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Published online by Cambridge University Press: 20 November 2018
We show that every Turaev-Viro invariant for 3-manifolds is a sum of three new invariants and discuss their properties. We also find a solution of a conjecture of L. H. Kauffman and S. Lins. Tables of the invariants for closed orientable 3-manifolds of complexity ≤ 3 are presented at the end of the paper.