Caseiro, Raquel; Fernandes, Rui Loja
The modular class of a Poisson map  [ La classe modulaire d’une application de Poisson ]
Annales de l'institut Fourier, Tome 63 (2013) no. 4 , p. 1285-1329
MR 3137356 | Zbl 06359590
doi : 10.5802/aif.2804
URL stable : http://www.numdam.org/item?id=AIF_2013__63_4_1285_0

Classification:  53D17,  58H05,  22A22
Mots clés: Variété de Poisson, application de Poisson, classe modulaire
Nous introduisons la classe modulaire d’une application de Poisson. Nous regardons quelques exemples et nous utilisons les classes modulaires des applications de Poisson pour étudier le comportement de la classe modulaire d’une variété de Poisson sous différents types de réduction. Nous discutons également leur version pour les groupoïdes symplectiques, qui prend ses valeurs dans la cohomologie du groupoïde.
We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology.

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