On 3-dimensional Homotopy Quantum Field Theory, I

TL;DR

This paper constructs a 3-dimensional Homotopy Quantum Field Theory using state-sum methods for a given group G and a spherical G-fusion category, targeting the space K(G,1).

Contribution

It introduces a new state-sum construction of 3D HQFTs with specific algebraic and topological conditions.

Findings

Constructs a 3D HQFT for a discrete group G

Uses spherical G-fusion categories with invertible neutral component

Provides a mathematical framework linking algebraic categories to topological quantum field theories

Abstract

Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane space K(G,1).