We give a detailed proof of the well-known classical fact that every symplectic circle action on a compact manifold admits a circle-valued momentum map relative to some symplectic form. This momentum map is Morse-Bott-Novikov and each connected component of the fixed point set has even index. These proofs do not seem to have appeared elsewhere.
Cite this article
Alvaro Pelayo, Tudor S. Ratiu, Circle-valued momentum maps for symplectic periodic flows. Enseign. Math. 58 (2012), no. 1, pp. 205–219