These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 28. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/4, 0/7, 0/28, 1/14, 1/7, 1/2, 1/1, 3/2, 5/2, 3/1, 5/1, 8/1, 9/1, 13/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.106137) (-1.105547,-1.101876) (-1.097807,-1.095568) (-1.086117,-1.085238) (-1.082159,-1.000000) (-1.000000,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 (-1.106419,-1.105382) -73/66 HST (-1.103330,-1.099819) -65/59 HST (-1.100137,-1.099867) -11/10 EXTENDED HST (-1.104167,-1.092593) -56/51 HST (-1.093227,-1.092317) -59/54 HST (-1.092374,-1.092258) -1763/1614 HST (-1.092314,-1.092302) -71/65 EXTENDED HST (-1.092274,-1.092131) -154/141 HST (-1.092136,-1.092119) -569/521 HST (-1.092121,-1.092114) -1067/977 HST (-1.092117,-1.092111) -1648/1509 HST (-1.092111,-1.092099) -83/76 EXTENDED HST (-1.092101,-1.091663) -95/87 HST (-1.091716,-1.090116) -12/11 EXTENDED HST (-1.090248,-1.089863) -109/100 HST (-1.089891,-1.089884) -97/89 EXTENDED HST (-1.089869,-1.089767) -182/167 HST (-1.089794,-1.089087) -61/56 HST (-1.089092,-1.088964) -159/146 HST (-1.088966,-1.088812) -49/45 EXTENDED HST (-1.088857,-1.088599) -135/124 HST (-1.088690,-1.088519) -86/79 HST (-1.088833,-1.088063) -123/113 HST (-1.088420,-1.087099) -37/34 EXTENDED HST -> HST (-1.087399,-1.086772) -337/310 HST (-1.087011,-1.086903) -25/23 EXTENDED HST (-1.086887,-1.086356) -88/81 HST (-1.086362,-1.086225) -151/139 HST (-1.086266,-1.086147) -63/58 EXTENDED HST (-1.086194,-1.086089) -227/209 HST (-1.085276,-1.085126) -191/176 HST (-1.085151,-1.084279) -51/47 HST (-1.084366,-1.083837) -103/95 HST (-1.083914,-1.083680) -181/167 HST (-1.083783,-1.083543) -272/251 HST (-1.083584,-1.083480) -441/407 HST (-1.083505,-1.083154) -13/12 EXTENDED HST (-1.083196,-1.083022) -417/385 HST (-1.083111,-1.082823) -248/229 HST (-1.082955,-1.082442) -157/145 HST (-1.082752,-1.081913) -105/97 HST (-1.082378,-1.081514) -79/73 HST (-1.009110,-0.988340) -1/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 11/12 1 7 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: 8484 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "b=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=<1,a*b,a*b,a*b,a*b,a*b,a*b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d*c^-1,c*d,c*d,c*d,c*d,c*d,c*d>(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "b=(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "c=<1,a*b,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d,c*d>(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "d=<1,1,a*b,a*b,a*b,a*b,a*b,a*b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d>(1,2)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "b=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "b=<1,a*b,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d,c*d>(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "c=(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "d=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "a*b*c*d");