The PSU(3) invariant of the Poincaré homology sphere
In the paper under discussion the author uses the \(R\)-matrix presentation of link and 3-manifold invariants to compute the \(PSU(3)\) pertubative invariant for the Poincaré homology sphere. The computation is based on a certain description of the \(\mathfrak{sl}_{3}\) colored Jones polynomial of a link and of the \(PSU(3)\) invariant of 3-manifolds (see also [\textit{Reshetikhin} and \textit{Turaev}, Commun. Math. Phys. 127, 1-26 (1990; Zbl 0768.57003)] and [\textit{T. Le}, Topology 39, 813-849 (2000; Zbl 0955.57010)]). From this description the author obtains a certain form for the colored Jones polynomial of the trefoil knot. This is applied to give an algorithm to compute the coefficients in the \(PSU(3)\) pertubative invariant for the Poincaré homology sphere.
scientific article; zbMATH DE number 1901932