JournalslemVol. 58, No. 1/2pp. 205–219

Circle-valued momentum maps for symplectic periodic flows

  • Alvaro Pelayo

    Institute for Advanced Study, Princeton, USA
  • Tudor S. Ratiu

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
Circle-valued momentum maps for symplectic periodic flows cover
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Abstract

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

DOI 10.4171/LEM/58-1-10