Induced differential characters on nonlinear Grassmannians

Journal article (2024)

Authors

T. Diez Analysis
B. Janssens Analysis
Karl-Hermann Neeb Friedrich-Alexander-Universität Erlangen-Nürnberg
Cornelia Vizman West University of Timisoara (UVT)
Research Group
Analysis
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Published Date

2024

Language

English

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Research Group

Analysis

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.

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