The structure of spatial slices of 3-dimensional causal triangulations

We consider causal 3-dimensional triangulations with the topology of S^2\times [0,1] or D^2\times [0,1] where S^2 and D^2 are the two-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that these slices can be mapped bijectively onto a set of certain coloured 2-dimensional cell complexes satisfying simple conditions. The cell complexes arise as the cross section of the individual slices.