These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 30. 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 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/3, 0/5, 0/6, 0/15, 0/30, 1/30, 1/10, 1/6, 2/5, 1/2, 3/6, 2/2, 4/3, 3/2 2/1, 4/2, 5/2, 8/3, 4/1, 6/1, 8/1, 10/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.225886) (-1.224731,-1.214802) (-1.211058,-1.210044) (-1.205251,-1.205011) (-1.195228,-1.195011) (-1.193733,-1.193353) (-1.185869,-1.183516) (-1.183211,-1.180173) (-1.179938,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 (-1.226258,-1.225531) -521/425 HST (-1.225872,-1.225740) -38/31 EXTENDED HST (-1.236157,-1.218515) -49/40 EXTENDED HST -> HST (-1.215387,-1.214154) -181/149 HST (-1.214346,-1.214226) -17/14 EXTENDED HST (-1.214207,-1.211344) -40/33 EXTENDED HST -> HST (-1.213238,-1.209959) -86/71 HST (-1.215165,-1.204463) -52/43 HST (-1.208649,-1.206942) -29/24 EXTENDED HST -> HST (-1.204727,-1.196890) -6/5 EXTENDED HST (-1.197007,-1.195418) -61/51 HST (-1.195962,-1.195290) -55/46 HST (-1.195634,-1.195015) -202/169 HST (-1.195111,-1.194745) -141/118 HST (-1.194851,-1.194519) -92/77 HST (-1.194580,-1.194450) -479/401 HST (-1.194454,-1.194435) -43/36 EXTENDED HST (-1.194438,-1.194422) -2273/1903 HST (-1.194430,-1.193951) -123/103 HST (-1.194103,-1.193962) -80/67 EXTENDED HST (-1.194021,-1.193756) -117/98 HST (-1.193788,-1.193679) -191/160 HST (-1.193806,-1.192084) -31/26 EXTENDED HST -> HST (-1.192408,-1.191663) -391/328 HST (-1.192058,-1.191941) -149/125 HST (-1.191926,-1.191913) -118/99 EXTENDED HST (-1.191911,-1.191672) -87/73 HST (-1.191904,-1.191340) -199/167 HST (-1.191518,-1.191461) -56/47 EXTENDED HST (-1.191472,-1.190922) -81/68 HST (-1.190923,-1.190916) -892/749 HST (-1.190920,-1.190826) -131/110 HST (-1.190833,-1.190792) -337/283 HST (-1.190808,-1.190640) -181/152 HST (-1.190675,-1.190576) -356/299 HST (-1.190601,-1.190361) -25/21 EXTENDED HST (-1.190406,-1.190157) -319/268 HST (-1.190294,-1.190145) -194/163 HST (-1.190145,-1.190143) -2222/1867 HST (-1.190145,-1.190141) -3574/3003 HST (-1.190142,-1.190139) -169/142 EXTENDED HST (-1.190154,-1.190124) -3524/2961 HST (-1.190138,-1.190091) -313/263 HST (-1.190099,-1.189987) -119/100 HST (-1.189989,-1.189956) -332/279 HST (-1.189963,-1.189924) -213/179 HST (-1.189944,-1.189883) -307/258 HST (-1.189884,-1.189863) -94/79 EXTENDED HST (-1.189888,-1.189837) -1291/1085 HST (-1.189861,-1.189482) -69/58 HST (-1.189495,-1.189455) -113/95 HST (-1.189507,-1.189197) -157/132 HST (-1.189225,-1.189154) -44/37 EXTENDED HST (-1.189197,-1.189102) -855/719 HST (-1.189150,-1.189099) -547/460 HST (-1.189129,-1.188835) -107/90 HST (-1.188879,-1.188422) -63/53 HST (-1.188425,-1.188415) -1129/950 HST (-1.188419,-1.188392) -82/69 EXTENDED HST (-1.188419,-1.188329) -675/568 HST (-1.188380,-1.188350) -347/292 HST (-1.188341,-1.188176) -101/85 HST (-1.188740,-1.187912) -120/101 HST (-1.188157,-1.187747) -196/165 HST (-1.187772,-1.187681) -310/261 HST (-1.187701,-1.187635) -424/357 HST (-1.187716,-1.187558) -557/469 HST (-1.187576,-1.187538) -1298/1093 HST (-1.187541,-1.187458) -19/16 EXTENDED HST (-1.187697,-1.186806) -260/219 HST (-1.187192,-1.187080) -184/155 HST (-1.187097,-1.186992) -165/139 HST (-1.187027,-1.186803) -127/107 HST (-1.186882,-1.186727) -108/91 HST (-1.186771,-1.186575) -89/75 HST (-1.186601,-1.186531) -159/134 HST (-1.186533,-1.186352) -70/59 EXTENDED HST (-1.186419,-1.185730) -51/43 HST (-1.183541,-1.183435) -129/109 HST (-1.183501,-1.183313) -200/169 HST (-1.183342,-1.183325) -71/60 EXTENDED HST (-1.183328,-1.183133) -226/191 HST (-1.180393,-1.179948) -190/161 HST (-1.180044,-1.179411) -59/50 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 5/6 2 5 No No No No NUMBER OF EQUATORS: 0 0 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 14656 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 either one of the above cycles or the nonslope. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "b=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "c=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "d=<1,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "c=<1,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "d=<1,1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(1,2)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "b=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "c=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "d=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "b=<1,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "c=(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "d=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.