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.
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