Geodesic
Convexity of Hamiltonian Manifolds
Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 571-582

Voir la notice de l'article provenant de la source Heldermann Verlag

Zbl   arXiv   EuDML

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.
Classification : 53D20
Mots-clés : Hamiltonian manifold, moment map, convexity 
F. Knop. Convexity of Hamiltonian Manifolds. Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 571-582. http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a17/
@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},
     zbl = {1038.53080},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a17/}
}
TY  - JOUR
AU  - F. Knop
TI  - Convexity of Hamiltonian Manifolds
JO  - Journal of Lie Theory
PY  - 2002
SP  - 571
EP  - 582
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a17/
ID  - JOLT_2002_12_2_a17
ER  - 
%0 Journal Article
%A F. Knop
%T Convexity of Hamiltonian Manifolds
%J Journal of Lie Theory
%D 2002
%P 571-582
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a17/
%F JOLT_2002_12_2_a17