Journal of Lie Theory

no. 2
Convexity of Hamiltonian Manifolds
Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 571-582
We study point set topological properties of the moment map. In particular, we introduce the notion of a convex Hamiltonian manifold. This notion combines convexity of the momentum image and connectedness of moment map fibers with a certain openness requirement for the moment map. We show that convexity rules out many pathologies for moment maps. Then we show that the most important classes of Hamiltonian manifolds (e.g., unitary vector spaces, compact manifolds, or cotangent bundles) are in fact convex. Moreover, we prove that every Hamiltonian manifold is locally convex.
DOI: 10.5802/jolt.283
Classification: 53D20
Keywords: Hamiltonian manifold, moment map, convexity 
@article{JOLT_2002_12_2_a17,
     author = {F. Knop},
     title = {Convexity of {Hamiltonian} {Manifolds}},
     journal = {Journal of Lie Theory},
     pages = {571--582},
     year = {2002},
     volume = {12},
     number = {2},
     doi = {10.5802/jolt.283},
     zbl = {1038.53080},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.283/}
}
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F. Knop. Convexity of Hamiltonian Manifolds. Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 571-582. doi: 10.5802/jolt.283

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