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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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9783540837169

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

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