  In this letter we show that in a Kaluza-Klein framework we can have arbitrary
topology change between the macroscopic (i.e. noncompactified) spacelike
3-hypersurfaces. This is achieved by using the compactified dimensions as a
catalyser for topology change. In the case of odd-dimensional spacetimes (such
as the 11-dimensional M-theory) this is always possible. In the
even-dimensional case, a sufficient condition is the existence of a closed,
odd-dimensional manifold as a factor (such as S^1, S^3) in the Kaluza-Klein
sector. Since one of the most common manifolds used for compactification is the
torus T^k = S^1 \times ... \times S^1, in this case we can again induce an
arbitrary topology change on the 3-hypersurfaces.
