Groupo\"ides de Lie et Feuilletages

TL;DR

This survey explores the deep connections between Lie groupoids and singular foliations, emphasizing their algebraic and geometric structures, with historical context and examples.

Contribution

It provides a comprehensive overview of the relationship between Lie groupoids and singular foliations, highlighting algebraic and geometric interactions.

Findings

Clarifies the link between Lie groupoids and singular foliations.

Examines the algebraic and differentiable structures of Lie groupoids.

Includes historical context and illustrative examples.

Abstract

This is a survey concerning the relationship between Lie Groupoids (and their morphisms) and singular foliations in the sense of Sussmann-Stefan (considered from a purely geometrical point of view). We focus on the interaction between the algebraic and differentiable structures underlying Lie groupoids, and between groups and graphs of equivalence relations, regarded as two basic degeneracies for groupoids. Historical remarks, motivations and examples are developed in five appendices.