# nLab Haefliger groupoid

category theory

## Applications

#### Topology

topology

algebraic topology

# Contemts

## Definition

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

## 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

Revised on March 15, 2013 15:58:10 by Tim Porter (95.147.236.94)