JournalsaihpdVol. 7 , No. 3pp. 365–393

The structure of spatial slices of 3-dimensional causal triangulations

  • Bergfinnur Durhuus

    University of Copenhagen, Denmark
  • Thordur Jonsson

    University of Iceland, Reykjavik, Iceland
The structure of spatial slices of 3-dimensional causal triangulations cover
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Abstract

We consider causal 3-dimensional triangulations with the topology of S2×[0,1]S^2\times [0,1] or D2×[0,1]D^2\times [0,1] where S2S^2 and D2D^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