2016/05/31 by Henrique Bursztyn, Hudson Lima, Eckhard Meinrenken · 1 citation
Mathematics · #math.DG #math.SG
published as J. Reine Angew. Math. 754 (2019), 281--312 · 30 pages. Minor correction in sec. 4.4 (v.2). Small changes, final version to appear in J. Reine Angew. Math. (v.3)
arxiv created 2017/02/03 · arxiv updated 2020/01/29
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.