From double Lie groupoids to local Lie 2-groupoids
Differential Geometry
2015-02-19 v2 Symplectic Geometry
Abstract
We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.
Keywords
Cite
@article{arxiv.1012.4103,
title = {From double Lie groupoids to local Lie 2-groupoids},
author = {Rajan Amit Mehta and Xiang Tang},
journal= {arXiv preprint arXiv:1012.4103},
year = {2015}
}
Comments
23 pages, a few minor changes, including a correction to Lemma 6.6