We shall recall the definition of graph of groups and we shall survey some results of Bass-Serre theory. Then we shall give the definition of acylindrical splitting of a finitely generated group and we shall present some basic examples of groups which possess acylindrical splittings. Next we shall briefly summarise some basic facts of 3-dimensional topology and we shall give a sketch of the proof of the fact that the fundamental groups of non-geometric 3-manifolds possess acylindrical splittings.
This seminar is aimed at students (PhD as well as Master students).
