Hamiltonian circle actions on symplectic manifolds and the signature

Abstract

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ ( M) = b 0( M) − b 2( M) + b 4( M) − b 6( M) + … where σ ( M) is the signature of M and b i ( M) is the ith Betti number of M.