Asian Journal of Mathematics

Tangential deformations on fibred Poisson manifolds

D. Arnal, N. Dahmene, A. Gammella, and M. Masmoudi

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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 (to the fibers) star products.

Article information

Asian J. Math., Volume 9, Number 2 (2005), 213-226.

First available in Project Euclid: 3 April 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D15: Almost contact and almost symplectic manifolds
Secondary: 53D17: Poisson manifolds; Poisson groupoids and algebroids


Arnal, D.; Dahmene, N.; Gammella, A.; Masmoudi, M. Tangential deformations on fibred Poisson manifolds. Asian J. Math. 9 (2005), no. 2, 213--226.

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