The strong simple connectedness of tame algebras with separating almost cyclic coherent Auslander-Reiten components (Q2118263)

It is a well-established fact that in the representation theory of algebras one can reduce, through covering methods, the study of the category of an algebra to the one which is simply connected. In this line, it is also useful to look at the so-called strongly simply connected algebras, that is, algebras such that all their convex subcategories are simply connected. On the other hand, the existence of special families of components in the Auslander-Reiten quiver of an algebra can give some important information on the whole category of modules. One of the most studied cases is the existence of a separating family. The author studies here the strong simple connectedness of tame algebras which admits a special kind of separating family consisting of almost cyclic coherent components. The introduction of the paper gives a very good review of the importance of all these notions.