Asian Journal of Mathematics

Volume 9 (2005)

Number 2

Tangential deformations on fibred Poisson manifolds

Pages: 213 – 226

DOI: http://dx.doi.org/10.4310/AJM.2005.v9.n2.a6

Authors

D. Arnal

N. Dahmene

A. Gammella

M. Masmoudi

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 (to the fibers) star products.

2010 Mathematics Subject Classification

Primary 53D15. Secondary 53D17.

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