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

• Κύριοι συγγραφείς: Akiyoshi, Hirotaka (Συγγραφέας), Sakuma, Makoto (Συγγραφέας), Wada, Masaaki (Συγγραφέας), Yamashita, Yasushi (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Σειρά: Lecture Notes in Mathematics, 1909
• Θέματα: 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 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. 

 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.