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Zbl 0948.53045
Alekseev, Anton; Malkin, Anton; Meinrenken, Eckhard
Lie group valued moment maps. (English)
[J] J. Differ. Geom. 48, No.3, 445-495 (1998). ISSN 0022-040X

Authors' abstract: ``We develop a theory of ``quasi''-Hamiltonian $G$-spaces for which the moment map takes values in the group $G$ itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg symplectic cross-section theorem and of convexity properties of the moment map. As an application, we obtain moduli spaces of flat connections on an oriented compact 2-manifold with boundary as quasi-Hamiltonian quotients of the space $G^2\times\cdots\times G^2$''.

MSC 2000:: *53D20 Momentum maps; symplectic reduction
58D27 Moduli problems for diff.geometric structures on spaces of mappings

Keywords: quasi-Hamiltonian $G$-space; Hamiltonian reduction; Guillemin-Sternberg symplectic cross-section theorem; convexity; moment map

Cited in: Zbl 1236.58019 Zbl 1157.53050 Zbl 1167.53070 Zbl 1151.53359 Zbl 1126.53055 Zbl 1123.53042 Zbl 1109.53077 Zbl 1156.53319 Zbl 1106.53057 Zbl 1076.53109 Zbl 1035.53114

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