INDUCED DIFFERENTIAL CHARACTERS ON NONLINEAR GRASSMANNIANS - Diez, Tobias; Janssens, Bas; Neeb, Karl Hermann; Vizman, Cornelia (Annales de l'Institut Fourier, 2024)
Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from M to the nonlinear Graßmannian GrS(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.
CRIS-Team Scopus Importer:2025-04-01
Keywords: Differential character; Nonlinear Graßmannian; Tautological bundle; Volume-preserving diffeomorphism