English

Poisson manifolds and their associated stacks

Symplectic Geometry 2018-04-04 v2 Differential Geometry

Abstract

We associate to any integrable Poisson manifold a stack, i.e. a category fibered in groupoids over a site. The site in question has objects Dirac manifolds and morphisms pairs consisting of a smooth map and a closed 2-form. We show that two Poisson manifolds are symplectically Morita equivalent if and only if their associated stacks are isomorphic.

Keywords

Cite

@article{arxiv.1703.03542,
  title  = {Poisson manifolds and their associated stacks},
  author = {Joel Villatoro},
  journal= {arXiv preprint arXiv:1703.03542},
  year   = {2018}
}

Comments

Made several improvements to the exposition and fixed typos

R2 v1 2026-06-22T18:41:56.102Z