Classifying semi-free Hamiltonian $S^1$-manifolds

Abstract

In this paper we describe a method to establish when a symplectic manifold $M$ with semi-free Hamiltonian $S^1$-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 $S^1$-action and isolated fixed points.

Many errors corrected. To appear in IMRN.

References in corpus (2)

• The topology of the space of symplectic balls in rational 4-manifolds
• Semifree circle actions, Bott towers, and quasitoric manifolds

Cited by in corpus (1)

• Semifree Hamiltonian circle actions on 6-dimensional symplectic manifolds with non-isolated fixed point set