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arXiv:1012.4103 [math.DG]AbstractReferencesReviewsResources

From double Lie groupoids to local Lie 2-groupoids

Rajan Amit Mehta, Xiang Tang

Published 2010-12-18, updated 2015-02-18Version 2

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.

Comments: 23 pages, a few minor changes, including a correction to Lemma 6.6
Journal: Bulletin of the Brazilian Mathematical Society 42 (2011), no. 4, 651-681
Categories: math.DG, math.SG
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