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Singular Poisson reduction of cotangent bundles

Simon Hochgerner·Armin Rainer
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Abstract

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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Simon Hochgerner, Armin Rainer. 2005-08-24. Singular Poisson reduction of cotangent bundles. https://arxiv.org/abs/math/0508455

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