Punctured torus groups and 2-bridge knot groups (I)

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書誌事項

Punctured torus groups and 2-bridge knot groups (I)

Hirotaka Akiyoshi ... [et al.]

(Lecture notes in mathematics, 1909)

Springer, c2007

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注記

Other authors: Makoto Sakuma, Masaaki Wada, Yasushi Yamashita

Includes bibliographical references (p. [239]-243) and index

内容説明・目次

内容説明

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.

目次

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.

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