These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 40. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 14. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/5, 0/20, 0/40, 1/10, 1/8, 1/5, 1/4, 2/5, 1/2, 3/4, 1/1, 2/2, 5/5 3/2, 2/1, 3/1, 6/2, 6/1, 7/1, 9/1, 11/1, 13/1, 19/1, 31/1, 37/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.000000) (-1.000000,-0.338192) (-0.328613,-0.202020) (-0.197274,-0.143615) (-0.142206,-0.074697) ( 0.075667,0.110717 ) ( 0.111569,0.140266 ) ( 0.145545,0.197274 ) ( 0.202020,0.328613 ) ( 0.338192,0.496489 ) ( 0.503824,1.000000 ) ( 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 (-1.007969,-0.992156) -1/1 EXTENDED HST (-0.340171,-0.335912) -24/71 HST (-0.336691,-0.335069) -44/131 HST (-0.335663,-0.334442) -65/194 HST (-0.334506,-0.332163) -1/3 EXTENDED HST (-0.332232,-0.331036) -65/196 HST (-0.331616,-0.330042) -44/133 HST (-0.330794,-0.326765) -24/73 HST (-0.203474,-0.200588) -20/99 HST (-0.200633,-0.199368) -1/5 EXTENDED HST (-0.199380,-0.198811) -44/221 HST (-0.199083,-0.197617) -24/121 HST (-0.198291,-0.196455) -15/76 HST (-0.143823,-0.143357) -28/195 HST (-0.143885,-0.142857) -41/286 HST (-0.143288,-0.142427) -1/7 EXTENDED HST (-0.142857,-0.141844) -40/281 HST (-0.142342,-0.142122) -32/225 HST (-0.085841,0.073268 ) 0/1 EXTENDED HST ( 0.068687,0.078322 ) 2/27 EXTENDED HST -> HST ( 0.110666,0.110799 ) 32/289 HST ( 0.110497,0.111111 ) 40/361 HST ( 0.110851,0.111371 ) 1/9 EXTENDED HST ( 0.111111,0.111732 ) 41/368 HST ( 0.111413,0.111695 ) 28/251 HST ( 0.139258,0.141461 ) 8/57 HST ( 0.141039,0.141983 ) 15/106 HST ( 0.141637,0.142389 ) 24/169 HST ( 0.142249,0.142541 ) 44/309 HST ( 0.142534,0.143180 ) 1/7 EXTENDED HST ( 0.143175,0.143470 ) 44/307 HST ( 0.143329,0.144098 ) 24/167 HST ( 0.143742,0.144723 ) 15/104 HST ( 0.144281,0.146647 ) 8/55 HST ( 0.196455,0.198291 ) 15/76 HST ( 0.197617,0.199083 ) 24/121 HST ( 0.198811,0.199380 ) 44/221 HST ( 0.199170,0.199603 ) 65/326 HST ( 0.199578,0.200421 ) 1/5 EXTENDED HST ( 0.200403,0.200777 ) 69/344 HST ( 0.200588,0.203474 ) 20/99 HST ( 0.326765,0.330794 ) 24/73 HST ( 0.330042,0.331616 ) 44/133 HST ( 0.331036,0.332232 ) 65/196 HST ( 0.331447,0.333008 ) 101/304 HST ( 0.332457,0.334214 ) 1/3 EXTENDED HST ( 0.333659,0.335241 ) 101/302 HST ( 0.334442,0.335663 ) 65/194 HST ( 0.335069,0.336691 ) 44/131 HST ( 0.335912,0.340171 ) 24/71 HST ( 0.494994,0.498100 ) 71/143 HST ( 0.498016,0.501969 ) 1/2 EXTENDED HST ( 0.500739,0.504274 ) 101/201 HST ( 0.502512,0.505232 ) 66/131 HST ( 0.991239,1.008918 ) 1/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points. Number of excluded intervals computed by the fixed point finder: 35587 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 the nonslope. If the slope function maps slope p/q to slope p'/q', then |p'| <= |p| for every slope p/q with |p| <= 50 and |q| <= 50. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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: 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=<1,b,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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=(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+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=<1,b,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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 caused the modular group computation to abort.