2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63520Let $(M, ω)$ 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 $ϕ$.4 pagesSymplectic GeometryAlgebraic Topology58xxxtext