How to construct ideal points of \(\text{SL}_2({\mathbb{C}})\) representation spaces of knot groups
type: Item
instance of: scholarly article
title: How to construct ideal points of \(\text{SL}_2({\mathbb{C}})\) representation spaces of knot groups
zbMATH Open document ID: 0924.57004
DOI: 10.1016/S0166-8641(97)00267-8
author: Tomotada Ohtsuki
published in: Topology and its Applications
publication date: 1999-10-20T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 1307857
zbMATH Keywords: ideal points
reviewed by: Nicolas Monod
MaRDI profile type: Publication
full work available at URL: s0166-8641(97)00267-8
OpenAlex ID: W2029744580
description: scientific article; zbMATH DE number 1307857