A geometric construction of $m$-cluster categories
We show that the $m$-cluster category of type $A_{n-1}$ is equivalent to a
certain geometrically-defined category of diagonals of a regular $nm+2$-gon.
This generalises a result of Caldero, Chapoton and Schiffler for $m=1$.
The approach uses the theory of translation quivers and their corresponding
mesh categories. We also introduce the notion of the $m$th power of a
translation quiver and show how it can be used to realise the
$m$-cluster category in terms of the cluster category.
pdf-file