These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 40. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/40, 1/40, 1/20, 1/10, 1/8, 1/5, 1/4, 2/8, 2/5, 1/2, 3/5, 3/4, 1/1, 5/5 3/2, 7/4, 2/1, 3/1, 7/2, 9/2, 11/2, 6/1, 7/1, 17/2, 9/1, 11/1, 13/1, 14/1 17/1, 18/1, 19/1, 21/1, 22/1, 23/1, 26/1, 31/1, 37/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-88.450850,-1.011651) ( -0.988615,-0.508889) ( -0.491416,-0.337217) ( -0.329538,-0.315147) ( -0.314517,-0.273074) ( -0.271429,-0.265371) ( -0.264985,-0.255644) ( -0.255466,-0.255180) ( -0.245026,-0.244763) ( -0.244599,-0.236619) ( -0.236313,-0.231707) ( -0.230521,-0.219616) ( -0.219512,-0.211689) ( -0.211482,-0.209718) ( -0.208996,-0.207762) ( -0.207173,-0.203883) ( -0.196263,-0.193307) ( -0.192797,-0.191747) ( -0.191143,-0.189701) ( -0.188813,-0.183673) ( -0.183496,-0.176616) ( -0.175356,-0.173361) ( -0.173077,-0.169811) ( -0.163636,-0.160714) ( -0.160470,-0.158798) ( -0.157373,-0.152665) ( -0.152542,-0.149170) ( -0.148621,-0.147747) ( -0.147389,-0.146774) ( -0.146480,-0.145413) ( -0.140389,-0.139409) ( -0.139144,-0.138596) ( -0.138280,-0.137524) ( -0.137057,-0.134328) ( -0.134233,-0.130793) ( -0.129391,-0.128728) ( -0.128571,-0.127136) ( -0.122935,-0.121622) ( -0.121482,-0.120898) ( -0.119698,-0.116955) ( -0.116883,-0.114893) ( -0.114567,-0.114047) ( -0.113833,-0.113466) ( -0.108852,-0.108516) ( -0.108323,-0.107858) ( -0.107570,-0.105882) ( -0.105823,-0.103674) ( -0.102790,-0.102372) ( -0.102273,-0.101852) ( -0.097736,-0.097357) ( -0.095812,-0.094784) ( -0.094044,-0.093425) ( -0.093209,-0.092865) ( -0.089034,-0.088720) ( -0.088525,-0.087976) ( -0.087338,-0.086483) ( -0.085262,-0.084974) ( -0.081755,-0.081490) ( -0.080405,-0.079679) ( -0.079156,-0.078717) ( -0.075209,-0.074813) ( -0.074351,-0.073730) ( -0.069266,-0.068727) ( -0.068337,-0.068010) ( -0.065376,-0.065076) ( -0.064726,-0.064255) ( -0.060838,-0.060422) ( -0.060120,-0.059867) ( -0.057308,-0.056938) ( -0.054239,-0.053908) ( -0.051415,-0.051117) ( -0.048931,-0.048661) ( -0.046621,-0.046376) ( -0.044569,-0.044345) ( -0.042644,-0.042440) ( -0.040921,-0.040733) ( 0.040733,0.040921 ) ( 0.042440,0.042644 ) ( 0.044345,0.044569 ) ( 0.046376,0.046621 ) ( 0.048661,0.048931 ) ( 0.051117,0.051415 ) ( 0.053908,0.054239 ) ( 0.056938,0.057308 ) ( 0.059867,0.060120 ) ( 0.060422,0.060838 ) ( 0.064255,0.064726 ) ( 0.065076,0.065376 ) ( 0.068010,0.068337 ) ( 0.068727,0.069266 ) ( 0.073730,0.074351 ) ( 0.074813,0.075209 ) ( 0.078717,0.079156 ) ( 0.079679,0.080405 ) ( 0.081490,0.081755 ) ( 0.084974,0.085262 ) ( 0.086483,0.087338 ) ( 0.087976,0.088525 ) ( 0.088720,0.089034 ) ( 0.092865,0.093209 ) ( 0.093425,0.094044 ) ( 0.094784,0.095812 ) ( 0.097357,0.097736 ) ( 0.101852,0.102273 ) ( 0.102372,0.102790 ) ( 0.103674,0.105823 ) ( 0.105882,0.107570 ) ( 0.107858,0.108323 ) ( 0.108516,0.108852 ) ( 0.113466,0.113833 ) ( 0.114047,0.114567 ) ( 0.114893,0.116883 ) ( 0.116955,0.119698 ) ( 0.120898,0.121482 ) ( 0.121622,0.122935 ) ( 0.127136,0.128571 ) ( 0.128728,0.129391 ) ( 0.130793,0.134233 ) ( 0.134328,0.137057 ) ( 0.137524,0.138280 ) ( 0.138596,0.139144 ) ( 0.139409,0.140389 ) ( 0.145413,0.146480 ) ( 0.146774,0.147389 ) ( 0.147747,0.148621 ) ( 0.149170,0.152542 ) ( 0.152665,0.157373 ) ( 0.158798,0.160470 ) ( 0.160714,0.163636 ) ( 0.169811,0.173077 ) ( 0.173361,0.175356 ) ( 0.176616,0.183496 ) ( 0.183673,0.188813 ) ( 0.189701,0.191143 ) ( 0.191747,0.192797 ) ( 0.193307,0.196263 ) ( 0.203883,0.207173 ) ( 0.207762,0.208996 ) ( 0.209718,0.211482 ) ( 0.211689,0.219512 ) ( 0.219616,0.230521 ) ( 0.231707,0.236313 ) ( 0.236619,0.244599 ) ( 0.244763,0.245026 ) ( 0.255180,0.255466 ) ( 0.255644,0.264985 ) ( 0.265371,0.271429 ) ( 0.273074,0.314517 ) ( 0.315147,0.329538 ) ( 0.337217,0.491416 ) ( 0.508889,0.988615 ) ( 1.011651,88.450850) 1/0 is the slope of a Thurston obstruction with c = 1 and d = 1. These NET maps are not rational. SLOPE FUNCTION INFORMATION EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 1/0 1 1 No No No No 2N/1 1 40 Yes Yes No No The fixed point finder is unable to determine whether there are any more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 8082 No nontrivial cycles were found. 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=(1,39)(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=(1,40)(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=(1,40)(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=(1,39)(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=(1,2)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)", "b=(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "c=(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "d=(1,2)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "b=(1,40)(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=(1,40)(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=(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,40)(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=(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "c=(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "d=(1,40)(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 halted evaluation of the slope function at slope -1234028/594255 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -861922/420171 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -2719140/1342381 during the search for all slope function fixed points. Imminent integer overflow halted computation of the slope function at slope -314748/1081379 during the modular group computation. This caused the modular group computation to abort.