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of Hamiltonian manifolds
Authors:Hui Li
Institution:Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois 61801
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 $\phi$.

Keywords:Circle action  symplectic manifold  symplectic quotient  Morse theory
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