"Easy" representations and the QSF property for groups

We define the class of easily-representable groups as the class of those finitely presented groups r admitting an inverse representation (which, roughly, is a map from some 2-complex to a certain singular 3-manifold [M.sup.3](Γ) associated to Γ, satisfying several topological properties) for which the set of double points is closed. Our main result is that easily-representable groups are QSF (i.e. quasi-simply filtered). Key words and phrases: Discrete groups, quasi-simple filtration (QSF), geometric simple connectivity, inverse representations, singularities.