Jds. Jones et Jh. Rawnsley, HAMILTONIAN CIRCLE-ACTIONS ON SYMPLECTIC-MANIFOLDS AND THE SIGNATURE, Journal of geometry and physics, 23(3-4), 1997, pp. 301-307
Let M be a symplectic manifold with a Hamiltonian circle action with i
solated fixed points. We prove that sigma (M) = b(0) (M) - b(2) (M) b(4) (M) - b(6) (M) + ... where sigma (M) is the signature of M and bi
(M) is the ith Betti number of M.