𝜋₁ of Hamiltonian 𝑆¹ manifolds

Li, Hui

doi:10.1090/S0002-9939-03-06881-3

$\pi _1$ of Hamiltonian $S^1$ manifolds
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Proc. Amer. Math. Soc. 131 (2003), 3579-3582 Request permission

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, $\pi _1(M)=\pi _1(\mathrm {minimum})=\pi _1(\mathrm {maximum})=\pi _1(M_{red})$, where $M_{red}$ is the symplectic quotient at any value in the image of the moment map $\phi$.

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