  We consider the construction of a topological version of F-theory on a
particular $Spin(7)$ 8-manifold which is a Calabi-Yau 3-fold times a 2-torus.
We write an action for this theory in eight dimensions and reduce it to lower
dimensions using Hitchin's gradient flow method. A symmetry of the
eight-dimensional theory which follows from modular transformations of the
torus induces duality transformations of the variables of the topological A-
and B-models. We also consider target space form actions in the presence of
background fluxes in six dimensions.
