We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.
@article{urn:eudml:doc:41909,
title = {Singular Poisson reduction of cotangent bundles.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {431-466},
zbl = {1116.53056},
mrnumber = {MR2241438},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41909}
}
Hochgerner, Simon; Rainer, Armin. Singular Poisson reduction of cotangent bundles.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 431-466. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41909/