03003nam 2200649 450 99646661000331620210218181636.01-280-86407-997866108640723-540-71807-910.1007/978-3-540-71807-9(CKB)1000000000282913(EBL)3036691(SSID)ssj0000307388(PQKBManifestationID)11212496(PQKBTitleCode)TC0000307388(PQKBWorkID)10244780(PQKB)11463391(DE-He213)978-3-540-71807-9(MiAaPQ)EBC3036691(MiAaPQ)EBC6351769(PPN)123161606(EXLCZ)99100000000028291320210218d2007 uy 0engur|n|---|||||txtccrPunctured torus groups and 2-bridge knot groups (I). /Hirotaka Akiyoshi1st ed. 2007.Berlin, Germany ;New York, New York :Springer,[2007]©20071 online resource (xliii, 252 p.)Lecture notes in mathematics ;1909Description based upon print version of record.3-540-71806-0 978-3-540-71806-2 Includes bibliographical references (pages [239]-243) and index.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.Lecture notes in mathematics (Springer-Verlag) ;1909.Torus (Geometry)Knot theoryKleinian groupsTorus (Geometry)Knot theory.Kleinian groups.515.93Akiyoshi HirotakaMiAaPQMiAaPQMiAaPQBOOK996466610003316Punctured torus groups and 2-bridge knot groups (I230605UNISA