Cluster categories, m-cluster categories and diagonals in polygons

TL;DR

This paper explains how to construct m-cluster categories from polygon triangulations and m+2-angulations, and how to use translation quivers and diagonals to directly obtain these categories.

Contribution

It provides a detailed exposition on constructing m-cluster categories from polygon dissections and introduces a method using translation quivers to derive categories from diagonals.

Findings

Construction methods for m-cluster categories from polygon dissections

Use of translation quivers to obtain categories from diagonals

Connection between polygon combinatorics and cluster categories

Abstract

The goals of this expository article are on one hand to describe how to construct ($m$-) cluster categories from triangulations (resp. from $m+2$-angulations) of polygons. On the other hand, we explain how to use translation quivers and their powers to obtain the $m$-cluster categories directly from the diagonals of a polygon.