H-mode operation in the low-shear stellarator W7-AS is achieved for specificplasma edge topologies characterized by three `operational windows' of theedge rotational transform. An explanation for this strong influence of themagnetic configuration could be the increase of viscous damping if rationalsurfaces and thus island structures occur within the relevant plasmaedge layer, thereby impeding the development of an edge transport barrier.Prior to the final transition to a quiescent state, the plasma edge passes arich phenomenology of dynamic behaviour such as dithering and ELMs. Plasmaedge parameters indicate that a quiescent H-mode occurs if a certain edgepressure is achieved.