# nLab proper Lie groupoid

∞-Lie theory

## Examples

### $\infty$-Lie algebras

#### Topology

topology

algebraic topology

# Contents

## Definition

A Lie groupoid $(C_1 \stackrel{\overset{s}{\to}}{\underset{t}{\to}} C_0)$ is proper if its underlying topological groupoid is a proper topological groupoid, hence if

$(s,t) : C_1 \to C_0 \times C_0$

is a proper map.

So in particular the automorphism group of any object in a proper Lie groupoid is a compact Lie group. In this sense proper Lie groupoids generalize compact Lie groups.

## References

• M.J. Pflaum, H. Posthuma, X. Tang, Geometry of orbit spaces of proper Lie groupoids (arXiv:1101.0180)

Revised on February 2, 2012 11:42:51 by Urs Schreiber (82.169.65.155)