On 3-dimensional homotopy quantum field theory. I. (Q2909612)

For a discrete group \(G\) and a spherical \(G\)-fusion category whose neutral component has invertible dimension (definition in Section 4.2), the paper under review constructs an HQFT invariant of homotopy classes of maps from a compact 3-manifold \((M,\partial M)\) to \(K(G,1)\) the Eilenberg-MacLane space of \(G\). For \(G=1\) these are the familiar Turaev-Viro TQFT invariants.NEWLINENEWLINEThe construction elegantly avoids the use of \(6j\)--symbols and allows non-generic skeletons of \(3\)--manifolds (skeletons with edges incident to \(\geq 4\) regions) in the spirit of [\textit{V. Turaev} and \textit{A. Virelizier}, ``On two approaches to 3-dimensional TQFTs'', \url{arXiv:1006.3501}].