Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita

Punctured Torus Groups and 2-Bridge Knot Groups (I) (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 256
• Erscheinungstermin: 26. Mai 2007
• Englisch
• ISBN-13: 9783540718079
• Artikelnr.: 44222734

Autorenporträt

Hirotaka Akiyoshi, Osaka University, Osaka, Japan / Makoto Sakuma, Hiroshima University, Higashi-Hiroshima, Japan / Masaaki Wada, Nara Women's University, Nara, Japan / Yasushi Yamashita, Nara Women's University, Nara, Japan

Inhaltsangabe

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.

Rezensionen

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)