Singular Reduction of Poisson Manifolds |
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| Authors: | Ortega Juan-Pablo Ratiu Tudor S. |
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| Affiliation: | (1) Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland;(2) Department of Mathematics, University of California, Santa Cruz, Santa Cruz, CA 95064, USA;(3) Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland. e-mail |
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| Abstract: | The conditions under which it is possible to reduce a Poisson manifold via a regular foliation have been completely characterized by Marsden and Ratiu. In this Letter we show that this characterization can be generalized in a natural way to the singular case and, as a corollary, we obtain that when the singular distribution is given by the tangent spaces to the orbits created by a Hamiltonian Lie group action, one reproduces the Universal Reduction Procedure of Arms, Cushman, and Gotay. |
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| Keywords: | Poisson manifold reduction symmetry singularity stratification |
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