The geometry of empty space is the key to arresting dynamics

We present the concept of dynamically available volume as a suitable order parameter for dynamical arrest. We show that dynamical arrest can be understood as a de-percolation transition of a vacancy network or available space. Beyond the arrest transition we find that droplets of available space are disconnected and the dynamics is frozen. This connection of the dynamics to the underlying geometrical structure of empty space provides us with a rich framework for studying the arrest transition.