Punctured Torus Groups and 2-Bridge Knot Groups (I)
Akiyoshi, Hirotaka.
Punctured Torus Groups and 2-Bridge Knot Groups (I) [electronic resource] / by Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita. - XLIII, 256 p. online resource. - Lecture Notes in Mathematics, 1909 0075-8434 ; . - Lecture Notes in Mathematics, 1909 .
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.
9783540718079
10.1007/978-3-540-71807-9 doi
Cell aggregation--Mathematics.
Functions of complex variables.
Group theory.
Manifolds and Cell Complexes (incl. Diff.Topology).
Functions of a Complex Variable.
Group Theory and Generalizations.
QA613-613.8 QA613.6-613.66
514.34
Punctured Torus Groups and 2-Bridge Knot Groups (I) [electronic resource] / by Hirotaka Akiyoshi, Makoto Sakuma, Masaaki Wada, Yasushi Yamashita. - XLIII, 256 p. online resource. - Lecture Notes in Mathematics, 1909 0075-8434 ; . - Lecture Notes in Mathematics, 1909 .
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.
9783540718079
10.1007/978-3-540-71807-9 doi
Cell aggregation--Mathematics.
Functions of complex variables.
Group theory.
Manifolds and Cell Complexes (incl. Diff.Topology).
Functions of a Complex Variable.
Group Theory and Generalizations.
QA613-613.8 QA613.6-613.66
514.34