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$\pi_1$ of Hamiltonian $S^1$ manifolds

Author: Hui Li
Journal: Proc. Amer. Math. Soc. 131 (2003), 3579-3582
MSC (2000): Primary 53D05, 53D20; Secondary 55Q05, 57R19
Published electronically: February 14, 2003
MathSciNet review: 1991771
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Abstract: Let $(M, \omega)$ be a connected, compact symplectic manifold equipped with a Hamiltonian $S^1$ action. We prove that, as fundamental groups of topological spaces, $\pi_1(M)=\pi_1(\hbox{minimum})=\pi_1(\hbox{maximum})=\pi_1(M_{red})$, where $M_{red}$ is the symplectic quotient at any value in the image of the moment map $\phi$.

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Additional Information

Hui Li
Affiliation: Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois 61801

Keywords: Circle action, symplectic manifold, symplectic quotient, Morse theory
Received by editor(s): January 10, 2002
Received by editor(s) in revised form: May 23, 2002
Published electronically: February 14, 2003
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2003 American Mathematical Society