Journal of Symplectic Geometry

On singular Poisson Sternberg spaces

M. Perlmutter and M. Rodriguez-Olmos

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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.

Article information

Source
J. Symplectic Geom., Volume 7, Number 2 (2009), 15-49.

Dates
First available in Project Euclid: 17 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1239974379

Mathematical Reviews number (MathSciNet)
MR2496413

Zentralblatt MATH identifier
1169.53063

Citation

Perlmutter, M.; Rodriguez-Olmos, M. On singular Poisson Sternberg spaces. J. Symplectic Geom. 7 (2009), no. 2, 15--49. https://projecteuclid.org/euclid.jsg/1239974379


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