  Using the generalised AdS/CFT correspondence, we show that there are certain
ten-dimensional differentiable manifolds such that string theory on such a
manifold is unstable [to the emission of "large branes"] no matter what the
metric may be. The instability is thus due to the [differential] topology of
the manifold, not to any particular choice of its geometry. We propose a
precise criterion for this "topology selection mechanism", and prove it in many
cases. The techniques employed may be useful in more general cases.
