Lie II theorem for Lie algebroids via higher groupoids
Differential Geometry
2010-05-21 v2 Category Theory
Abstract
Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie groups, Lie algebroids (integrable or not) one-to-one correspond to a sort of etale Lie 2-groupoids with 2-connected source fibres. Finally, we discuss how to lift Lie algebroid morphisms to Lie 2-groupoid morphisms (Lie II Theorem).
Cite
@article{arxiv.math/0701024,
title = {Lie II theorem for Lie algebroids via higher groupoids},
author = {Chenchang Zhu},
journal= {arXiv preprint arXiv:math/0701024},
year = {2010}
}
Comments
30 pages, 4 figures, many revisions