Acyclic groups and wild arcs

Abstract

We discuss two classes of acyclic groups that are commutator subgroups of finitely presented groups with infinite cyclic abelianization. The first is algebraic and includes groups first exhibited by Baumslag and Gruenberg, of which it is shown that Epstein's acyclic group is a special case. The second class is geometric, and is shown to include a number of wild arc groups in the literature.