Orbifolds as Groupoids: an Introduction

TL;DR

This survey introduces the use of groupoids and their classifying spaces as a foundational framework for understanding orbifolds, connecting geometric and algebraic perspectives.

Contribution

It provides an accessible introduction to the role of groupoids in orbifold theory, emphasizing their importance as a unifying foundation.

Findings

Groupoids serve as a natural language for orbifold structures

Classifying spaces of groupoids underpin orbifold theory

The approach bridges geometric intuition and algebraic formalism

Abstract

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.