How to construct ideal points of \(\text{SL}_2({\mathbb{C}})\) representation spaces of knot groups
Following an idea of \textit{M. Culler} and \textit{P. B. Shalen} [Ann. Math., II. Ser. 117, 109-146 (1983; Zbl 0529.57005)], the author investigates limit points of the space of \(SL_2(\mathbb C)\)-representations of certain knot groups. His approach consists in choosing concretely certain knot groups (see below) in order to perform concrete calculations and derive concrete statements. It is shown that the trefoil knot group has exactly one such ideal point, the figure eight knot group two and the \(5_2\) knot group three of them. The author also investigates the trees that Culler and Shalen associated to ideal points in [loc. cit.] these are subtrees of the Serre tree of \(SL_2\) over the complex formal power series field in one indeterminate.
scientific article; zbMATH DE number 1307857