English

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.

Keywords

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

R2 v1 2026-06-22T18:44:18.140Z