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 $\phi$.