On local integration of Lie brackets
Differential Geometry
2020-11-05 v2 Symplectic Geometry
Abstract
We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field lifting the underlying anchor map. This construction leads to a complete account of local Lie theory and, in particular, to a finite-dimensional proof of the fact that the category of germs of local Lie groupoids is equivalent to that of Lie algebroids.
Cite
@article{arxiv.1703.04411,
title = {On local integration of Lie brackets},
author = {Alejandro Cabrera and Ioan Marcut and Maria Amelia Salazar},
journal= {arXiv preprint arXiv:1703.04411},
year = {2020}
}
Comments
26 pages; the previous version (v1) was split into two papers, this is the first one and the second one will appear separatedly