Poisson geometry around Poisson submanifolds
Symplectic Geometry
2023-07-18 v2 Differential Geometry
Abstract
We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases all the known linearization theorems for fixed points and symplectic leaves. The symplectic groupoid version of these results gives a solution to the groupoid coisotropic embedding problem.
Cite
@article{arxiv.2205.11457,
title = {Poisson geometry around Poisson submanifolds},
author = {Rui Loja Fernandes and Ioan Marcut},
journal= {arXiv preprint arXiv:2205.11457},
year = {2023}
}
Comments
75 pages; several improvements in the exposition, with two sections moved to appendices; conventions for algebroids/groupoids were changed. Final version accepted for publication in JEMS