From Double Lie Groupoids to Local Lie 2-Groupoids

Authors

Rajan Amit Mehta, Pennsylvania State UniversityFollow
Xiang Tang, Washington University in St. Louis

Document Type

Article

Publication Date

12-1-2011

Publication Title

Bulletin of the Brazilian Mathematical Society

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

bar construction, bisimplicial manifold, symplectic groupoid, double groupoid, Lie 2-groupoid

Volume

42

Issue

4

First Page

651

Last Page

681

DOI

10.1007/s00574-011-0033-4

ISSN

16787544

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Mehta, Rajan Amit and Tang, Xiang, "From Double Lie Groupoids to Local Lie 2-Groupoids" (2011). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/91