Linearity and Indiscreteness of Amalgamated Products of Hyperbolic Groups

Abstract

AbstractWe discuss the linearity and discreteness of amalgamated products of linear word hyperbolic groups. In particular, we prove that the double of a torsion-free Anosov group along a maximal cyclic subgroup is always linear, and we construct examples of such groups, which do not admit discrete and faithful representations into any simple Lie group of real rank $1$. We also build new examples of non-linear word hyperbolic groups, elaborating on a previous work of Canary–Stover–Tsouvalas.