nLab
proper Lie groupoid

Context

Lie theory

∞-Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Topology

Contents

Definition

A Lie groupoid (C 1tsC 0)(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 1C 0×C 0 (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.

Examples

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)