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L’Enseignement Mathématique

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Volume 58, Issue 1/2, 2012, pp. 205–219
DOI: 10.4171/LEM/58-1-10

Published online: 2012-06-30

Circle-valued momentum maps for symplectic periodic flows

Alvaro Pelayo[1] and Tudor S. Ratiu[2]

(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