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The approach reveals smooth structures in nonlinear grassmannians, highlighting their role in coadjoint orbits.
Decorated and augmented nonlinear Grassmannians can be used to parametrize coadjoint orbits of classical diffeomorphism groups. We provide a general framework for decoration and augmentation functors that facilitates the construction of a smooth structure on decorated or augmented nonlinear Grassmannians. This permits to equip the corresponding coadjoint orbits with the structure of a smooth symplectic Frechet manifold. The coadjoint orbits obtained in this way are not new. Here, we provide a uniform description of their smooth structures.
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Haller et al. (2025) studied this question.
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