  We define a lattice statistical model on a triangulated manifold in four
dimensions associated to a group $G$. When $G=SU(2)$, the statistical weight is
constructed from the $15j$-symbol as well as the $6j$-symbol for recombination
of angular momenta, and the model may be regarded as the four-dimensional
version of the Ponzano-Regge model. We show that the partition function of the
model is invariant under the Alexander moves of the simplicial complex, thus it
depends only on the piecewise linear topology of the manifold. For an
orientable manifold, the model is related to the so-called $BF$ model. The
$q$-analogue of the model is also constructed, and it is argued that its
partition function is invariant under the Alexander moves. It is discussed how
to realize the 't Hooft operator in these models associated to a closed surface
in four dimensions as well as the Wilson operator associated to a closed loop.
Correlation functions of these operators in the $q$-deformed version of the
model would define a new type of invariants of knots and links in four
dimensions.
