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Annales de l’Institut Henri Poincaré D

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Volume 7, Issue 3, 2020, pp. 365–393
DOI: 10.4171/AIHPD/91

Published online: 2020-09-15

The structure of spatial slices of 3-dimensional causal triangulations

Bergfinnur Durhuus[1] and Thordur Jonsson[2]

(1) University of Copenhagen, Denmark
(2) University of Iceland, Reykjavik, Iceland

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.

Keywords: 3-dimensional random triangulations, causal triangulations

Durhuus Bergfinnur, Jonsson Thordur: The structure of spatial slices of 3-dimensional causal triangulations. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), 365-393. doi: 10.4171/AIHPD/91