  We analyse a simple example of a holographically dual pair in which we
topologically twist both theories. The holography is based on the
two-dimensional N=2 supersymmetric Liouville conformal field theory that
defines a unitary bulk quantum supergravity theory in three-dimensional anti-de
Sitter space. The supersymmetric version of three-dimensional Liouville quantum
gravity allows for a topological twist on the boundary and in the bulk. We
define the topological bulk supergravity theory in terms of twisted boundary
conditions. We corroborate the duality by calculating the chiral configurations
in the bulk supergravity theory and by quantising the solution space. Moreover,
we note that the boundary calculation of the structure constants of the chiral
ring carries over to the bulk theory as well. We thus construct a topological
AdS/CFT duality in which the bulk theory is independent of the boundary metric.
