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

Häftad, Engelska, 2007

Del 1909 i serien Lecture Notes in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2007-06-08
Mått:155 x 235 x 17 mm
Vikt:464 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:256
Upplaga:2007
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540718062

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "The present monograph is Part 1 of a book intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. ... This monograph written by well-known experts is an excellent presentation of Jorgensen'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)

Innehållsförteckning

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.