These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 39. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/13, 0/39, 1/13, 1/3, 2/3, 1/1, 3/3, 4/3, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1 8/1, 9/1, 10/1, 14/1, 16/1, 17/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.676620) (-0.670818,-0.533333) (-0.531388,-0.507520) (-0.489417,-0.476682) (-0.476349,-0.450068) (-0.443556,-0.403239) (-0.396936,-0.375488) (-0.367618,-0.353812) (-0.352696,-0.339004) (-0.313087,-0.298378) (-0.293063,-0.265567) (-0.263957,-0.247021) (-0.246240,-0.015321) ( 0.014799,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 (-0.685534,-0.668525) -23/34 EXTENDED HST -> HST (-0.533554,-0.533112) -8/15 EXTENDED HST (-0.533333,-0.532609) -97/182 HST (-0.532951,-0.532578) -65/122 HST (-0.532774,-0.530713) -25/47 EXTENDED HST -> HST (-0.509369,-0.505174) -34/67 HST (-0.505922,-0.504493) -49/97 HST (-0.504574,-0.495508) -1/2 EXTENDED HST (-0.497098,-0.493360) -52/105 HST (-0.495200,-0.491453) -36/73 HST (-0.493103,-0.487127) -24/49 EXTENDED HST -> HST (-0.480854,-0.473196) -51/107 HST (-0.450691,-0.447894) -9/20 EXTENDED HST -> HST (-0.447930,-0.446390) -17/38 EXTENDED HST -> HST (-0.451829,-0.440619) -29/65 HST (-0.444987,-0.443891) -4/9 EXTENDED HST (-0.404548,-0.402499) -25/62 HST (-0.402965,-0.401646) -33/82 HST (-0.403361,-0.400000) -49/122 HST (-0.400597,-0.399413) -2/5 EXTENDED HST (-0.399544,-0.399199) -127/318 HST (-0.399364,-0.398884) -93/233 HST (-0.399135,-0.398487) -69/173 HST (-0.398817,-0.397937) -51/128 HST (-0.398432,-0.397277) -35/88 HST (-0.397675,-0.395998) -27/68 HST (-0.376445,-0.374553) -98/261 HST (-0.375233,-0.374770) -3/8 EXTENDED HST (-0.375943,-0.369118) -16/43 EXTENDED HST -> HST (-0.371741,-0.366231) -7/19 EXTENDED HST -> HST (-0.355164,-0.348506) -6/17 EXTENDED HST -> HST (-0.339787,-0.337954) -20/59 HST (-0.338798,-0.337017) -49/145 HST (-0.337840,-0.337836) -25/74 EXTENDED HST (-0.337267,-0.329490) -1/3 EXTENDED HST (-0.330498,-0.323652) -14/43 EXTENDED HST -> HST (-0.325085,-0.324465) -13/40 EXTENDED HST -> HST (-0.324338,-0.324311) -12/37 EXTENDED HST (-0.323710,-0.323633) -78/241 HST (-0.324310,-0.322908) -100/309 HST (-0.323542,-0.323517) -11/34 EXTENDED HST (-0.323006,-0.322826) -41/127 HST (-0.323659,-0.321857) -51/158 HST (-0.322596,-0.322565) -10/31 EXTENDED HST (-0.322056,-0.316813) -8/25 EXTENDED HST -> HST (-0.318316,-0.311277) -6/19 EXTENDED HST -> HST (-0.298507,-0.285714) -5/17 EXTENDED HST -> HST (-0.265579,-0.264719) -13/49 EXTENDED HST -> HST (-0.265021,-0.263702) -9/34 EXTENDED HST -> HST (-0.247413,-0.245315) -17/69 HST (-0.019113,-0.011089) -1/66 HST (-0.012021,-0.010148) -11/992 HST (-0.011089,-0.010891) -1/91 HST (-0.012795,-0.007361) -1/99 HST (-0.009404,-0.005386) -1/136 HST (-0.006963,0.007267 ) 0/1 EXTENDED HST ( 0.005320,0.009521 ) 1/134 HST ( 0.007463,0.013422 ) 1/97 HST ( 0.010348,0.018738 ) 1/68 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS FOUND: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 3/1 1 13 No No No No NUMBER OF EQUATORS FOUND: 0 0 0 0 Number of excluded intervals computed by the fixed point finder: 31895 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 either one of the above cycles or 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=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "b=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "c=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "d=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "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,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,c,c,c>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "b=<1,a*b,b,c^-1*b,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,c,b^-1*c,b^-1>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "c=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "d=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "b=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "c=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "d=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "b=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "c=<1,a*b,b,c^-1*b,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,c,b^-1*c,b^-1>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "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,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,b^-1*c,b^-1*d*a*c,c*d^2*a>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -49472/49433. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -49472/49433. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -49472/49433. Imminent integer overflow halted computation of the slope function at slope -4129034/1596221 during the modular group computation. This caused the modular group computation to abort.