These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 29. 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 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/29, 1/29, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 8/1, 9/1, 10/1, 11/1, 12/1, 14/1 15/1, 16/1, 23/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.113208) (-1.104398,-1.102623) (-1.097188,-1.096412) (-1.093574,-1.087290) (-1.086872,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 (-1.113417,-1.112304) -59/53 HST (-1.112501,-1.111932) -109/98 HST (-1.112229,-1.111551) -159/143 HST (-1.111618,-1.111448) -289/260 HST (-1.111508,-1.111377) -369/332 HST (-1.111471,-1.111274) -469/422 HST (-1.111303,-1.111243) -769/692 HST (-1.111265,-1.111216) -949/854 HST (-1.111218,-1.111212) -1179/1061 HST (-1.111230,-1.111192) -1219/1097 HST (-1.111206,-1.111177) -1529/1376 HST (-1.111188,-1.111033) -10/9 EXTENDED HST (-1.111801,-1.110032) -261/235 HST (-1.110635,-1.110449) -221/199 HST (-1.110530,-1.110044) -151/136 HST (-1.110269,-1.110009) -131/118 HST (-1.110122,-1.108613) -71/64 HST (-1.109219,-1.108634) -51/46 HST (-1.108675,-1.108239) -92/83 HST (-1.108544,-1.107956) -256/231 HST (-1.108122,-1.108094) -41/37 EXTENDED HST (-1.108325,-1.107553) -113/102 HST (-1.107778,-1.107602) -72/65 HST (-1.107603,-1.107502) -484/437 HST (-1.107529,-1.107525) -103/93 EXTENDED HST (-1.107511,-1.107472) -340/307 HST (-1.107488,-1.107387) -134/121 HST (-1.107467,-1.107230) -165/149 HST (-1.107235,-1.107207) -475/429 HST (-1.107242,-1.107170) -630/569 HST (-1.107184,-1.107102) -31/28 EXTENDED HST (-1.107117,-1.107052) -703/635 HST (-1.107086,-1.105738) -52/47 HST (-1.105764,-1.105616) -136/123 HST (-1.105647,-1.105532) -178/161 HST (-1.105574,-1.105480) -220/199 HST (-1.105489,-1.105420) -283/256 HST (-1.105440,-1.105386) -388/351 HST (-1.105629,-1.105110) -493/446 HST (-1.105317,-1.105210) -21/19 EXTENDED HST (-1.105115,-1.105055) -347/314 HST (-1.105093,-1.105025) -305/276 HST (-1.105069,-1.104976) -242/219 HST (-1.105019,-1.104928) -200/181 HST (-1.104952,-1.104843) -179/162 HST (-1.104904,-1.104076) -74/67 HST (-1.103655,-1.100825) -43/39 EXTENDED HST -> HST (-1.101367,-1.100061) -142/129 HST (-1.100064,-1.099936) -11/10 EXTENDED HST (-1.099954,-1.099835) -1046/951 HST (-1.099895,-1.099846) -848/771 HST (-1.099870,-1.099517) -375/341 HST (-1.099701,-1.099560) -309/281 HST (-1.099641,-1.098420) -133/121 HST (-1.099155,-1.098615) -111/101 HST (-1.098934,-1.098193) -78/71 HST (-1.098556,-1.097401) -45/41 EXTENDED HST -> HST (-1.097546,-1.097138) -124/113 HST (-1.097275,-1.097008) -79/72 HST (-1.098151,-1.087351) -23/21 EXTENDED HST -> HST (-1.087513,-1.086978) -162/149 HST (-1.087017,-1.086896) -25/23 EXTENDED HST (-1.087673,-1.086001) -563/518 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 2 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 9/10 1 29 Yes No Yes No 23/26 1 29 Yes No Yes No NUMBER OF EQUATORS: 2 0 2 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 3960 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=(2,29)(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=(1,29)(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=(1,29)(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,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d>(2,29)(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 lambda1: NewSphereMachine( "a=(1,2)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "b=(2,29)(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)", "c=<1,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d,c*d>(2,29)(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)", "d=<1,1,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(1,2)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "a*b*c*d"); When the translation term of the affine map is 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=(1,29)(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=(1,29)(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"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,29)(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,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d,c*d>(2,29)(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)", "c=(2,29)(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)", "d=(1,29)(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"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.