Foliated groupoids and their infinitesimal data
Abstract
In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicative foliation in terms of its core and sides together with a partial connection satisfying special properties, giving rise to the concept of IM-foliation on a Lie algebroid. The main result of this paper shows that if is a source simply connected Lie groupoid with Lie algebroid , then there exists a one-to-one correspondence between multiplicative foliations on and IM-foliations on the Lie algebroid .
Cite
@article{arxiv.1109.4515,
title = {Foliated groupoids and their infinitesimal data},
author = {Madeleine Jotz and Cristian Ortiz},
journal= {arXiv preprint arXiv:1109.4515},
year = {2012}
}
Comments
We have found out that one of the main results can already be found in the paper "A groupoid approach to quantization" by Eli Hawkins, Journal of symplectic geometry (2008). We were not aware of this paper while working on this problem. An adapted version of our paper will be uploaded here later