The Fundamental Group of Symplectic Manifolds with Hamiltonian Lie Group Actions
نویسنده
چکیده
Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian G action, where G is a connected compact Lie group. Let φ be the moment map. In [12], we proved the following result for G = S action: as fundamental groups of topological spaces, π1(M) = π1(Mred), where Mred is the symplectic quotient at any value of the moment map φ, and = denotes “isomorphic to”. In this paper, we generalize this result to other connected compact Lie group G actions. We also prove that the above fundamental group is isomorphic to that of M/G. We briefly discuss the generalization of the first part of the results to non-compact manifolds with proper moment maps.
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