Homologically trivial part of the Turaev-Viro invariant order 7

Abstract

A 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 colour weights in terms of $\gamma$, where $\gamma$ is a root of the polynomial $\mathcal{T}(x)=x^3-2x^2-x+1$.

This is a translation into English of the paper published in Siberian Electronic Mathematical Reports, 2022, Vol. 19, no. 2