# The structure of spatial slices of 3-dimensional causal triangulations

### Bergfinnur Durhuus

University of Copenhagen, Denmark### Thordur Jonsson

University of Iceland, Reykjavik, Iceland

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## Abstract

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.

## Cite this article

Bergfinnur Durhuus, Thordur Jonsson, The structure of spatial slices of 3-dimensional causal triangulations. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), no. 3 pp. 365–393

DOI 10.4171/AIHPD/91