Compact generation for Lie groupoids

TL;DR

This paper generalizes Haefliger's concept of compact generation from pseudogroups to Lie groupoids, providing a Morita-invariant framework that advances understanding of holonomy in foliations on compact manifolds.

Contribution

It introduces a Morita-invariant generalization of compact generation from pseudogroups to object-separated Lie groupoids, expanding the theoretical framework.

Findings

Generalization of compact generation to Lie groupoids

Morita invariance established for the new property

Enhanced understanding of holonomy in foliations

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.