LEADER 03003nam 2200649 450 001 996466610003316 005 20210218181636.0 010 $a1-280-86407-9 010 $a9786610864072 010 $a3-540-71807-9 024 7 $a10.1007/978-3-540-71807-9 035 $a(CKB)1000000000282913 035 $a(EBL)3036691 035 $a(SSID)ssj0000307388 035 $a(PQKBManifestationID)11212496 035 $a(PQKBTitleCode)TC0000307388 035 $a(PQKBWorkID)10244780 035 $a(PQKB)11463391 035 $a(DE-He213)978-3-540-71807-9 035 $a(MiAaPQ)EBC3036691 035 $a(MiAaPQ)EBC6351769 035 $a(PPN)123161606 035 $a(EXLCZ)991000000000282913 100 $a20210218d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aPunctured torus groups and 2-bridge knot groups (I). /$fHirotaka Akiyoshi 205 $a1st ed. 2007. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2007] 210 4$dİ2007 215 $a1 online resource (xliii, 252 p.) 225 1 $aLecture notes in mathematics ;$v1909 300 $aDescription based upon print version of record. 311 $a3-540-71806-0 311 $a978-3-540-71806-2 320 $aIncludes bibliographical references (pages [239]-243) and index. 327 $aJorgensen'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. 330 $aThis monograph is Part 1 of a book project intended to give a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization, with application to knot theory. Although Jorgensen's original work was not published in complete form, it has been a source of inspiration. In particular, it has motivated and guided Thurston's revolutionary study of low-dimensional geometric topology. In this monograph, we give an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1909. 606 $aTorus (Geometry) 606 $aKnot theory 606 $aKleinian groups 615 0$aTorus (Geometry) 615 0$aKnot theory. 615 0$aKleinian groups. 676 $a515.93 702 $aAkiyoshi$b Hirotaka 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466610003316 996 $aPunctured torus groups and 2-bridge knot groups (I$9230605 997 $aUNISA