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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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.
|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.|
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|Deposited By:||Ruth Sustaita|
|Deposited On:||15 Sep 2010 20:59|
|Last Modified:||26 Dec 2012 12:23|
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