| Culler and Morgan proved that the length function of a minimal action of a group on a tree completely determines the action. As a consequence the space of minimal actions of a free group on trees, up to scaling (also known as Outer Space), embeds in infinite projective space via the map sending an action to its projectivized length function. They also proved that the image of this map has compact closure.;For a right-angled Artin group whose defining graph is connected and triangle-free, we investigate the space of minimal actions on 2-dimensional CAT(0) rectangle complexes. Charney and Margolis showed that such actions are completely determined by their length functions; hence this space embeds into infinite projective space. The goal of this thesis is to show that the set of projectivized length functions associated to these actions has compact closure. |
