INDUCED DIFFERENTIAL CHARACTERS ON NONLINEAR GRASSMANNIANS

Diez T, Janssens B, Neeb KH, Vizman C (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Annales de l'Institut Fourier Association des Annales de l'Institute Fourier; 1999

Book Volume: 74

Pages Range: 2483-2503

Journal Issue: 6

DOI: 10.5802/aif.3661

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.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Delft University of Technology (TU Delft) NL Netherlands (NL) West University Timisoara (WUT) RO Romania (RO)

How to cite

APA:

Diez, T., Janssens, B., Neeb, K.H., & Vizman, C. (2024). INDUCED DIFFERENTIAL CHARACTERS ON NONLINEAR GRASSMANNIANS. Annales de l'Institut Fourier, 74(6), 2483-2503. https://doi.org/10.5802/aif.3661

MLA:

Diez, Tobias, et al. "INDUCED DIFFERENTIAL CHARACTERS ON NONLINEAR GRASSMANNIANS." Annales de l'Institut Fourier 74.6 (2024): 2483-2503.

BibTeX: Download