These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 35. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/5, 0/7, 0/35, 1/7, 1/5, 2/7, 2/5, 1/1, 2/1, 4/1, 5/1, 6/1, 7/1, 8/1, 10/1 11/1, 12/1, 14/1, 15/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.506633) (-0.488303,-0.481654) (-0.480370,-0.415558) (-0.411178,-0.402690) (-0.396174,-0.337272) (-0.328100,-0.131019) (-0.130310,-0.054054) (-0.051721,-0.027462) (-0.025339,-0.024670) (-0.024174,-0.023456) (-0.022489,-0.021961) (-0.020675,-0.019788) ( 0.019788,0.020675 ) ( 0.021961,0.022489 ) ( 0.023456,0.024174 ) ( 0.024670,0.025339 ) ( 0.026869,infinity ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-0.506977,-0.506228) -77/152 HST (-0.506570,-0.506419) -39/77 HST (-0.507842,-0.504626) -41/81 HST (-0.505102,-0.495000) -1/2 EXTENDED HST (-0.495396,-0.493039) -43/87 HST (-0.494187,-0.491025) -32/65 HST (-0.492267,-0.483459) -21/43 EXTENDED HST -> HST (-0.486408,-0.478665) -13/27 EXTENDED HST -> HST (-0.422866,-0.407206) -12/29 EXTENDED HST -> HST (-0.412118,-0.409265) -7/17 EXTENDED HST -> HST (-0.403716,-0.401453) -31/77 HST (-0.402492,-0.397377) -2/5 EXTENDED HST (-0.398270,-0.395340) -21/53 HST (-0.337373,-0.336938) -29/86 HST (-0.338347,-0.335180) -32/95 HST (-0.335971,-0.334351) -61/182 HST (-0.334538,-0.332138) -1/3 EXTENDED HST (-0.332397,-0.330861) -67/202 HST (-0.331661,-0.329094) -36/109 HST (-0.330194,-0.328541) -28/85 HST (-0.329409,-0.326603) -21/64 HST (-0.140273,-0.115360) -3/23 EXTENDED HST -> HST (-0.060590,-0.046325) -1/19 EXTENDED HST -> HST (-0.030535,-0.022976) -1/37 EXTENDED HST -> HST (-0.025746,-0.019324) -1/44 EXTENDED HST -> HST (-0.019417,-0.018692) -1/52 HST (-0.021293,-0.015944) -1/54 HST (-0.016034,-0.015715) -1/63 HST (-0.017355,-0.014091) -3/191 HST (-0.015629,-0.015621) -1/64 EXTENDED HST (-0.014580,-0.014003) -1/71 HST (-0.015821,-0.011813) -1/72 HST (-0.011839,-0.011691) -1/85 HST (-0.013218,-0.009925) -1/86 HST (-0.012848,-0.006800) -1/101 HST (-0.008796,0.009287 ) 0/1 EXTENDED HST ( 0.006674,0.013090 ) 1/102 HST ( 0.009822,0.013356 ) 1/86 HST ( 0.011668,0.016018 ) 1/72 HST ( 0.013958,0.019034 ) 1/61 HST ( 0.016481,0.022515 ) 1/51 HST ( 0.018939,0.026272 ) 1/44 EXTENDED HST -> HST ( 0.023246,0.023266 ) 1/43 EXTENDED HST ( 0.017333,0.035051 ) 1/38 EXTENDED HST -> HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points p/q with |p| <= 50 and |q| <= 50. Number of excluded intervals computed by the fixed point finder: 36631 The union of the excluded intervals computed by the fixed point finder became a union of 10,000 disjoint intervals: the search for all slope function fixed points aborted. No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in the nonslope. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "b=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "c=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=<1,a*b,b,c^-1*b,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,b^-1*c,b^-1>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "b=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "d=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "b=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=<1,a*b,b,c^-1*b,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,b^-1*c,b^-1>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=<1,b*c*a*b,c^-1*b*c*b,c^-1*b,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,b^-1*c,b^-1*d*a*c,c*d^2*a>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow halted evaluation of the slope function at slope 218926850/68437671 while computing a fixed point excluded interval about -7721957/24701947. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -239781/767041. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -183991/588996. Imminent integer overflow caused the modular group computation to abort.