Topological quantum field theory for the universal quantum invariant (Q1374760)

The authors and \textit{Thang T. Q. Le} defined the universal quantum invariant \(\Omega (M)\) of a 3-manifold \(M\) in [Topology 37, No. 3, 539-574 (1998; Zbl 0897.57017)]. In this paper, the authors extend the universal quantum invariant \(\Omega (M)\) to an invariant of a 3-manifold \(\Omega (M,G)\) with an embedded trivalent graph \(G\), which is regarded as an invariant of \(M-N(G)\). So, they extend the universal quantum invariant to an invariant of 3-manifolds with boundaries, and show that the extended invariant satisfies modified axioms of topological quantum field theory.