Normal Forms and Lie Groupoid Theory

TL;DR

This paper explores the Linearization Theorem for Lie groupoids, connecting it to classical linearization theorems for submersions, foliations, and group actions, with a focus on the recent metric approach.

Contribution

It provides a detailed discussion of the Linearization Theorem for Lie groupoids and its relation to classical theorems, highlighting the metric approach.

Findings

Clarifies the relation between Lie groupoid linearization and classical theorems

Details the recent metric approach to linearization

Provides insights into the structure of Lie groupoids

Abstract

In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the recent metric approach to this problem.