free Hamiltonian S¹-action is unique up to isomorphism (equivariant symplectomorphism). This will rely on a study of the symplectic topology of the reduced spaces. We prove that if the reduced spaces satisfy a rigidity condition, then the manifold M is uniquely determined by fixed point data. In particular we can prove that there is a unique family up to isomorphism of 6-dimensional symplectic manifolds with semi-free S¹-action and isolated fixed points.