Lie groups of Poisson diffeomorphisms
Symplectic Geometry
2022-12-09 v2 Differential Geometry
Abstract
By considering suitable Poisson groupoids, we develop an approach to obtain Lie group structures on (subgroups of) the Poisson diffeomorphism groups of various classes of Poisson manifolds. As applications, we show that the Poisson diffeomorphism groups of (normal-crossing) log-symplectic, elliptic symplectic, scattering-symplectic and cosymplectic manifolds are regular infinite-dimensional Lie groups.
Cite
@article{arxiv.2108.11490,
title = {Lie groups of Poisson diffeomorphisms},
author = {Wilmer Smilde},
journal= {arXiv preprint arXiv:2108.11490},
year = {2022}
}
Comments
35 pages. Accepted for publication in Journal of Symplectic Geometry