  We calculate transition probabilities for various processes involving giant
gravitons and small gravitons in AdS space, using the dual N=4 SYM theory. The
normalization factors for these probabilities involve, in general, correlators
for manifolds of non-trivial topology which are obtained by gluing simpler
four-manifolds. This follows from the factorization properties which relate CFT
correlators for different topologies. These points are illustrated, in the
first instance, in the simpler example of a two dimensional Matrix CFT. We give
the bulk five dimensional interpretation, involving neighborhoods of Witten
graphs, of these gluing properties of the four dimensional boundary CFT. As a
corollary we give a simple description, based on Witten graphs, of a
multiplicity of bulk topologies corresponding to a fixed boundary topology. We
also propose to interpret the correlators as topology-changing transition
amplitudes between LLM geometries.
