  We study the role that both vacuum fluctuations and vacuum entanglement of a
scalar field play in identifying the spacetime topology, which is not
prescribed from first principles---neither in general relativity or quantum
gravity. We analyze how the entanglement and observable correlations acquired
between two particle detectors are sensitive to the spatial topology of
spacetime. We examine the detector's time evolution to all orders in
perturbation theory and then study the phenomenon of vacuum entanglement
harvesting in Minkowski spacetime and two flat topologically distinct
spacetimes constructed from identifications of the Minkowski space. We show
that, for instance, if the spatial topology induces a preferred direction, this
direction may be inferred from the dependence of correlations between the two
detectors on their orientation. We therefore show that vacuum fluctuations and
vacuum entanglement harvesting makes it, in principle, possible to distinguish
spacetimes with identical local geometry that differ only in their topology.
