Obstruction to circle group actions preserving symplectic structure (Q1190709)

Let \(M\) be a closed symplectic manifold. The main result of this paper is, that if the second homotopy group of \(M\) is zero, then every symplectic circle action on \(M\) has no fixed points; and if, moreover, every abelian subgroup of the fundamental group of \(M\) is cyclic, then there are no symplectic circle actions on \(M\).