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From momentum maps and dual pairs to symplectic and Poisson groupoids

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The Breadth of Symplectic and Poisson Geometry

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

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Abstract

In this survey, we will try to indicate some important ideas, due in large part to Alan Weinstein, which led from the study of momentum maps and dual pairs to the current interest in symplectic and Poisson groupoids. We hope that it will be useful for readers new to the subject; therefore, we begin by recalling the definitions and properties which will be used in what follows. More details can be found in [4], [26], [47].

It is a great pleasure to submit a contribution for this volume in honour of Alan Weinstein. He is one of the four or five persons whose works have had the greatest influence on my own scientific interests, and I am glad to have this opportunity to express to him my admiration and my thanks.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Charles-Michel Marle

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  1. Charles-Michel Marle
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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

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Marle, CM. (2005). From momentum maps and dual pairs to symplectic and Poisson groupoids. 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_17

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