On a class of topological quantum field theories in three-dimensions

TL;DR

This paper reformulates a 3D topological quantum field theory as a Turaev-Viro type state-sum, providing a functor satisfying Atiyah's axioms and extending to manifolds with boundary.

Contribution

It introduces a new functorial formulation of the Chung-Fukuma-Shapere theory as a Turaev-Viro state-sum, satisfying Atiyah's axioms and applicable to manifolds with boundary.

Findings

Constructed a functor satisfying Atiyah's axioms

Reformulated the theory as a Turaev-Viro state-sum

Extended the theory to manifolds with boundary

Abstract

We investigate the Chung-Fukuma-Shapere theory, or Kuperberg theory, of three-dimensional lattice topological field theory. We construct a functor which satisfies the Atiyah's axioms of topological quantum field theory by reformulating the theory as Turaev-Viro type state-sum theory on a triangulated manifold. The theory can also be extended to give a topological invariant of manifolds with boundary.