From double Lie groupoids to local Lie 2-groupoids

Details From double Lie groupoids to local Lie 2-groupoids From double Lie groupoids to local Lie 2-groupoids

2010-12-18

arxiv.org/abs/1012.4103v1

Bulletin of the Brazilian Mathematical Society 42 (2011), no. 4, 651-681

Mathematics

Differential Geometry

23 pages

Scientific paper

10.1007/s00574-011-0033-4

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.

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