# nLab Haefliger groupoid

category theory

## Applications

#### Topology

topology

algebraic topology

# Contents

## Definition

For $n \in \mathbb{N}$, the Haefliger groupoid $\Gamma^n$ is the groupoid whose set of objects is the Cartesian space $\mathbb{R}^n$ and for which a morphism $x \to y$ is a germ of a diffeomorphism $(\mathbb{R}^n ,x) \to (\mathbb{R}^n ,y)$.

## Properties

### Geometric structure

The Haefliger groupoid is naturally a topological groupoid. As such it is an étale groupoid.

### Classification of foliations

The Haefliger groupoid classifies foliations. See at Haefliger theorem.

## References

Original articles include

• André Haefliger, Groupoïdes d’holonomie et espaces classiants , Astérisque 116 (1984), 70-97

• Raoul Bott, Lectures on characteristic classes and foliations , Springer LNM 279, 1-94

A textbook account is in

See also

Discussion of jet-restrictions of the Haefliger groupoid is in

• Arne Lorenz, Jet Groupoids, Natural Bundles and the Vessiot Equivalence Method, Thesis (pdf)

Revised on January 31, 2014 12:24:51 by Anonymous Coward (130.126.255.231)