Punctured Torus Groups and 2-Bridge Knot Groups (I)

  • Hirotaka Akiyoshi
  • Makoto Sakuma
  • Masaaki Wada
  • Yasushi Yamashita
Part of the Lecture Notes in Mathematics book series (LNM, volume 1909)

Table of contents

About this book

Introduction

This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory.

Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology.

In this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.

Keywords

2-bridge know Ford domain Knot theory Natural Punctured torus algebra boundary element method diagrams evolution form group history of mathematics quasifuchsian group story unknotting tunnel

Authors and affiliations

  • Hirotaka Akiyoshi
    • 1
  • Makoto Sakuma
    • 2
  • Masaaki Wada
    • 3
  • Yasushi Yamashita
    • 3
  1. 1.Advanced Mathematical InstituteOsaka City UniversityOsakaJapan
  2. 2.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Department of Information and Computer SciencesNara Women's UniversityNaraJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71807-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71806-2
  • Online ISBN 978-3-540-71807-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book