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research article
On Singular Poisson Sternberg Spaces
Perlmutter, M.
•
Rodriguez-Olmos, M.
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.
Type
research article
Web of Science ID
WOS:000265791200002
Authors
Perlmutter, M.
•
Rodriguez-Olmos, M.
Publication date
2009
Published in
Volume
7
Start page
15
End page
49
Subjects
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 30, 2010
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