Punctured torus groups and 2-bridge knot groups (I) / Hirotaka Akiyoshi ... [and others].

Format:

Book

Contributor:

Akiyoshi, Hirotaka.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 1909.

Lecture notes in mathematics, 0075-8434 ; 1909

Language:

English

Subjects (All):

Kleinian groups.

Torus (Geometry).

Knot theory.

Physical Description:

xliii, 252 pages : illustrations ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2007]

Summary:

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.

Notes:

Includes bibliographical references and index.

ISBN:

9783540718062

3540718060

OCLC:

123375614