Induced differential characters on nonlinear Graßmannians
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866912060975087616 |
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| author | Diez, Tobias Janssens, Bas Neeb, Karl-Hermann Vizman, Cornelia |
| author_facet | Diez, Tobias Janssens, Bas Neeb, Karl-Hermann Vizman, Cornelia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_02556 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Induced differential characters on nonlinear Graßmannians Diez, Tobias Janssens, Bas Neeb, Karl-Hermann Vizman, Cornelia Differential Geometry Mathematical Physics Symplectic Geometry 53D50, 53D20, 58D10, 58D05 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. |
| title | Induced differential characters on nonlinear Graßmannians |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry 53D50, 53D20, 58D10, 58D05 |
| url | https://arxiv.org/abs/2009.02556 |