  It is shown that the standard mod-$p$ valued intersection form can be used to
define Boltzmann weights of subdivision invariant lattice models with gauge
group $Z_{p}$. In particular, we discuss a four dimensional model which is
based upon the assignment of field variables to the $2$-simplices of the
simplicial complex. The action is taken to be the intersection form defined on
the second cohomology group of the complex, with coefficients in $Z_{p}$.
Subdivision invariance of the theory follows when the coupling constant is
quantized and the field configurations are restricted to those satisfying a
mod-$p$ flatness condition. We present an explicit computation of the partition
function for the manifold $\pm CP^{2}$, demonstrating non-triviality.
