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| Berzürcheley Symplectic Geometry Seminar
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| 939 Evans |
02:10 PM - 04:10 PM
03/17/2006 |
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Marco Zambon, Universität Zürich
Prequantization and reduction of groupoids by S1
Exactly as a prequantization circle bundle of a symplectic manifold is a manifold with a contact 1-form, a circle bundle Q prequantizing a Poisson manifolds P is a Jacobi manifold. We view this as a way to associate to a Poisson manifold another geometric object in a non-trivial fashion. In this talk we look at the Lie algebroids that encode the Poisson and Jacobi structures of P and Q, and we notice that they are related in an interesting way: not by a morphism, but by reduction by the group S1. We will also explain what this implies for the corresponding Lie groupoids.
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