These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 35.
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 7.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/35, 1/7, 1/5, 3/7, 3/5, 1/1, 5/5, 3/1, 9/1, 11/1, 13/1, 17/1, 19/1, 23/1
27/1, 29/1, 31/1, 33/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.031124)
( 0.031511,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
(0.030683,0.031206) 8/257 HST
(0.031192,0.031216) 22/705 HST
(0.031209,0.031225) 30/961 HST
(0.031206,0.031238) 39/1249 HST
(0.031236,0.031241) 84/2689 HST
(0.031239,0.031242) 105/3361 HST
(0.031241,0.031244) 126/4033 HST
(0.031243,0.031245) 155/4961 HST
(0.031244,0.031246) 189/6049 HST
(0.031245,0.031255) 1/32 EXTENDED HST
(0.031250,0.031309) 17/543 HST
(0.031309,0.031310) 33/1054 HST
(0.031310,0.031310) 507/16193 HST
(0.031310,0.031310) 49/1565 HST
(0.031309,0.031310) 163/5206 HST
(0.031310,0.031310) 65/2076 HST
(0.031310,0.031312) 16/511 HST
(0.031311,0.031312) 79/2523 HST
(0.031312,0.031313) 47/1501 HST
(0.031312,0.031313) 109/3481 HST
(0.031313,0.031313) 31/990 EXTENDED HST
(0.031313,0.031313) 108/3449 HST
(0.031313,0.031314) 46/1469 HST
(0.031313,0.031315) 61/1948 HST
(0.031315,0.031316) 15/479 HST
(0.031316,0.031319) 29/926 HST
(0.031318,0.031323) 14/447 HST
(0.031321,0.031327) 40/1277 HST
(0.031324,0.031327) 13/415 HST
(0.031323,0.031337) 25/798 HST
(0.031330,0.031357) 11/351 HST
(0.031346,0.031449) 8/255 HST
(0.031379,0.031512) 6/191 HST
(0.031446,0.031634) 4/127 HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 5 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-32/1 1 35 Yes Yes No No
0/1 1 35 Yes Yes No No
-990/31 1 35 Yes Yes No No
-2906/91 1 35 Yes Yes No No
-7632/239 1 35 Yes Yes No No
NUMBER OF EQUATORS FOUND: 5 5 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: 1431
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,0.031316)
( 0.031316,0.031365)
( 0.031365,0.031365)
( 0.031365,0.031365)
( 0.031365,infinity)
NONTRIVIAL CYCLES
-479/15 -> -511/16 -> -479/15
-2427/76 -> -2523/79 -> -2427/76
The slope function maps every slope to a slope:
no slope maps to the nonslope.
There are 3096 slopes s = p/q with |p| <= 50 and |q| <= 50.
The 1 slopes s in the following list have the property that the
slope function orbit of s contains a slope t whose numerator or
denominator exceeds 1,000,000 in absolute value, and the slopes between
s and t are not among the slopes p/q with |p| <= 50 and |q| <= 50.
36/35
The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50
either contains an extended rational number whose numerator or
denominator exceeds 1,000,000 in absolute value or ends in one of the above cycles.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)",
"b=**(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"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^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)",
"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^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(1,2)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=****(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"b=****(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)",
"c=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"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^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"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^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)",
"c=****(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"d=****(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)",
"b=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"c=****(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)",
"d=****(1,33)(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(34,35)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -2038690/63839 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -8021104/251185 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -4450936/139603 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -4442774/139347 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -8771822/275127 during the search for all slope function fixed points.
**