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 0/1, 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, 16/1, 17/1, 18/1, 19/1, 22/1, 25/1, 28/1, 31/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.455219) (-0.454484,-0.402423) (-0.397344,-0.384062) (-0.383074,-0.381652) (-0.380465,-0.379544) (-0.377738,-0.372580) (-0.371810,-0.367304) (-0.367224,-0.366128) (-0.364015,-0.358180) (-0.358012,-0.351947) (-0.350421,-0.337823) (-0.328381,-0.317834) (-0.313123,-0.311837) (-0.311710,-0.307421) (-0.305931,-0.305170) (-0.301567,-0.298271) (-0.295874,-0.295025) (-0.292506,-0.287475) (-0.284112,-0.267109) (-0.266309,-0.263178) (-0.262933,-0.236062) (-0.234272,-0.203819) (-0.198462,-0.143839) (-0.142526,-0.017657) ( 0.017396,infinity ) 1/0 is the slope of a Thurston obstruction with c = 2 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 2 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. 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=<1,1,c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c>(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=<1,a*b,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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,c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c,c*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)", "d=<1,1,d*a*c^-1,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,1,c^2,c^2,c^2,c^2,c^2,c^2,c^2,c^2,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c*b*c>(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=<1,c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c,c*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)", "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,d*a^2*b,b*d*a*c^-1,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,b*c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^-2,c^2,c^2,c^2,c^2,c^2,c^2,c^2,c^2,c^2,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c^2*b^-1,c*b*c*b^-1,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)", "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=<1,c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,b*c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c*b^-1,c,c*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)", "c=<1,a*b,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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");