Numerical work with sage 4 – All possible triangulations of a simplicial complex using pachner moves

So what I’ve been able to do using sagemath is triangulate a simplicial complex using Pachner moves. The complete set of all possible triangulations can be recorded, saved and plotted in 3d using jmol. The value of this is that in the path integral formulation it is necessary to be able to calculate the probability of each spin network and use the result to form a partition function.

fixed vertices all possible triangualtions via pachner moves

The next steps following on from this are to add SU(2) spins as edge labels and SU(2) interwiners as node labels. I would also like to investigate moving between simplicial complexes, spin networks and weighted digraphs as representations of discrete spacetimes.

numerical work with sage 4 fig 1

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