The fundamental group of symplectic manifolds with Hamiltonian SU(2) or SO(3) actions

Abstract

Let $(M,\omega )$ be a connected compact symplectic manifold equipped with a Hamiltonian SU(2) or SO(3) action. We prove that, as fundamental group of topological spaces, ${\pi }_1(M)={\pi }_1(M_{red})$, where $M_{red}$ is the symplectic quotient at any value of the moment map $\varphi$.

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