no. 4
The modular class of a Poisson map
[La classe modulaire d’une application de Poisson]
Caseiro, Raquel1 ; Fernandes, Rui Loja2
1 Universidade de Coimbra CMUC, Department of Mathematics 3001-454 Coimbra, (Portugal)
2 University of Illinois at Urbana-Champaign Department of Mathematics 1409 W. Green Street Urbana, IL 61801 (USA)
Annales de l'Institut Fourier, Tome 63 (2013) no. 4, pp. 1285-1329.

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.

DOI : 10.5802/aif.2804
Classification : 53D17, 58H05, 22A22
Keywords: Poisson manifold, Poisson map, modular class
Mot clés : Variété de Poisson, application de Poisson, classe modulaire
Caseiro, Raquel 1 ; Fernandes, Rui Loja 2

1 Universidade de Coimbra CMUC, Department of Mathematics 3001-454 Coimbra, (Portugal)
2 University of Illinois at Urbana-Champaign Department of Mathematics 1409 W. Green Street Urbana, IL 61801 (USA) 
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Caseiro, Raquel; Fernandes, Rui Loja. The modular class of a Poisson map. Annales de l'Institut Fourier, Tome 63 (2013) no. 4, pp. 1285-1329. doi : 10.5802/aif.2804. http://www.numdam.org/articles/10.5802/aif.2804/

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