Invariants of links and 3-manifolds from the modular category with two simple objects
0000-0001-8510-0040 In this paper we construct a modular category $\mathfrak{E}$ containing exactly two simple objects. Using a special technique, two invariants are extracted fr om it: a complex-valued invariant of Reshetikhin -- Turaev type $rt_{\varepsilon}$ of unoriented links in the 3-sphere and of 3-manifolds, and a real-valued invariant of Turaev -- Viro type $tv_{\varepsilon}$ of 3-manifolds. The values of these two invariants of 3-manifolds are related by the equality $|rt_{\varepsilon}|^2\cdot (\varepsilon + 2) = tv_{\varepsilon}$, wh ere $\varepsilon$ is the root of the equation $\varepsilon^2 = \varepsilon + 1$. It is proved that the $tv_{\varepsilon}$ invariant exactly coincides with the $\varepsilon$-invariant of 3-manifolds.
УДК 515.16
${file_?????}Keywords: modular category, Reshetikhin -- Turaev type invariant, Turaev -- Viro type invariant, $\varepsilon$-invariant.