These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 37. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/37, 1/37, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1, 12/1 13/1, 14/1, 15/1, 16/1, 17/1, 18/1, 19/1, 20/1, 21/1, 22/1, 23/1, 24/1, 25/1 28/1, 31/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-42.830952,-31.169048) (-29.025098,-1.017290 ) ( -0.983288,-0.610016 ) ( -0.608496,-0.599335 ) ( -0.595990,-0.592797 ) ( -0.592288,-0.572075 ) ( -0.568695,-0.567676 ) ( -0.567405,-0.565944 ) ( -0.563811,-0.561241 ) ( -0.559398,-0.558260 ) ( -0.558220,-0.534817 ) ( -0.531574,-0.530932 ) ( -0.528639,-0.521239 ) ( -0.520977,-0.520692 ) ( -0.480424,-0.474304 ) ( -0.472474,-0.471966 ) ( -0.469439,-0.452777 ) ( -0.452751,-0.452005 ) ( -0.450809,-0.449164 ) ( -0.447820,-0.446909 ) ( -0.443098,-0.432595 ) ( -0.432324,-0.431305 ) ( -0.425611,-0.424378 ) ( -0.423603,-0.422625 ) ( -0.421795,-0.401058 ) ( -0.397859,-0.367165 ) ( -0.367017,-0.338832 ) ( -0.327190,-0.315423 ) ( -0.315179,-0.305313 ) ( -0.303519,-0.296915 ) ( -0.295996,-0.286835 ) ( -0.285177,-0.279889 ) ( -0.279638,-0.275544 ) ( -0.275191,-0.274778 ) ( -0.271123,-0.267154 ) ( -0.264996,-0.264427 ) ( -0.263754,-0.258411 ) ( -0.240718,-0.237609 ) ( -0.237066,-0.236610 ) ( -0.234916,-0.231976 ) ( -0.229321,-0.229034 ) ( -0.228790,-0.226043 ) ( -0.225404,-0.224582 ) ( -0.221549,-0.216376 ) ( -0.215888,-0.212525 ) ( -0.209445,-0.207160 ) ( -0.207054,-0.203856 ) ( -0.196287,-0.193411 ) ( -0.193319,-0.191370 ) ( -0.188869,-0.186290 ) ( -0.185928,-0.182271 ) ( -0.180268,-0.179742 ) ( -0.179338,-0.177646 ) ( -0.175771,-0.174120 ) ( -0.159825,-0.158459 ) ( -0.156966,-0.155668 ) ( -0.153523,-0.151021 ) ( -0.150783,-0.149135 ) ( -0.147612,-0.146473 ) ( -0.146420,-0.145278 ) ( -0.140516,-0.139463 ) ( -0.139416,-0.138399 ) ( -0.137086,-0.135723 ) ( -0.131995,-0.131076 ) ( -0.119463,-0.118709 ) ( -0.115848,-0.114872 ) ( -0.113966,-0.113286 ) ( -0.109018,-0.108396 ) ( -0.107588,-0.106747 ) ( -0.104427,-0.103851 ) ( -0.094055,-0.093412 ) ( -0.088537,-0.087966 ) ( -0.079164,-0.078707 ) ( -0.075218,-0.074806 ) ( -0.068343,-0.068003 ) ( -0.065382,-0.065070 ) ( -0.060125,-0.059861 ) ( 0.059861,0.060125 ) ( 0.065070,0.065382 ) ( 0.068003,0.068343 ) ( 0.074806,0.075218 ) ( 0.078707,0.079164 ) ( 0.087966,0.088537 ) ( 0.093412,0.094055 ) ( 0.103851,0.104427 ) ( 0.106747,0.107588 ) ( 0.108396,0.109018 ) ( 0.113286,0.113966 ) ( 0.114872,0.115848 ) ( 0.118709,0.119463 ) ( 0.131076,0.131995 ) ( 0.135723,0.137086 ) ( 0.138399,0.139416 ) ( 0.139463,0.140516 ) ( 0.145278,0.146420 ) ( 0.146473,0.147612 ) ( 0.149135,0.150783 ) ( 0.151021,0.153523 ) ( 0.155668,0.156966 ) ( 0.158459,0.159825 ) ( 0.174120,0.175771 ) ( 0.177646,0.179338 ) ( 0.179742,0.180268 ) ( 0.182271,0.185928 ) ( 0.186290,0.188869 ) ( 0.191370,0.193319 ) ( 0.193411,0.196287 ) ( 0.203856,0.207054 ) ( 0.207160,0.209445 ) ( 0.212525,0.215888 ) ( 0.216376,0.221549 ) ( 0.224582,0.225404 ) ( 0.226043,0.228790 ) ( 0.229034,0.229321 ) ( 0.231976,0.234916 ) ( 0.236610,0.237066 ) ( 0.237609,0.240718 ) ( 0.258411,0.263754 ) ( 0.264427,0.264996 ) ( 0.267154,0.271123 ) ( 0.274778,0.275191 ) ( 0.275544,0.279638 ) ( 0.279889,0.285177 ) ( 0.286835,0.295996 ) ( 0.296915,0.303519 ) ( 0.305313,0.315179 ) ( 0.315423,0.327190 ) ( 0.338832,0.367017 ) ( 0.367165,0.397859 ) ( 0.401058,0.421795 ) ( 0.422625,0.423603 ) ( 0.424378,0.425611 ) ( 0.431305,0.432324 ) ( 0.432595,0.443098 ) ( 0.446909,0.447820 ) ( 0.449164,0.450809 ) ( 0.452005,0.452751 ) ( 0.452777,0.469439 ) ( 0.471966,0.472474 ) ( 0.474304,0.480424 ) ( 0.520692,0.520977 ) ( 0.521239,0.528639 ) ( 0.530932,0.531574 ) ( 0.534817,0.558220 ) ( 0.558260,0.559398 ) ( 0.561241,0.563811 ) ( 0.565944,0.567405 ) ( 0.567676,0.568695 ) ( 0.572075,0.592288 ) ( 0.592797,0.595990 ) ( 0.599335,0.608496 ) ( 0.610016,0.983288 ) ( 1.017290,29.025098 ) ( 31.169048,42.830952 ) 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 37 Yes Yes No No There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 5744 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=(1,36)(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=(1,37)(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=(1,37)(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"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(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=(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=(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=(1,2)(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=(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=(1,37)(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=(1,37)(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=(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=(1,37)(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=(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=(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=(1,37)(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");