The structure of spatial slices of 3-dimensional causal triangulations

Abstract

. We consider causal 3-dimensional triangulations with the topology of S 2 × [0 , 1] or D 2 × [0 , 1] where S 2 and D 2 are the 2-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.