On simplicial resolutions of groups

In this paper we firstly present an overview of several topological tameness conditions at infinity of finitely presented groups which are related to the notion of geometric simple connectivity, with a particular regard to the concept of simplicial resolution developed by V. Poénaru (under the name of “inverse-representation”). Then, we generalize some existing results that correlate some of these properties. Finally, we propose few open problems and questions in the fields of geometric topology and geometric group theory, which revolve around the notions of geometric simple connectivity, simplicial resolution and qsf, both for discrete groups and universal covering spaces.