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The Breadth of Symplectic and Poisson Geometry pp 571–581Cite as

The universal covering and covered spaces of a symplectic Lie algebra action

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Part of the book series: Progress in Mathematics ((PM,volume 232))

Abstract

We show that the category of Hamiltonian covering spaces of a given connected and paracompact symplectic manifold (M, ω) acted canonically upon by a Lie algebra admits a universal covering and covered space.

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References

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Author information

Authors and Affiliations

  1. Centre National de la Recherche Scientifique Département de Mathématiques de Besançon, Université de Franche-Comté UFR des Sciences et Techniques, 16, route de Gray, F-25030, Besançon Cedex, France

    Juan-Pablo Ortega

  2. Centre Bernoulli, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Tudor S. Ratiu

Authors
  1. Juan-Pablo Ortega
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  2. Tudor S. Ratiu
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Editor information

Editors and Affiliations

  1. Department of Engineering and Applied Science Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, 91125, USA

    Jerrold E. Marsden

  2. Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Tudor S. Ratiu

Additional information

Dedicated to Alan Weinstein on the occasion of his 60th birthday.

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© 2005 Birkhäuser Boston

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Ortega, JP., Ratiu, T.S. (2005). The universal covering and covered spaces of a symplectic Lie algebra action. In: Marsden, J.E., Ratiu, T.S. (eds) The Breadth of Symplectic and Poisson Geometry. Progress in Mathematics, vol 232. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4419-9_19

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