Compact generation for Lie groupoids

Abstract

Thirty years after the birth of foliations in the 1950's, Andr\'e Haefliger has introduced a special property satisfied by holonomy pseudogroups of foliations on compact manifolds, called compact generation. Up to now, this is the only general property known about holonomy on compact manifolds. In this article, we give a Morita-invariant generalization of Haefliger's compact generation, from pseudogroups to object-separated Lie groupoids.