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Rigidity of Hamiltonian Actions

Open Access article
 Printed: Jun 2003
  • Frédéric Rochon
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This paper studies the following question: Given an $\omega'$-symplectic action of a Lie group on a manifold $M$ which coincides, as a smooth action, with a Hamiltonian $\omega$-action, when is this action a Hamiltonian $\omega'$-action? Using a result of Morse-Bott theory presented in Section~2, we show in Section~3 of this paper that such an action is in fact a Hamiltonian $\omega'$-action, provided that $M$ is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In this paper, we prove it using classical methods only.
MSC Classifications: 53D05, 37J25 show english descriptions Symplectic manifolds, general
Stability problems
53D05 - Symplectic manifolds, general
37J25 - Stability problems

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