LEADER 04196nam 2200613 450 001 9910827874503321 005 20180731044137.0 010 $a1-4704-0140-1 035 $a(CKB)3360000000464745 035 $a(EBL)3113846 035 $a(SSID)ssj0000889285 035 $a(PQKBManifestationID)11488400 035 $a(PQKBTitleCode)TC0000889285 035 $a(PQKBWorkID)10876376 035 $a(PQKB)10237412 035 $a(MiAaPQ)EBC3113846 035 $a(RPAM)2559333 035 $a(PPN)195414438 035 $a(EXLCZ)993360000000464745 100 $a20140904h19951995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTwo-generator discrete subgroups of PSL (2, R) /$fJane Gilman 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1995. 210 4$dİ1995 215 $a1 online resource (221 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 117, Number 561 300 $a"September 1995, volume 117, number 561 (fourth of 5 numbers)." 311 $a0-8218-0361-1 320 $aIncludes bibliographical references. 327 $a""Contents""; ""I: Introduction""; ""1 Introduction""; ""1.1 Overview Intersecting Axes""; ""1.2 Overview of the intertwining cases""; ""1.3 Why an algorithm is needed""; ""2 The Acute Triangle Theorem""; ""2.1 Nielsen equivalence""; ""2.2 Idea of proof: Acute triangle theorem""; ""2.3 Labeling Conventions""; ""2.4 Ascending order conventions""; ""2.5 The Triangle Algorithm""; ""2.6 Q and the last triangle along A""; ""2.7 Combining triangle algorithm steps""; ""2.8 The sides and heights converge to 0""; ""2.9 Acute triangle theorem: proof""; ""3 Discreteness Theorem Proof Outline"" 327 $a""3.1 The Discreteness Theorem""""3.2 Discreteness theorem""; ""3.3 Geometric equivalence theorems""; ""II: Preliminaries""; ""4 Triangle Groups and their Tilings""; ""4.1 Basic facts about triangle groups""; ""4.2 Minimal tiling distances""; ""4.3 The wedge at a vertex""; ""4.4 Proofs of lemmas and theorems""; ""4.5 Additional Notation""; ""4.6 Distances in the extended wedge""; ""5 Pentagons""; ""5.1 Constructing the pentagon, P[sub(A,B)]""; ""5.2 Notation""; ""5.3 Applying the Poincare Polygon Theorem""; ""5.4 Pentagon Tilings""; ""5.5 Distances in the shingling"" 327 $a""8.4 Pentagon distances (2,3, n) t = 3 k = 3""; ""9 Nielsen Eq: (2,3, n) t = 3; k = 3""; ""9.1 Introduction""; ""9.2 Types of triples: distances""; ""9.3 Locating t[sub(2)] and t[sub(3)]""; ""10 Nielsen Eq: (2,4, n) t = 2; k = 2""; ""10.1 Introduction""; ""10.2 Types of triples""; ""10.3 Location of t[sub(1)],t[sub(2)] and t[sub(3)]""; ""11 Pentagon t = 9 & 2a???2 Spectrum""; ""11.1 Step 1: Label the wedge""; ""11.2 Step 2: Double and Extend""; ""11.3 Step 3: Drop perpendiculars""; ""11.4 The twoa???two spectrum""; ""11.5 More distance computations""; ""11.6 Distances to qA??[sub(0)]"" 327 $a""11.7 Locate three order two points""""12 The Seven & Geometric Eq t = 9""; ""12.1 Introduction""; ""12.2 The variation of h and b""; ""12.3 Rule out a seven on the I?² side""; ""12.4 Rule out a seven on the D side""; ""12.5 Interior sevens""; ""12.6 Notation""; ""12.7 Geometric equivalence (2,3, 7) t = 9; k = 2""; ""13 Discreteness Theorem Proof""; ""13.1 The Proof of the Discreteness Theorem""; ""13.2 The proof of sufficiency""; ""IV: The Real Number Algorithm and the Turing Machine Algorithm""; ""14 Forms of the Algorithm""; ""14.1 What is an algorithm?"" 327 $a""14.2 The Elliptic Order Algorithm"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 117, Number 561. 606 $aFuchsian groups 606 $aKleinian groups 606 $aTeichmu?ller spaces 615 0$aFuchsian groups. 615 0$aKleinian groups. 615 0$aTeichmu?ller spaces. 676 $a515/.223 700 $aGilman$b Jane$f1945-$01606330 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827874503321 996 $aTwo-generator discrete subgroups of PSL (2, R)$93932076 997 $aUNINA