Induced differential characters on nonlinear Grassmannians
Tobias Diez (TU Delft - Analysis)
Bas Janssens (TU Delft - Analysis)
Karl Hermann Neeb (Friedrich-Alexander-Universität Erlangen-Nürnberg)
Cornelia Vizman (West University of Timisoara (UVT))
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Abstract
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.