  The dS/CFT proposal of Anninos, Hartman, and Strominger relates quantum
Vasiliev gravity in dS_4 to a large N vector theory in three dimensions. We use
this proposal to compute the Wheeler-de Witt wave function of a universe having
a particular topology at future infinity. This amplitude is found to grow
rapidly with the topological complexity of the spatial slice; this is due to
the plethora of states of the Chern-Simons theory that is needed to impose the
singlet constraint. Various mechanisms are considered which might ameliorate
this growth, but none seems completely satisfactory. We also study the topology
dependence in Einstein gravity by computing the action of complex instantons;
the wave function then depends on a choice of contour through the space of
metrics. The most natural contour prescription leads to a growth with genus
similar to the one found in Vasiliev theory, albeit with a different power of
Newton's constant.
