scholarly journals Fredholm theory and transversality for the parametrized and for the S1-invariant symplectic action

2010 ◽  
pp. 1181-1229 ◽  
Author(s):  
Frédéric Bourgeois ◽  
Alexandru Oancea
Keyword(s):  
Fredholm Theory ◽  
Symplectic Action

Rigidity of Hamiltonian Actions

2003 ◽  
Vol 46 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Frédéric Rochon
Keyword(s):  
General Theory ◽  
Lie Group ◽  
Geometric Analysis ◽  
Smooth Action ◽  
Symplectic Action ◽  
Hamiltonian Actions

AbstractThis paper studies the following question: Given an ω′-symplectic action of a Lie group on a manifoldMwhich coincides, as a smooth action, with a Hamiltonian ω-action, when is this action a Hamiltonian ω′-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 ω′-action, provided thatM 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.

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