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Punctured Torus Groups and 2-Bridge Knot Groups (I) [electronic resource] /by Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita.

by Akiyoshi, Hirotaka [author.]; Sakuma, Makoto [author.]; Wada, Masaaki [author.]; Yamashita, Yasushi [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 1909Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.Description: XLIII, 252 p. online resource.ISBN: 9783540718079.Subject(s): Mathematics | Group theory | Functions of complex variables | Cell aggregation -- Mathematics | Mathematics | Manifolds and Cell Complexes (incl. Diff.Topology) | Functions of a Complex Variable | Group Theory and GeneralizationsDDC classification: 514.34 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give 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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QA613.6-613.66 (Browse shelf) Available
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QA613-613.8 (Browse shelf) Available

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.

This monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give 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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