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The structure of simplicial manifolds in a model of Causal DynamicalTriangulations in 3+1 dimensions with the spatial topology of a 3-torus isanalyzed with the help of topological observables, such as loops with nonzerowinding numbers and coordinates based on scalar fields with jumps at theboundaries of the elementary cell of the torus. The results are given aninterpretation and used in the measurements of a more local observable that isthe quantum Ricci curvature. We moreover analyze the influence of scalar matterfields on the geometry of CDT spacetimes.

New topological observables in a model of Causal Dynamical Triangulations on a torus