Homologically trivial part of the Turaev -- Viro invariant order~$7$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 698-707.

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Homologically trivial part of any Turaev – Viro invariant odd order $r$ is a Turaev – Viro type invariant order $\frac{r + 1}{2}$. In this paper we find an explicit formulas for this Turaev – Viro type invariant, corresponding to the invariant order $r = 7$. Our formulas express $6j$-symbols and color weights in the term of $\gamma$, where $\gamma$ is a root of the polynomial $\mathcal{T}(x) = x^3 - 2x^2 - x + 1$.
Mots-clés : Turaev – Viro invariant, $6j$-symbol.
Keywords: quantum number
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F. G. Korablev. Homologically trivial part of the Turaev -- Viro invariant order~$7$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 698-707. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a23/

[1] V.G. Turaev, O.Ya. Viro, “State sum invariants of 3-manifolds and quantum 6j-symbols”, Topology, 31:4 (1992), 865–902 | DOI | MR | Zbl

[2] S. Matveev, Algorithmic topology and classification of 3-manifolds, Springer, Berlin, 2007 | MR | Zbl

[3] V.G. Turaev, Quantum invariants of knots and 3-manifolds, de Gruyter Studies in Mathematics, 18, Walter de Gruyter, Berlin, 2016 | MR | Zbl

[4] S.V. Matveev, M.V. Sokolov, “On a simple invariant of Turaev-Viro type”, J. Math. Sci., New York, 94:2 (1999), 1226–1229 | DOI | MR | Zbl

[5] M.V. Sokolov, “The Turaev-Viro invariant for 3-manifolds is a sum of three invariants”, Can. Math. Bull., 39:4 (1996), 468–475 | DOI | MR | Zbl

[6] G. Masbaum, J.D. Roberts, “A simple proof of integrality of quantum invariants at prime roots of unity”, Math. Proc. Camb. Philos. Soc., 121:3 (1997), 443–454 | DOI | MR | Zbl