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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Frankel's theorem in the symplectic category


Author: Min Kyu Kim
Journal: Trans. Amer. Math. Soc. 358 (2006), 4367-4377
MSC (2000): Primary 53D05, 53D20; Secondary 55Q05, 57R19
Published electronically: January 24, 2006
MathSciNet review: 2231381
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03844-X
PII: S 0002-9947(06)03844-X
Keywords: Symplectic geometry, symplectic action, Hamiltonian action
Received by editor(s): April 6, 2004
Received by editor(s) in revised form: August 11, 2004
Published electronically: January 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.