On Dijkgraaf-Witten-type invariants

We explicitly construct a series of lattice models based upon the gauge group Z_p which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-p flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a 3-manifold and is based upon a single link, or 1-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher-dimensional simplices.Supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM).