# Ribbon graphs and the fundamental group of surfaces

## TL;DR

This paper provides a formal exposition of ribbon graphs, a combinatorial tool used to study surfaces, based on Labourie's notes, filling a gap in the literature.

## Contribution

It offers a detailed, formal presentation of ribbon graphs and their relation to the fundamental group of surfaces, which was previously not well documented.

## Key findings

- Clarifies the structure of ribbon graphs
- Connects ribbon graphs to surface fundamental groups
- Provides a comprehensive exposition based on Labourie's notes

## Abstract

In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie \cite{Lab}, since is difficult to find as such in the literature.