From double Lie groupoids to local Lie 2-groupoids

By R. Mehta, Xiang Tang. 2010

52 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b844c9bb3c5a740df64f8accb49ff190a3bd09d

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In Algebra and Number Theory

1. Markus J. Pflaum
2. X. Tang
3. H. Posthuma
4. L. Ambrozio

In Geometry and Topology

1. Markus J. Pflaum
2. X. Tang
3. H. Posthuma

In Mathematical Physics

1. Markus J. Pflaum
2. X. Tang
3. H. Posthuma

Citations in the corpus

• The transverse index theorem for proper cocompact actions of Lie groupoids (2013, background): “that this metric is invariant. 1.2. The van Est morphism. The action of G on Z gives a natural example of a double groupoid, which is essentially a groupoid in the category of groupoids, c.f. [BrMa], [MeTa]. More concretely, we have a square of groupoids (4) Gt×µZ oo Gt×µ(Zµ×µZ) oo Z Zoo µ×µZ oo .”