Symplectic manifolds with semi-free Hamiltonian \(S^ 1\)-action (Q1210366)

Following the previous research [the author, Circle actions on symplectic manifolds, Lect. Notes Math. 1375, 89-97 (1985; Zbl 0674.57033)], the author proves that if \(M\) is a connected closed symplectic \(S^ 1\)- manifold such that the \(S^ 1\)-action admits a momentum map, the fixed points are isolated and the action is semifree, then \(M\) has the same cohomology ring and the same Chern classes as \(S^ 2\times\dots\times S^ 2\). The relations among the momentum map, \(C^*\)-orbits and and complex line bundles are discussed and the Chern classes of \(M\) are identified.