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  • © 2007

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

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1909)

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Table of contents (9 chapters)

About this book

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

Reviews

From the reviews:

"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. … 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 researchers working on modern problems in quasifuchsian group theory, hyperbolic and geometry and hyperbolic knot theory." (Andrei Vesnin, Zentralblatt MATH, Vol. 1132 (10), 2008)

Authors and Affiliations

  • Advanced Mathematical Institute, Osaka City University, Osaka, Japan

    Hirotaka Akiyoshi

  • Department of Mathematics, Hiroshima University, Higashi-Hiroshima, Japan

    Makoto Sakuma

  • Department of Information and Computer Sciences, Nara Women's University, Nara, Japan

    Masaaki Wada, Yasushi Yamashita

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions