Symplectic 4-manifolds with fixed point free circle actions

Abstract

We show that recent results of Friedl-Vidussi and Chen imply that a symplectic 4-manifold admits a fixed point free circle action if and only if it admits a symplectic structure that is invariant under the action and we give a complete description of the symplectic cone in this case. This then completes the topological characterisation of symplectic 4-manifolds that admit non-trivial circle actions.