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

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  • © 2007

Overview

Authors:
  1. Hirotaka Akiyoshi

    1. Advanced Mathematical Institute, Osaka City University, Osaka, Japan

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  2. Makoto Sakuma

    1. Department of Mathematics, Hiroshima University, Higashi-Hiroshima, Japan

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  3. Masaaki Wada

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

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  4. Yasushi Yamashita

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

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XLIII
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  2. Jorgensen's picture of quasifuchsian punctured torus groups

    Pages 1-14

  3. Fricke surfaces and PSL(2, ℂ)-representations

    Pages 15-35

  4. Labeled representations and associated complexes

    Pages 37-47

  5. Chain rule and side parameter

    Pages 49-99

  6. Special examples

    Pages 101-132

  7. Reformulation of Main Theorem 1.3.5 and outline of the proof

    Pages 133-154

  8. Openness

    Pages 155-169

  9. Closedness

    Pages 171-214

  10. Algebraic roots and geometric roots

    Pages 215-231

  11. Back Matter

    Pages 233-256
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Keywords

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.

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

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