Ordered exchange graphs (Q2829361)

Exchange graphs codify the possible cluster mutations for a given cluster algebra of a quiver. In the framework of finite dimensional algebras or dg categories, many types of exchange graphs arise, according to the objects to be mutated. For example, the vertices could be tilting modules, torsion classes, \(t\)-structures, support \(\tau\)-tilting modules, or their prototype: clusters. The authors discuss, in handbook style, not less than twelve different types of exchange graphs, and give a careful explanation of the connections between them. The paper will give a quick orientation for those who want to get from one viewpoint to another in the cluster tilting zoo.NEWLINENEWLINEFor the entire collection see [Zbl 1279.00041].