Splitting theorems for Poisson and related structures
Differential Geometry
2020-01-29 v3 Symplectic Geometry
Abstract
According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results are known e.g. for Lie algebroids, Dirac structures and generalized complex structures. In this paper, we develop a novel approach towards these results that leads to various generalizations, including their equivariant versions as well as their formulations in new contexts.
Cite
@article{arxiv.1605.05386,
title = {Splitting theorems for Poisson and related structures},
author = {Henrique Bursztyn and Hudson Lima and Eckhard Meinrenken},
journal= {arXiv preprint arXiv:1605.05386},
year = {2020}
}
Comments
30 pages. Minor correction in sec. 4.4 (v.2). Small changes, final version to appear in J. Reine Angew. Math. (v.3)