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
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References

SHOWING 1-10 OF 28 REFERENCES
Nonlinear flag manifolds as coadjoint orbits
TLDR
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
Representations of the Virasoro algebra by the orbit method
A geometric background is given for representation with a highest weight of the Virasoro algebra. The representation space consists of holomorphic sections of an analytic line bundle over theExpand
Lichnerowicz cocycles and central Lie group extensions
We present a geometric construction of central extensions of covering groups of the group of volume preserving diffeomorphisms, integrating central extensions of the Lie algebra of divergence freeExpand
Induced differential forms on manifolds of functions
Differential forms on the Fr\'echet manifold F(S,M) of smooth functions on a compact k-dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hatExpand
Extensions centrales d'algèbres et de groupes de lie de dimension infinie, algèbre de virasoro et généralisations
Abstract This article surveys problems related to central extensions of Lie algebra of vector fields, both from the pure algebraic point of view (cohomological computations) and from the point ofExpand
Loop groups
In these notes, we introduce matrix Lie groups G and their Lie algebras Lie(G), and we exhibit the (continuous) loop group LG as a smooth Banach Lie group. Prerequisites are basic calculus and pointExpand
Towards a Lie theory of locally convex groups
Abstract.In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras,Expand
Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids
This paper is a study of incompressible fluids, especially their Clebsch variables and vortices, using symplectic geometry and the Lie-Poisson structure on the dual of a Lie algebra. Following ideasExpand
Central Extensions of Lie Groups Preserving a Differential Form
Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega$, and let $G$ be a Fr\'echet-Lie group acting on $(M,\omega)$. As a generalization of the Kostant-Souriau extension for symplecticExpand
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