  We investigate the sensitivity of an Unruh-DeWitt detector to the global
features of a deficit angle that are otherwise classically inaccessible.
Specifically, we consider a detector placed inside an infinite thin hollow
cylinder whose spacetime is everywhere flat but outside of which the spacetime
has a deficit angle and study its response to a scalar field to which it
couples. We find that the response of the detector is sensitive to the deficit
angle, despite the fact that it does not interact with the cylinder.
