nLab
Haefliger groupoid

Contents

Definition

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