  If the diffeomorphism symmetry of general relativity is fully implemented
into a path integral quantum theory, the path integral leads to a partition
function which is an invariant of smooth manifolds. We comment on the physical
implications of results on the classification of smooth and piecewise-linear
4-manifolds which show that the partition function can already be computed from
a triangulation of space-time. Such a triangulation characterizes the topology
and the differentiable structure, but is completely unrelated to any physical
cut-off. It can be arbitrarily refined without affecting the physical
predictions and without increasing the number of degrees of freedom
proportionally to the volume. Only refinements at the boundary have a physical
significance as long as the experimenters who observe through this boundary,
can increase the resolution of their measurements. All these are consequences
of the symmetries. The Planck scale cut-off expected in quantum gravity is
rather a dynamical effect.
