Singular Poisson reduction of cotangent bundles

Details Singular Poisson reduction of cotangent bundles Singular Poisson reduction of cotangent bundles

2005-08-24

arxiv.org/abs/math/0508455v1

Rev. Mat. Complut. 19 (2006), No. 2, 431--466.

Mathematics

Symplectic Geometry

28 pages

Scientific paper

We consider the Poisson reduced space $(T^*Q)/K$ with respect to a cotangent lifted action. It is assumed that $K$ is a compact Lie group which acts by isometries on the Riemannian manifold $Q$ and that the action on $Q$ is of single isotropy type. 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 $Q\to Q/K$.

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