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$π_1$ of Hamiltonian $S^1$ manifolds

Hui Li
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Abstract

Let $(M, ω)$ be a connected, compact symplectic manifold equipped with a Hamiltonian $S^1$ action. We prove that, as fundamental groups of topological spaces, $π_1(M)=π_1(\hbox{minimum})=π_1(\hbox{maximum})=π_1(M_{red})$, where $M_{red}$ is the symplectic quotient at any value in the image of the moment map $ϕ$.

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Hui Li. 2002-10-28. $π_1$ of Hamiltonian $S^1$ manifolds. https://arxiv.org/abs/math/0203075

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