Induced differential characters on nonlinear Graßmannians
[Caractères induits sur les grassmanniennes non-linéaires]
Diez, Tobias1 ; Janssens, Bas1 ; Neeb, Karl-Hermann2 ; Vizman, Cornelia3
1 Institute of Applied Mathematics, Delft University of Technology, 2628 XE Delft, The Netherlands
2 Department of Mathematics, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
3 Department of Mathematics, West University of Timişoara. RO–300223 Timişoara. Romania
Annales de l'Institut Fourier, Online first, 21 p.

En utilisant une version non-linéaire du fibré tautologique sur les Graßmanniennes, nous construisons une application de transgression pour les caractères différentiels de M à la Graßmannienne non-linéaire Gr S (M) des sous-variétés de M d’un type fixé S. En particulier, nous obtenons des fibrés en cercles préquantiques au dessus de la Graßmannienne non-linéaire doté de la forme symplectique de Marsden–Weinstein. L’extension préquantique de Kostant–Souriau associée donne des extensions centrales de groupes de Lie d’un groupe de difféomorphismes préservant le volume et intégrant les cocycles de Lichnerowicz.

Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from M to the nonlinear Graßmannian Gr S (M) of submanifolds of M of a fixed type S. In particular, we obtain prequantum circle bundles of the nonlinear Graßmannian endowed with the Marsden–Weinstein symplectic form. The associated Kostant–Souriau prequantum extension yields central Lie group extensions of a group of volume-preserving diffeomorphisms integrating Lichnerowicz cocycles.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3661
Classification : 58D05, 58D10, 53D50, 53C08, 37K65
Keywords: Volume-preserving diffeomorphism, Nonlinear Graßmannian, Tautological bundle, Differential character
Mot clés : Difféomorphisme préservant le volume, Grassmannienne non-linéaire, Fibré tautologique, Caractère différentiel
Diez, Tobias 1 ; Janssens, Bas 1 ; Neeb, Karl-Hermann 2 ; Vizman, Cornelia 3

1 Institute of Applied Mathematics, Delft University of Technology, 2628 XE Delft, The Netherlands
2 Department of Mathematics, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
3 Department of Mathematics, West University of Timişoara. RO–300223 Timişoara. Romania 
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Diez, Tobias; Janssens, Bas; Neeb, Karl-Hermann; Vizman, Cornelia. Induced differential characters on nonlinear Graßmannians. Annales de l'Institut Fourier, Online first, 21 p.

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