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The Orbit Bundle Picture of Cotangent Bundle Reduction

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. http://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
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.
Record Number:CaltechAUTHORS:20100907-082631805
Persistent URL:http://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:26 Dec 2012 12:23

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