π₁ of Hamiltonian S¹ manifolds

2002/03/08 by Hui Li, Li, Hui
Mathematics · #58xxx #Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AT #math.SG #msc:58xxx

paper · pdf · doi:10.48550/arxiv.math/0203075

4 pages

arxiv created 2002/10/28 · arxiv updated 2009/11/30

Abstract

Let (M, ω) be a connected, compact symplectic manifold equipped with a Hamiltonian S¹ action. We prove that, as fundamental groups of topological spaces, π₁(M)=π₁(\hboxminimum)=π₁(\hboxmaximum)=π₁(M_red), where M_red is the symplectic quotient at any value in the image of the moment map ϕ.

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