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

• Main Authors: Akiyoshi, Hirotaka (Author), Sakuma, Makoto (Author), Wada, Masaaki (Author), Yamashita, Yasushi (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Lecture Notes in Mathematics, 1909
• Subjects: Mathematics.; Group theory.; Functions of complex variables.; Manifolds (Mathematics).; Complex manifolds.; Manifolds and Cell Complexes (incl. Diff.Topology).; Functions of a Complex Variable.; Group Theory and Generalizations.

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 inspir...

Table of Contents:

• Jorgensen's picture of quasifuchsian punctured torus groups
• Fricke surfaces and PSL(2, ?)-representations
• Labeled representations and associated complexes
• Chain rule and side parameter
• Special examples
• Reformulation of Main Theorem 1.3.5 and outline of the proof
• Openness
• Closedness
• Algebraic roots and geometric roots.