In this talk, I will introduce a class of groups called generalised triangle groups. These groups were originally defined by Stallings, and later studied by Caprace, Conder, Kaluba, and Witzel as candidates for non-residually finite hyperbolic groups. Generalised triangle groups have corresponding complexes which allow us to study them using combinatorial and geometric techniques. I will demonstrate this through the automaticity of non-positively curved k-fold triangle groups and briefly talk about applications.
