State sum models and simplicial cohomology

We study a class of subdivision invariant lattice models based on the gauge groupZ _p , with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the 1- and 2-dimensional simplices of the simplicial complex. The property of subdivision invariance is achieved when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-p flatness condition. By explicit computation of the partition function for the manifoldRP ³×S ¹, we establish that the theory has a quantum Hilbert space which differs from the classical one.Supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM)