These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 34. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 14. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/17, 0/34, 1/2, 1/1, 2/2, 3/2, 4/2, 5/2, 3/1, 4/1, 5/1, 7/1, 8/1, 9/1 11/1, 13/1, 19/1, 25/1, 31/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.000000) (-1.000000,-0.504535) (-0.495899,-0.335259) ( 0.335259,1.000000 ) ( 1.000000,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 (-1.021238,-0.979626) -1/1 EXTENDED HST (-0.505146,-0.494746) -1/2 EXTENDED HST (-0.335660,-0.331038) -1/3 EXTENDED HST (-0.331430,-0.322537) -17/52 HST (-0.326923,-0.314815) -10/31 EXTENDED HST -> HST (-0.322121,-0.307833) -5/16 EXTENDED HST -> HST (-0.312392,-0.295236) -3/10 EXTENDED HST -> HST (-0.299426,-0.287042) -5/17 EXTENDED HST -> HST (-0.310413,-0.263427) -31/108 HST (-0.286698,-0.284737) -2/7 EXTENDED HST (-0.275195,-0.247357) -5/19 EXTENDED HST -> HST (-0.254022,-0.238574) -1/4 EXTENDED HST -> HST (-0.245844,-0.212912) -2/9 EXTENDED HST -> HST (-0.213606,-0.206275) -4/19 EXTENDED HST -> HST (-0.207317,-0.202381) -7/34 EXTENDED HST -> HST (-0.204099,-0.200692) -17/84 HST (-0.200835,-0.199172) -1/5 EXTENDED HST (-0.199313,-0.196062) -17/86 HST (-0.197674,-0.193182) -10/51 HST (-0.195908,-0.190530) -5/26 EXTENDED HST -> HST (-0.192267,-0.185628) -3/16 EXTENDED HST -> HST (-0.187276,-0.182355) -5/27 EXTENDED HST -> HST (-0.197233,-0.167379) -31/170 HST (-0.182216,-0.181422) -2/11 EXTENDED HST (-0.170741,-0.159277) -1/6 EXTENDED HST -> HST (-0.169565,-0.144888) -2/13 EXTENDED HST -> HST (-0.145755,-0.143622) -11/76 HST (-0.144068,-0.143258) -27/188 HST (-0.143283,-0.142434) -1/7 EXTENDED HST (-0.142506,-0.140837) -17/120 HST (-0.141667,-0.139344) -10/71 HST (-0.140757,-0.137959) -5/36 EXTENDED HST -> HST (-0.138867,-0.135371) -3/22 EXTENDED HST -> HST (-0.136245,-0.133622) -5/37 EXTENDED HST -> HST (-0.144534,-0.122657) -31/232 HST (-0.133547,-0.133120) -2/15 EXTENDED HST (-0.128585,-0.119543) -1/8 EXTENDED HST -> HST (-0.129412,-0.109806) -2/17 EXTENDED HST -> HST (-0.111368,-0.110855) -1/9 EXTENDED HST (-0.109837,-0.108125) -5/46 EXTENDED HST -> HST (-0.108683,-0.106529) -3/28 EXTENDED HST -> HST (-0.107070,-0.105443) -5/47 EXTENDED HST -> HST (-0.114059,-0.096794) -31/294 HST (-0.105396,-0.105130) -2/19 EXTENDED HST (-0.103124,-0.095676) -1/10 EXTENDED HST -> HST (-0.104635,-0.088401) -2/21 EXTENDED HST -> HST (-0.091081,-0.090738) -1/11 EXTENDED HST (-0.089277,-0.087818) -3/34 EXTENDED HST -> HST (-0.088186,-0.087079) -5/57 HST (-0.094197,-0.079939) -31/356 HST (-0.087047,-0.086866) -2/23 EXTENDED HST (-0.086079,-0.079753) -1/12 EXTENDED HST -> HST (-0.079897,-0.078987) -5/63 HST (-0.079284,-0.078132) -3/38 EXTENDED HST -> HST (-0.078422,-0.077546) -5/64 HST (-0.077982,-0.077273) -10/129 HST (-0.077522,-0.077025) -17/220 HST (-0.077046,-0.076800) -1/13 EXTENDED HST (-0.076821,-0.076333) -17/222 HST (-0.076577,-0.075893) -10/131 HST (-0.076310,-0.075480) -5/66 HST (-0.075751,-0.074699) -3/40 EXTENDED HST -> HST (-0.074964,-0.074163) -5/67 HST (-0.080227,-0.068083) -31/418 HST (-0.074140,-0.074008) -2/27 EXTENDED HST (-0.073870,-0.068373) -1/14 EXTENDED HST -> HST (-0.068113,-0.067350) -4/59 HST (-0.067460,-0.066929) -7/104 HST (-0.067116,-0.066743) -17/254 HST (-0.066759,-0.066574) -1/15 EXTENDED HST (-0.066590,-0.066223) -17/256 HST (-0.066406,-0.065891) -10/151 HST (-0.066206,-0.065580) -5/76 HST (-0.065785,-0.064989) -3/46 EXTENDED HST -> HST (-0.065190,-0.064584) -5/77 HST (-0.064694,-0.059836) -1/16 EXTENDED HST -> HST (-0.059947,-0.059355) -4/67 HST (-0.059441,-0.059028) -7/118 HST (-0.059173,-0.058883) -17/288 HST (-0.058896,-0.058752) -1/17 EXTENDED HST (-0.058764,-0.058478) -17/290 HST (-0.058621,-0.058219) -10/171 HST (-0.058464,-0.057976) -5/86 HST (-0.058136,-0.057514) -3/52 HST (-0.057545,-0.053194) -1/18 EXTENDED HST -> HST (-0.055553,0.062508 ) 0/1 EXTENDED HST ( 0.062377,0.062638 ) 512/8191 HST ( 0.057409,0.070007 ) 3/47 EXTENDED HST -> HST ( 0.064466,0.064566 ) 2/31 EXTENDED HST ( 0.066574,0.066759 ) 1/15 EXTENDED HST ( 0.068542,0.074937 ) 1/14 EXTENDED HST -> HST ( 0.074699,0.075751 ) 3/40 EXTENDED HST -> HST ( 0.075480,0.076310 ) 5/66 HST ( 0.075893,0.076577 ) 10/131 HST ( 0.076333,0.076821 ) 17/222 HST ( 0.076800,0.077046 ) 1/13 EXTENDED HST ( 0.077025,0.077522 ) 17/220 HST ( 0.077273,0.077982 ) 10/129 HST ( 0.077546,0.078422 ) 5/64 HST ( 0.078132,0.079284 ) 3/38 EXTENDED HST -> HST ( 0.078987,0.079897 ) 5/63 HST ( 0.073363,0.086449 ) 31/388 HST ( 0.079982,0.087532 ) 1/12 EXTENDED HST -> HST ( 0.087079,0.088186 ) 5/57 HST ( 0.087818,0.089277 ) 3/34 EXTENDED HST -> HST ( 0.088901,0.090054 ) 5/56 HST ( 0.089474,0.090426 ) 10/111 HST ( 0.090087,0.090767 ) 17/188 HST ( 0.090738,0.091081 ) 1/11 EXTENDED HST ( 0.086827,0.106532 ) 2/21 EXTENDED HST -> HST ( 0.096006,0.105216 ) 1/10 EXTENDED HST -> HST ( 0.106529,0.108683 ) 3/28 EXTENDED HST -> HST ( 0.108125,0.109837 ) 5/46 EXTENDED HST -> HST ( 0.108974,0.110390 ) 10/91 HST ( 0.109885,0.110899 ) 17/154 HST ( 0.110855,0.111368 ) 1/9 EXTENDED HST ( 0.107388,0.132327 ) 2/17 EXTENDED HST -> HST ( 0.120059,0.131854 ) 1/8 EXTENDED HST -> HST ( 0.123552,0.141176 ) 9/68 HST ( 0.133120,0.133547 ) 2/15 EXTENDED HST ( 0.140072,0.142100 ) 12/85 HST ( 0.141667,0.142458 ) 27/190 HST ( 0.142434,0.143283 ) 1/7 EXTENDED HST ( 0.140707,0.174604 ) 2/13 EXTENDED HST -> HST ( 0.160194,0.176554 ) 1/6 EXTENDED HST -> HST ( 0.163942,0.194345 ) 5/28 EXTENDED HST -> HST ( 0.181422,0.182216 ) 2/11 EXTENDED HST ( 0.193182,0.197674 ) 7/36 EXTENDED HST -> HST ( 0.196062,0.199313 ) 17/86 HST ( 0.199172,0.200835 ) 1/5 EXTENDED HST ( 0.200787,0.202381 ) 27/134 HST ( 0.201503,0.205727 ) 11/54 HST ( 0.204004,0.256579 ) 2/9 EXTENDED HST -> HST ( 0.240638,0.267104 ) 1/4 EXTENDED HST -> HST ( 0.238752,0.302531 ) 3/11 EXTENDED HST -> HST ( 0.284738,0.286698 ) 2/7 EXTENDED HST ( 0.301342,0.317248 ) 4/13 EXTENDED HST -> HST ( 0.314815,0.326923 ) 7/22 EXTENDED HST -> HST ( 0.322537,0.331430 ) 17/52 HST ( 0.331039,0.335660 ) 1/3 EXTENDED HST ( 0.979627,1.021240 ) 1/1 EXTENDED 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: 30164 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 |p'| <= |p| for every slope p/q with |p| <= 50 and |q| <= 50. 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=(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=(1,34)(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=(1,34)(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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c>(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=(1,2)(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=(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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c>(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,d,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c>(1,2)(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"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,33)(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "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=(1,34)(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=(1,33)(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: 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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c>(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=(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=(1,34)(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"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.