Symplectic forms invariant under free circle actions on 4--manifolds

الأصل · EN

Let M⁴ be a smooth compact manifold with a free circle action generated by a vector field X. Then for any invariant symplectic form ω on M the contracted form ιₓ ω is nondegenerate. Using the map ω--> ιₓ ω and the related map to H¹(M / S¹, R) we study the topology of the space Sinv of invariant symplectic forms. In particular we give a description of π₀ Sinv(M⁴) in terms of the unit Thurston ball.