Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1909)
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Table of contents (9 chapters)
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
Bibliographic Information
Book Title: Punctured Torus Groups and 2-Bridge Knot Groups (I)
Authors: Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-71807-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2007
Softcover ISBN: 978-3-540-71806-2Published: 08 June 2007
eBook ISBN: 978-3-540-71807-9Published: 26 May 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XLIII, 256
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Functions of a Complex Variable, Group Theory and Generalizations