Marsden, Jerrold E. and Perlmutter, Matthew (2000) The Orbit Bundle Picture of Cotangent Bundle Reduction. Comptes Rendus Mathématiques de l'Académie des Sciences. La Société Royale du Canada, 22 (1). pp. 33-54. ISSN 0706-1994. https://resolver.caltech.edu/CaltechAUTHORS:20100907-082631805
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Abstract
Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on a configuration manifold Q, considers its natural cotangent lift to T*Q and then one seeks realizations of the corresponding symplectic or Poisson reduced space. We further develop this theory by explicitly identifying the symplectic leaves of the Poisson manifold T^*Q/G, decomposed as a Whitney sum bundle, T^*⊕(Q/G)g^* over Q/G. The splitting arises naturally from a choice of connection on the G-principal bundle Q → Q/G. The symplectic leaves are computed and a formula for the reduced symplectic form is found.
Item Type: | Article |
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Additional Information: | © 2000. Royal Society of Canada. December, 1998; this version: March 18, 2000. We thank Anthony Bloam, Hernan Cendra, Sameer Jalnapurkar, Gerard Misio lek and Tudor Ratiu for helpful comments and inspiration. |
Issue or Number: | 1 |
Record Number: | CaltechAUTHORS:20100907-082631805 |
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100907-082631805 |
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 19791 |
Collection: | CaltechAUTHORS |
Deposited By: | Ruth Sustaita |
Deposited On: | 15 Sep 2010 20:59 |
Last Modified: | 03 Oct 2019 02:01 |
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