R. Weidemann: Acylindrical accessibility

Abstract: We review various situations in which the complexity of a splitting of a group can be bounded. These so-called accessibility results include Grushko's theorem and the Dunwoody accessibility theorem that implies that any finitely presented group can be written as the fundamental group of a finite graph of 1-ended groups with finite edge groups.
We will then study Sela's acylindrical accessibility and a proof thereof in more detail. Acylindrical accessibility is used to guarantee the existence of the JSJ-decomposition of limit groups. Some generalisations are also discussed.