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Lecture Notes in Mathematics

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

Authors: Akiyoshi, H., Sakuma, M., Wada, M., Yamashita, Y.

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eBook $44.99
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  • ISBN 978-3-540-71807-9
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Softcover $59.99
price for USA in USD
  • ISBN 978-3-540-71806-2
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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)


Table of contents (9 chapters)

  • Jorgensen's picture of quasifuchsian punctured torus groups

    Pages 1-14

  • Fricke surfaces and PSL(2, ℂ)-representations

    Pages 15-35

  • Labeled representations and associated complexes

    Pages 37-47

  • Chain rule and side parameter

    Pages 49-99

  • Special examples

    Pages 101-132

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-540-71807-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-540-71806-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Punctured Torus Groups and 2-Bridge Knot Groups (I)
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1909
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-71807-9
DOI
10.1007/978-3-540-71807-9
Softcover ISBN
978-3-540-71806-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XLIII, 256
Topics