The Fundamental Group of G-manifolds
نویسنده
چکیده
Let M be a connected smooth G-manifold, where G is a connected compact Lie group. In this paper, we first study the relation between π1 (M) and π1 (M/G). Then we particularly focus on the case when M is a connected Hamiltonian G-manifold with an equivariant moment map φ. In [13], for compact M , we proved that π1 (M) = π1 (M/G) = π1 (Ma) for all a ∈ image(φ), where Ma is the symplectic quotient at a. We generalize and extend these results to Hamiltonian G-manifolds with proper moment maps. Our main results are Proposition 1, Theorems 2 and 3.
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تاریخ انتشار 2009