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arXiv · 2009.02556

Induced differential characters on nonlinear Graßmannians

Tobias Diez·Bas Janssens·Karl-Hermann Neeb·Cornelia Vizman
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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 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.

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Tobias Diez, Bas Janssens, Karl-Hermann Neeb, Cornelia Vizman. 2021-12-10. Induced differential characters on nonlinear Graßmannians. https://doi.org/10.5802/aif.3661

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