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June 2009 On singular Poisson Sternberg spaces
M. Perlmutter, M. Rodriguez-Olmos
J. Symplectic Geom. 7(2): 15-49 (June 2009).

Abstract

We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced spaces are stratified topological fiber bundles over the cotangent bundle of the orbit space. We also obtain a Poisson stratification of the Sternberg space. To construct the singular Poisson Sternberg space we develop an appropriate theory of singular connections for proper group actions on a single orbit type manifold including a theory of holonomy extending the usual Ambrose– Singer theorem for principal bundles.

Citation

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M. Perlmutter. M. Rodriguez-Olmos. "On singular Poisson Sternberg spaces." J. Symplectic Geom. 7 (2) 15 - 49, June 2009.

Information

Published: June 2009
First available in Project Euclid: 17 April 2009

zbMATH: 1169.53063
MathSciNet: MR2496413

Rights: Copyright © 2009 International Press of Boston

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Vol.7 • No. 2 • June 2009
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