Frankel’s theorem in the symplectic category
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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.References
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Additional Information
- Min Kyu Kim
- Affiliation: Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1, Kusong-Dong, Yusong-Gu, Taejon, 305-701, Korea
- Address at time of publication: School of Math, Korea Institute for Advanced Study, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, Republic of Korea
- Email: minkyu@kaist.ac.kr, mkkim@kias.re.kr
- Received by editor(s): April 6, 2004
- Received by editor(s) in revised form: August 11, 2004
- Published electronically: January 24, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 4367-4377
- MSC (2000): Primary 53D05, 53D20; Secondary 55Q05, 57R19
- DOI: https://doi.org/10.1090/S0002-9947-06-03844-X
- MathSciNet review: 2231381