On Dijkgraaf-Witten Type Invariants

Abstract

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.

18 pages

References in corpus (4)

• Chern-Simons Theory with Finite Gauge Group
• Quasi-Quantum Groups, Knots, Three-Manifolds, and Topological Field Theory
• State Sum Models and Simplicial Cohomology
• Combinatorial Invariants from Four Dimensional Lattice Models

Cited by in corpus (2)

• Orbifolds by 2-groups and decomposition
• 4-dimensional BF Gravity on the Lattice