These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 32. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/8, 0/16, 1/32, 2/4, 1/1, 2/2, 4/4, 2/1, 4/2, 3/1, 4/1, 5/1, 6/1, 12/2 7/1, 9/1, 10/1, 11/1, 12/1, 13/1, 15/1, 17/1, 20/1, 23/1, 28/1, 29/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.183313) (-0.182049,-0.155007) (-0.153076,-0.136933) (-0.136709,-0.134205) (-0.132032,-0.120441) (-0.120268,-0.118325) (-0.116633,-0.107494) (-0.107356,-0.105805) (-0.104450,-0.097898) (-0.096948,-0.096579) (-0.094572,-0.092842) (-0.092168,-0.089168) (-0.088380,-0.088073) (-0.086401,-0.084954) (-0.084390,-0.081868) (-0.081203,-0.080944) (-0.079530,-0.078302) (-0.077822,-0.075673) (-0.075104,-0.074883) (-0.073671,-0.072616) (-0.072203,-0.070350) (-0.069858,-0.069666) (-0.068616,-0.067700) (-0.067341,-0.065726) (-0.065296,-0.065129) (-0.064210,-0.063407) (-0.063092,-0.061672) (-0.061294,-0.061146) (-0.060336,-0.059627) (-0.059348,-0.058090) (-0.056023,-0.054901) (-0.053051,-0.052043) (-0.050378,-0.049469) (-0.047962,-0.047137) (-0.045767,-0.045015) (-0.043764,-0.043076) (-0.041929,-0.041297) (-0.040242,-0.039659) (-0.038685,-0.038146) (-0.037244,-0.036745) (-0.035907,-0.035442) (-0.034662,-0.034229) (-0.033501,-0.033096) (-0.032415,-0.032036) (-0.031397,-0.031042) (-0.030442,-0.030107) (-0.029542,-0.029227) (-0.028695,-0.028397) (-0.027894,-0.027613) (-0.027137,-0.026871) (-0.026420,-0.026168) (-0.025740,-0.025501) (-0.025094,-0.024867) (-0.024480,-0.024263) (-0.023895,-0.023688) (-0.023337,-0.023140) (-0.022805,-0.022617) (-0.022297,-0.022117) (-0.021810,-0.021638) (-0.021345,-0.021180) (-0.020899,-0.020741) (-0.020471,-0.020319) (-0.020060,-0.019914) ( 0.019940,0.020086 ) ( 0.020346,0.020498 ) ( 0.020768,0.020927 ) ( 0.021209,0.021374 ) ( 0.021668,0.021841 ) ( 0.022148,0.022329 ) ( 0.022650,0.022839 ) ( 0.023175,0.023373 ) ( 0.023725,0.023932 ) ( 0.024301,0.024519 ) ( 0.024906,0.025135 ) ( 0.025543,0.025783 ) ( 0.026212,0.026465 ) ( 0.026918,0.027185 ) ( 0.027662,0.027944 ) ( 0.028449,0.028748 ) ( 0.029282,0.029599 ) ( 0.030166,0.030502 ) ( 0.031104,0.031461 ) ( 0.032103,0.032483 ) ( 0.033167,0.033574 ) ( 0.034305,0.034740 ) ( 0.035524,0.035990 ) ( 0.036832,0.037334 ) ( 0.038241,0.038782 ) ( 0.039761,0.040347 ) ( 0.041407,0.042043 ) ( 0.043196,0.043888 ) ( 0.045146,0.045903 ) ( 0.047281,0.048111 ) ( 0.049627,0.050543 ) ( 0.052219,0.053233 ) ( 0.055096,0.056226 ) ( 0.058308,0.059576 ) ( 0.059933,0.060075 ) ( 0.060879,0.061618 ) ( 0.061919,0.063350 ) ( 0.063754,0.063915 ) ( 0.064825,0.065664 ) ( 0.066006,0.067635 ) ( 0.068096,0.068279 ) ( 0.069319,0.070279 ) ( 0.070670,0.072541 ) ( 0.073072,0.073283 ) ( 0.074482,0.075592 ) ( 0.076044,0.078215 ) ( 0.078832,0.079078 ) ( 0.080476,0.081773 ) ( 0.082303,0.084852 ) ( 0.085578,0.085868 ) ( 0.087519,0.089055 ) ( 0.089684,0.092719 ) ( 0.093587,0.093934 ) ( 0.095913,0.097762 ) ( 0.098520,0.103123 ) ( 0.103250,0.104726 ) ( 0.106089,0.114980 ) ( 0.115138,0.116977 ) ( 0.118679,0.129918 ) ( 0.130120,0.132473 ) ( 0.134661,0.152702 ) ( 0.154625,0.180347 ) ( 0.181588,infinity ) 1/0 is the slope of a Thurston obstruction with c = 1 and d = 1. These NET maps are not rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 1/0 1 1 No No No No NUMBER OF EQUATORS: 0 0 0 0 There are no more slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and there can be at most one obstruction. No nontrivial cycles were found. "INFINITE CYCLES" -> N/1 -> (N-1)/1 -> The slope function maps some slope to the nonslope. If the slope function maps slope s to a slope s' and if the intersection pairing of s with 1/0 is n, then the intersection pairing of s' with 1/0 is at most n. The slope function orbit of every slope whose intersection pairing with 1/0 is at most 50 ends in either the nonslope or one of the slopes described above. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(1,31)(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=(1,32)(2,31)(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)", "c=(1,32)(2,31)(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)", "d=(1,31)(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,d,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(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,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(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)", "d=(1,2)(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 lambda2: NewSphereMachine( "a=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(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=(1,32)(2,31)(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)", "c=(1,32)(2,31)(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)", "d=<1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*b>(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=(1,32)(2,31)(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(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)", "c=<1,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)", "d=(1,32)(2,31)(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");