These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 36. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/9, 0/18, 1/36, 1/12, 1/9, 1/4, 1/3, 2/6, 2/3, 1/1, 2/2, 3/3, 5/4, 5/3 2/1, 4/2, 8/3, 3/1, 9/3, 5/1, 7/1, 14/2, 8/1, 10/1, 11/1, 13/1, 15/1, 16/1 17/1, 21/1, 32/1, 33/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.182796) (-0.182692,-0.157015) (-0.156757,-0.154676) (-0.154122,-0.137056) (-0.136910,-0.135707) (-0.135514,-0.134783) (-0.133047,-0.120536) (-0.120423,-0.119491) (-0.119342,-0.118774) (-0.117424,-0.107570) (-0.107480,-0.106737) (-0.106618,-0.106164) (-0.105085,-0.098039) (-0.097049,-0.096443) (-0.095054,-0.092216) (-0.092105,-0.089286) (-0.088464,-0.087960) (-0.086803,-0.084430) (-0.084337,-0.081967) (-0.081274,-0.080848) (-0.079870,-0.077857) (-0.077778,-0.075758) (-0.075165,-0.074801) (-0.073962,-0.072233) (-0.072165,-0.070423) (-0.069910,-0.069595) (-0.068869,-0.067367) (-0.067308,-0.065789) (-0.065342,-0.065067) (-0.064431,-0.063115) (-0.063063,-0.061728) (-0.061334,-0.061092) (-0.060531,-0.059368) (-0.059322,-0.058140) (-0.056000,-0.054945) (-0.053030,-0.052083) (-0.050360,-0.049505) (-0.047945,-0.047170) (-0.045752,-0.045045) (-0.043750,-0.043103) (-0.041916,-0.041322) (-0.040230,-0.039683) (-0.038674,-0.038168) (-0.037234,-0.036765) (-0.035897,-0.035461) (-0.034653,-0.034247) (-0.033493,-0.033113) (-0.032407,-0.032051) (-0.031390,-0.031056) (-0.030435,-0.030120) (-0.029536,-0.029240) (-0.028689,-0.028409) (-0.027888,-0.027624) (-0.027132,-0.026882) (-0.026415,-0.026178) (-0.025735,-0.025510) (-0.025090,-0.024876) (-0.024476,-0.024272) (-0.023891,-0.023697) (-0.023333,-0.023148) (-0.022801,-0.022624) (-0.022293,-0.022124) (-0.021807,-0.021645) (-0.021341,-0.021186) (-0.020896,-0.020747) (-0.020468,-0.020325) (-0.020057,-0.019920) ( 0.019943,0.020080 ) ( 0.020349,0.020492 ) ( 0.020772,0.020921 ) ( 0.021212,0.021368 ) ( 0.021672,0.021834 ) ( 0.022152,0.022321 ) ( 0.022654,0.022831 ) ( 0.023179,0.023364 ) ( 0.023729,0.023923 ) ( 0.024306,0.024510 ) ( 0.024911,0.025126 ) ( 0.025547,0.025773 ) ( 0.026217,0.026455 ) ( 0.026923,0.027174 ) ( 0.027668,0.027933 ) ( 0.028455,0.028736 ) ( 0.029289,0.029586 ) ( 0.030172,0.030488 ) ( 0.031111,0.031447 ) ( 0.032110,0.032468 ) ( 0.033175,0.033557 ) ( 0.034314,0.034722 ) ( 0.035533,0.035971 ) ( 0.036842,0.037313 ) ( 0.038251,0.038760 ) ( 0.039773,0.040323 ) ( 0.041420,0.042017 ) ( 0.043210,0.043860 ) ( 0.045161,0.045872 ) ( 0.047297,0.048077 ) ( 0.049645,0.050505 ) ( 0.052239,0.053191 ) ( 0.055118,0.056180 ) ( 0.058333,0.059524 ) ( 0.059895,0.060128 ) ( 0.060681,0.061897 ) ( 0.061947,0.063291 ) ( 0.063711,0.063975 ) ( 0.064601,0.065981 ) ( 0.066038,0.067568 ) ( 0.068046,0.068347 ) ( 0.069063,0.070642 ) ( 0.070707,0.072464 ) ( 0.073014,0.073361 ) ( 0.074186,0.076012 ) ( 0.076087,0.078125 ) ( 0.078765,0.079169 ) ( 0.080131,0.082265 ) ( 0.082353,0.084746 ) ( 0.085500,0.085976 ) ( 0.087111,0.089639 ) ( 0.089744,0.092593 ) ( 0.093494,0.094063 ) ( 0.095423,0.098465 ) ( 0.098592,0.103053 ) ( 0.103136,0.103829 ) ( 0.103943,0.104377 ) ( 0.105442,0.114894 ) ( 0.114996,0.115859 ) ( 0.116000,0.116541 ) ( 0.117871,0.129808 ) ( 0.129939,0.131041 ) ( 0.131222,0.131915 ) ( 0.133621,0.150803 ) ( 0.151042,0.153025 ) ( 0.153571,0.180851 ) ( 0.180952,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. Number of excluded intervals computed by the fixed point finder: 623 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=(1,35)(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=(1,36)(2,35)(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)", "c=(1,36)(2,35)(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)", "d=(1,35)(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,d,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(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,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "d=(1,2)(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 lambda2: NewSphereMachine( "a=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "b=(1,36)(2,35)(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)", "c=(1,36)(2,35)(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)", "d=<1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*b>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,36)(2,35)(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "c=<1,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "d=(1,36)(2,35)(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");