Frankel’s theorem in the symplectic category

Kim, Min

doi:10.1090/S0002-9947-06-03844-X

Frankel’s theorem in the symplectic category
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by Min Kyu Kim PDF

Trans. Amer. Math. Soc. 358 (2006), 4367-4377 Request permission

Abstract:

We prove that if an $(n-1)$-dimensional torus acts symplectically on a $2n$-dimensional symplectic manifold, then the action has a fixed point if and only if the action is Hamiltonian. One may regard it as a symplectic version of Frankel’s theorem which says that a Kähler circle action has a fixed point if and only if it is Hamiltonian. The case of $n=2$ is the well-known theorem by McDuff.

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