Corpus ID: 221517076

# Induced differential characters on nonlinear Graßmannians

@article{Diez2020InducedDC,
title={Induced differential characters on nonlinear Gra{\ss}mannians},
author={Tobias Diez and Bas Janssens and Karl-Hermann Neeb and Cornelia Vizman},
journal={arXiv: Differential Geometry},
year={2020}
}
Using a nonlinear version of the tautological bundle over Grasmannians, we construct a transgression map for differential characters from $M$ to the nonlinear Grasmannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed type $S$. In particular, we obtain prequantum circle bundles of the nonlinear Grasmannian endowed with the Marsden-Weinstein symplectic form. The associated Kostant-Souriau prequantum extension yields central Lie group extensions of a group of volume-preserving… Expand
2 Citations
Nonlinear flag manifolds as coadjoint orbits
• Mathematics, Medicine
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A class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplectic submanifolds, i.e., symplectic nonlinear flags, are described. Expand
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• 2019
In this paper, we describe the coadjoint orbits of the group of volume preserving diffeomorphisms associated to the motion of codimension one singular membranes in ideal fluids, i.e. filaments in 2D,Expand

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