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

2007
ISBN: 978-3-540-71806-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1909, 256 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 464 g

Reihe: Lecture Notes in Mathematics

Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers 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.

Zielgruppe

Research

Autoren/Hrsg.

Akiyoshi, Hirotaka

Yamashita, Yasushi

Sakuma, Makoto

Wada, Masaaki

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.