Comptes Rendus
no. 1
Differential Geometry
The isotropy lattice of a lifted action

Presented by: Étienne Ghys

Miguel Rodríguez-Olmos1
1 Section de Mathématiques, EPFL-Lausanne, CH-1015 Lausanne, Switzerland
Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 41-46.

We obtain a characterization of the isotropy lattice for the lifted action of a Lie group G on TM and T∗M based only on the knowledge of G and its action on M. Some applications to symplectic geometry are also shown.

Nous obtenons une caractérisation du réseau d'isotropie de l'action induite d'un groupe de Lie G sur TM et T∗M basée uniquement sur la connaissance de G et de son action sur M. Quelques applications en géométrie symplectique sont également donées.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.05.012

Miguel Rodríguez-Olmos 1

1 Section de Mathématiques, EPFL-Lausanne, CH-1015 Lausanne, Switzerland 
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Miguel Rodríguez-Olmos. The isotropy lattice of a lifted action. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 41-46. doi : 10.1016/j.crma.2006.05.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.05.012/

[1] J.J. Duistermaat; J.A.C. Kolk Lie Groups, Universitext, Springer-Verlag, 2000

[2] J.E. Marsden Lectures on Mechanics, London Math. Soc. Lecture Note Ser., vol. 174, Cambridge University Press, 1992

[3] J.-P. Ortega; T.S. Ratiu Momentum Maps and Hamiltonian Reduction, Progress in Mathematics, vol. 222, Birkhäuser-Verlag, 2004

[4] R.S. Palais On the existence of slices for non-compact Lie group, Ann. of Math., Volume 73 (1961), pp. 265-323

[5] R. Sjamaar; E. Lerman Stratified symplectic spaces and reduction, Ann. of Math., Volume 134 (1991), pp. 375-422

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