``Easy" Representations and the {\sc qsf} property for groups

Abstract

We define the class of \textit{easily-representable groups} as the class of those finitely presented groups $\Gamma $ admitting an \textit{inverse representation} (which, roughly, is a map from some $2$-complex to a certain singular 3-manifold $M^3 (\Gamma )$ associated to $\Gamma$, satisfying several topological properties) for which the set of double points is closed. Our main result is that easily-representable groups are {\sc qsf} (i.e. quasi-simply filtered).