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Frankel's theorem in the symplectic category

Min Kyu Kim
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Abstract

We prove that if an (n-1)-dimensional torus acts symplectically on a 2n-dimensional 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 theorem. The case of n=2 is the well known theorem of McDuff. From the well known example of McDuff (a six dimensional symplectic non-Hamiltonian circle action with fixed tori) and its products with copies of a two dimensional sphere with the usual rotation, the condition on the dimension of the acting torus is optimal to obtain the result.

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Min Kyu Kim. 2004-09-06. Frankel's theorem in the symplectic category. https://arxiv.org/abs/math/0204016

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