We show that the cluster complex of an arbitrary hereditary artin algebra has the structure of an abstract simplicial polytope. In particular, the cluster-tilting objects form one equivalence class under mutation.
The cluster complex for cluster Poisson varieties and representations of acyclic quivers
Linear independence of cluster monomials for skew-symmetric cluster algebras
A geometric realization of the $m$-cluster category of type $\tilde{A}$
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