for noncompact spatial topology there are no closed timelike curves [@hoekzema]. For compact spatial slices, where the spacetime topology is that of a cylinder, one can construct explicit geometries which exhibit noncontractible, closed timelike curves. Of course, we do not know a priori whether the presence of closed timelike curves in individual path integral configurations has any influence on the continuum limit of the model, and perhaps leads to undesirable continuum properties. It appears that in the context of our present investigation this issue is largely circumvented. Although the causality conditions we impose are of a local nature, and may admit the presence of closed timelike curves, it turns out that the geometries dominating the sum over histories dynamically retain a weak degree of foliation (see Sec. \[sec:tetdist\] below), which suggests that such curves are certainly not abundant. We have not seen closed timelike curves in random samples, but have not systematically tested for their presence either.

Anticipating the choice of boundary conditions we will make in 2+1 dimensions, we may relax the local causality constraint slightly by allowing for the presence of an isolated “source" and “sink" of time. By this we mean a vertex where only timelike links 