6533b85dfe1ef96bd12bdebd
RESEARCH PRODUCT
TANGENTIAL DEFORMATIONS ON FIBRED POISSON MANIFOLDS
Najla DahmeneDidier ArnalMohsen MasmoudiAngela Gammellasubject
Applied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysis[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Vector bundle01 natural sciences53D15Volume formPoisson bracket53D17[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Mathematics::Quantum Algebra0103 physical sciencesHermitian manifold010307 mathematical physics[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]0101 mathematicsMathematics::Symplectic GeometryFirst class constraintMathematicsSymplectic manifoldSymplectic geometryPoisson algebradescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-06-01 |