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Rigidity of Hamiltonian Actions

Published online by Cambridge University Press:  20 November 2018

Frédéric Rochon
Frédéric Rochon*
Affiliation:
Département de mathématiques, Université du Québec à Montréal, Québec, Canada
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Abstract

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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.

Keywords

53D0537J25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 2 , 01 June 2003 , pp. 277 - 290
Copyright
Copyright © Canadian Mathematical Society 2003

References

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