TANGENTIAL DEFORMATIONS ON FIBRED POISSON MANIFOLDS

Abstract : In a recent article, Cattaneo, Felder and Tomassini explained how the notion of formality can be used to construct flat Fedosov connections on formal vector bundles on a Poisson manifold M and thus a star product on M through the original Fedosov method for symplectic manifolds. In this paper, we suppose that M is a fibre bundle manifold equipped with a Poisson tensor tangential to the fibers. We show that in this case the construction of Cattaneo-Felder-Tomassini gives tangential star products.
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Submitted on : Tuesday, September 12, 2006 - 12:51:46 PM
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  • HAL Id : hal-00092824, version 1

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Didier Arnal, Najla Dahmene, Angela Gammella, Mohsen Masmoudi. TANGENTIAL DEFORMATIONS ON FIBRED POISSON MANIFOLDS. Asian Journal of Mathematics, International Press, 2005, 9, pp.213-226. ⟨hal-00092824⟩

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