These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 27.
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 10.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/27, 1/9, 1/3, 1/1, 5/3, 7/3, 5/1, 7/1, 11/1, 13/1, 17/1, 19/1, 23/1, 25/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.041401)
( 0.042229,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
(0.041337,0.041487) 7/169 HST
(0.041429,0.041543) 10/241 HST
(0.041412,0.041603) 15/361 HST
(0.041579,0.041623) 28/673 HST
(0.041555,0.041667) 41/985 HST
(0.041643,0.041643) 74/1777 HST
(0.041643,0.041686) 1/24 EXTENDED HST
(0.041667,0.041806) 13/311 HST
(0.041803,0.041808) 25/598 HST
(0.041805,0.041810) 37/885 HST
(0.041809,0.041814) 12/287 HST
(0.041813,0.041816) 47/1124 HST
(0.041816,0.041816) 35/837 HST
(0.041816,0.041818) 58/1387 HST
(0.041817,0.041819) 23/550 HST
(0.041819,0.041819) 80/1913 HST
(0.041818,0.041821) 57/1363 HST
(0.041820,0.041821) 34/813 HST
(0.041819,0.041824) 45/1076 HST
(0.041822,0.041827) 11/263 HST
(0.041827,0.041831) 43/1028 HST
(0.041829,0.041831) 32/765 HST
(0.041828,0.041834) 53/1267 HST
(0.041831,0.041834) 21/502 HST
(0.041833,0.041838) 31/741 HST
(0.041835,0.041847) 10/239 HST
(0.041844,0.041860) 19/454 HST
(0.041851,0.041877) 9/215 HST
(0.041871,0.041887) 33/788 HST
(0.041880,0.041892) 8/191 HST
(0.041880,0.041909) 23/549 HST
(0.041896,0.041902) 15/358 HST
(0.041901,0.042122) 6/143 HST
(0.041983,0.042381) 4/95 HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 3 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-24/1 1 27 Yes Yes No No
0/1 1 27 Yes Yes No No
-1458/61 1 27 Yes Yes No No
NUMBER OF EQUATORS FOUND: 3 3 0 0
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: 1309
Here is their union. There are no more slope function fixed points
whose negative reciprocals lie in any of the following intervals.
EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION
(-infinity,0.041533)
( 0.041533,0.041889)
( 0.041889,infinity)
No nontrivial cycles were found.
The slope function maps every slope to a slope:
no slope maps to the nonslope.
The slope function orbit of every slope p/q with |p| <= 50
and |q| <= 50 ends in one of the above cycles.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=<1,a*b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)",
"c=<1,c^-1,c^-1,c^-1,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,c,c,c*d>(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=<1,1,c^-1,c^-1,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,c,c,c>(1,2)(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=(1,27)(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=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)",
"c=(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)",
"d=<1,c^-1,c^-1,c^-1,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,c,c,c*d>(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 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,c^-1,c^-1,c^-1,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,c,c,c*d>(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=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)",
"d=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)",
"b=(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)",
"c=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)",
"d=**(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)(26,27)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -31342709/1301761 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1641838/68775 during the search for all slope function fixed points.
**