We study dimensionally restricted non-perturbative causal set quantum dynamics in two and three spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into latticisations of flat background spacetimes with global spatial topology 
and 
in two and three dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations via an analytic continuation of a parameter 
analogous to an inverse temperature. In both two and three dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by "layered" posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. These results are similar in character to those obtained for topologically trivial causal set dynamics over the sample space of 2-orders. The current simulations use a newly developed framework for causal set MCMC calculations, and provide the first implementation of a three-dimensional causal set dynamics.
arXiv paper: https://arxiv.org/abs/1908.11647