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Published online: 2012-06-30
Circle-valued momentum maps for symplectic periodic flowsAlvaro Pelayo and Tudor S. Ratiu (1) Institute for Advanced Study, Princeton, USA
(2) Ecole Polytechnique Fédérale de Lausanne, Switzerland
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.
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Pelayo Alvaro, Ratiu Tudor: Circle-valued momentum maps for symplectic periodic flows. Enseign. Math. 58 (2012), 205-219. doi: 10.4171/LEM/58-1-10