  We investigate the proposed duality between a quantum information metric in a
$\mbox{CFT}_{d+1}$ and the volume of a maximum time slice in the dual
$\mbox{AdS}_{d+2}$ for topological geons. Examining the specific cases of BTZ
black holes and planar Schwarzschild-AdS black holes, along with their geon
counterparts, we find that the proposed duality relation for geons is the same
apart from a factor of 4. The information metric therefore provides a probe of
the topology of the bulk spacetime.
