Punctured torus groups and 2-bridge knot groups. I
type: Item
instance of: scholarly article
title: Punctured torus groups and 2-bridge knot groups. I
zbMATH Open document ID: 1132.57001
DOI: 10.1007/978-3-540-71807-9
author: Hirotaka Akiyoshi
author: Masaaki Wada
author: Yasushi Yamashita
author: Makoto Sakuma
published in: Lecture Notes in Mathematics
publication date: 2007-05-14T00:00:00Z
review text: In the late 70's \textit{T. Jørgensen} has made a series of detailed studies on the space \(\mathcal{QF}\) of quasifuchsian (once) punctured torus groups from the view point of their Ford fundamental domains. These studies are summarized in [Lond. Math. Soc. Lect. Note Ser. 299, 183--207 (2003; Zbl 1061.30038)]. He gave a complete description of the combinatorial structure of the Ford domain of every quasifuchsian punctured torus group, and showed that the space \(\mathcal{QF}\) can be described in terms of the Farey triangulations, or the modular diagrams. The present monograph is Part 1 of a book intended to give a full account of Jørgensen's theory of punctured torus Kleinian groups and its generalization. The authors give an intuitive and self-contained description of the theory with a complete proof. The method is based on Poincaré's theorem on fundamental polyhedra. This geometric approach enables them to extend Jørgensen's theory beyond quasifuchsian spaces and to apply it to knot theory. They find a very natural way to understand the hyperbolic structure and the canonical decompositions of the 2-bridge link complements in the context of Jørgensen's work. This monograph written by well-known experts is an excellent presentation of Jørgensen's theory with many informative illustrations. It will be very useful for researches working on modern problems in quasifuchsian group theory, hyperbolic and geometry and hyperbolic knot theory.
reviewed by: Andrei Vesnin
Mathematics Subject Classification ID: 57-02
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 5152430
zbMATH Keywords: punctured torus group
zbMATH Keywords: quasifuchsian group
zbMATH Keywords: 2-bridge link
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-540-71807-9
OpenAlex ID: W3208026693
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description: scientific article; zbMATH DE number 5152430