The Fundamental Group of Symplectic Manifolds with Hamiltonian Lie Group Actions

Content Provider	Semantic Scholar
Copyright Year	2006
Abstract	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.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/math/0605133v1.pdf
Alternate Webpage(s)	http://arxiv.org/pdf/math/0605133v2.pdf
Alternate Webpage(s)	http://arxiv.org/pdf/math/0605133v3.pdf
Language	English
Access Restriction	Open
Subject Keyword	Generalization (Psychology) Hamiltonian (quantum mechanics) Map Symplectic integrator manifold
Content Type	Text
Resource Type	Article