These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 37.
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 10.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/37, 1/1, 3/1, 5/1, 7/1, 9/1, 11/1, 13/1, 15/1, 17/1, 19/1, 21/1, 23/1
25/1, 27/1, 29/1, 31/1, 33/1, 35/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.029297)
( 0.029650,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
(0.029207,0.029347) 8/273 HST
(0.029322,0.029369) 14/477 HST
(0.029359,0.029380) 21/715 HST
(0.029375,0.029387) 28/953 HST
(0.029381,0.029392) 35/1191 HST
(0.029388,0.029396) 45/1531 HST
(0.029391,0.029401) 57/1939 HST
(0.029398,0.029403) 78/2653 HST
(0.029401,0.029404) 97/3299 HST
(0.029403,0.029406) 118/4013 HST
(0.029405,0.029407) 143/4863 HST
(0.029406,0.029408) 174/5917 HST
(0.029407,0.029408) 210/7141 HST
(0.029408,0.029416) 1/34 EXTENDED HST
(0.029415,0.029416) 220/7479 HST
(0.029416,0.029417) 186/6323 HST
(0.029416,0.029418) 157/5337 HST
(0.029417,0.029419) 134/4555 HST
(0.029418,0.029420) 115/3909 HST
(0.029419,0.029423) 93/3161 HST
(0.029421,0.029424) 80/2719 HST
(0.029423,0.029426) 69/2345 HST
(0.029424,0.029428) 60/2039 HST
(0.029426,0.029430) 52/1767 HST
(0.029429,0.029433) 45/1529 HST
(0.029431,0.029439) 37/1257 HST
(0.029435,0.029436) 36/1223 HST
(0.029436,0.029441) 32/1087 HST
(0.029439,0.029446) 28/951 HST
(0.029443,0.029450) 25/849 HST
(0.029446,0.029455) 22/747 HST
(0.029452,0.029494) 17/577 HST
(0.029465,0.029477) 15/509 HST
(0.029473,0.029489) 13/441 HST
(0.029482,0.029506) 11/373 HST
(0.029491,0.029512) 10/339 HST
(0.029503,0.029561) 8/271 HST
(0.029527,0.029639) 6/203 HST
(0.029561,0.030024) 4/135 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
-34/1 1 37 Yes Yes No No
0/1 1 37 Yes Yes No No
NUMBER OF EQUATORS: 2 2 0 0
There are no more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 447
NONTRIVIAL CYCLES
-543/16 -> -1053/31 -> -543/16
-512/15 -> -1324/39 -> -512/15
-509/15 -> -815/24 -> -509/15
-372/11 -> -1052/31 -> -1868/55 -> -372/11
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.
38/37
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=<1,a*b,b,b,b,b,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,b^-1,b^-1,b^-1,b^-1,b^-1>(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"b=(1,37)(2,36)(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)",
"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^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"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^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(1,2)(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:
NewSphereMachine(
"a=(1,37)(2,36)(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)",
"b=(1,36)(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=(1,37)(2,36)(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)",
"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^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,37)(2,36)(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)",
"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^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"c=(1,37)(2,36)(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)",
"d=(1,36)(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 lambda1+lambda2:
NewSphereMachine(
"a=(1,36)(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=(1,37)(2,36)(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)",
"c=(1,36)(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=**(1,35)(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)(36,37)",
"a*b*c*d");
**