  We define a holographic dual to the Donaldson-Witten topological twist of
$\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described
by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$
gauged supergravity in five dimensions, with the four-manifold as conformal
boundary. Under AdS/CFT, minus the logarithm of the partition function of the
gauge theory is identified with the holographically renormalized supergravity
action. We show that the latter is independent of the metric on the boundary
four-manifold, as required for a topological theory. Supersymmetric solutions
in the bulk satisfy first order differential equations for a twisted $Sp(1)$
structure, which extends the quaternionic Kahler structure that exists on any
Riemannian four-manifold boundary. We comment on applications and extensions,
including generalizations to other topological twists.
