From double Lie groupoids to local Lie 2-groupoids

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.

23 pages, a few minor changes, including a correction to Lemma 6.6

References in corpus (2)

• Integration of Exact Courant Algebroids
• Tag Clusters as Information Retrieval Interfaces

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