Induced differential characters on nonlinear Graßmannians

Abstract

Using a nonlinear version of the tautological bundle over Graßmannians, we construct a transgression map for differential characters from $M$ to the nonlinear Graßmannians ${\mathrm{Gr}}^S(M)$ 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.