  Motivated by the search for new observables in nonperturbative quantum
gravity, we consider Causal Dynamical Triangulations (CDT) in 2+1 dimensions
with the spatial topology of a torus. This system is of particular interest,
because one can study not only the global scale factor, but also global shape
variables in the presence of arbitrary quantum fluctuations of the geometry.
Our initial investigation focusses on the dynamics of the scale factor and
uncovers a qualitatively new behaviour, which leads us to investigate a novel
type of boundary conditions for the path integral. Comparing large-scale
features of the emergent quantum geometry in numerical simulations with a
classical minisuperspace formulation, we find partial agreement. By measuring
the correlation matrix of volume fluctuations we succeed in reconstructing the
effective action for the scale factor directly from the simulation data. Apart
from setting the stage for the analysis of shape dynamics on the torus, the new
set-up highlights the role of nontrivial boundaries and topology.
