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 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 0/1, 0/7, 0/28, 1/28, 1/14, 1/7, 1/4, 1/2, 2/4, 3/4, 1/1, 4/4, 5/4, 3/2 6/4, 5/2, 3/1, 9/2, 5/1, 11/2, 13/2, 9/1, 11/1, 13/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.096011) (-1.095840,-1.094905) (-1.093157,-1.092941) (-1.090742,infinity ) 32/35 is the slope of a Thurston obstruction with c = 4 and d = 4. These NET maps are not rational. SLOPE FUNCTION INFORMATION EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 32/35 4 4 No No No No (128N+53)/(140N+58) 1 14 No No No No The fixed point finder is unable to determine whether there are any more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 4099 No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function maps some slope p/q to a slope p'/q' such that the intersection pairing of p'/q' with the obstruction slope is greater than the intersection pairing of p/q with the obstruction slope. The slope function orbit of every slope whose intersection pairing with 32/35 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=(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"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2315919/2117648. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2315919/2117648. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1735815/1587208. Imminent integer overflow halted evaluation of the slope function at slope 3154657/3450021 while computing a fixed point excluded interval about -3227728/2951395. Imminent integer overflow halted evaluation of the slope function at slope 3154657/3450021 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 4486311/4906355 while computing a fixed point excluded interval about -4685744/4284587. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1260953/1153000. Imminent integer overflow halted evaluation of the slope function at slope 200922028/219733941 while computing a fixed point excluded interval about -36850120/33695299. Imminent integer overflow halted evaluation of the slope function at slope 11578383/12662443 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 30977659/33878033 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 30880893/33772207 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 10610723/11604183 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 15399871/16841729 while computing a fixed point excluded interval about -15792428/14440403. Imminent integer overflow halted evaluation of the slope function at slope 21059913/23031709 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 35342361/38651393 while computing a fixed point excluded interval about -13057188/11939333. Imminent integer overflow halted evaluation of the slope function at slope 3079359/3367673 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 3900033/4265185 while computing a fixed point excluded interval about -3627157/3316628. Imminent integer overflow halted evaluation of the slope function at slope 6281267/6869369 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1499447/1371076. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1499447/1371076. Imminent integer overflow halted evaluation of the slope function at slope 12181227/13321730 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -4896999/4477756. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -4896999/4477756. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1898105/1735604. Imminent integer overflow halted evaluation of the slope function at slope 20220879/22114094 while computing a fixed point excluded interval about -13601123/12436714. Imminent integer overflow halted evaluation of the slope function at slope 10008605/10945143 while computing a fixed point excluded interval about -14192195/12977818. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -264157/241554. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1395043/1275674. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1395043/1275674. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2224643/2034288. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2224643/2034288.