  We investigate quantum effects on topological black hole space-times within
the framework of quantum field theory on curved space-times. Considering a
quantum scalar field, we extend a recent mode-sum regularization prescription
for the computation of the renormalized vacuum polarization to asymptotically
anti-de Sitter black holes with nonspherical event horizon topology. In
particular, we calculate the vacuum polarization for a massless,
conformally-coupled scalar field on a four-dimensional topological
Schwarzschild-anti-de Sitter black hole background, comparing our results with
those for a spherically-symmetric black hole.
