  We define an invariant of graphs embedded in a three-manifold and a partition
function for 2-complexes embedded in a triangulated four-manifold by specifying
the values of variables in the Turaev-Viro and Crane-Yetter state sum models.
In the case of the three-dimensional invariant, we prove a duality formula
relating its Fourier transform to another invariant defined via the coloured
Jones polynomial. In the case of the four-dimensional partition function, we
give a formula for it in terms of a regular neighbourhood of the 2-complex and
the signature of its complement. Some examples are computed which show that the
partition function determines an invariant which can detect non locally-flat
surfaces in a four-manifold.
