These Thurston maps are NET maps for every choice of translation term.
They have degree 34. They are imprimitive, each factoring as a NET map
with degree 17 followed by a Euclidean NET map with degree 2.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0} {lambda1} {lambda2} {lambda1+lambda2}
Since no Thurston multiplier is 1, this modular group Hurwitz class
contains only finitely 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
1/34, 2/17, 1/2, 3/2, 2/1, 5/2, 7/2, 9/2, 11/2, 6/1, 13/2, 15/2, 10/1, 14/1
18/1, 22/1, 26/1, 30/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-0.506939)
(-0.493249,-0.017536)
( 0.017357,infinity )
1/0 is the slope of a Thurston obstruction with c = 2 and d = 1.
These NET maps are not rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS: 2 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
2/1 1 34 Yes Yes No No
1/0 2 1 No No No No
NUMBER OF EQUATORS: 1 1 0 0
There are no more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 1208
No nontrivial cycles were found.
Here is the action of the slope function on an invariant set S of slopes.
N/1 -> (2N-2)/1
The set S contains infinitely many infinite slope function trajectory tails.
The slope function maps every slope to a slope:
no slope maps to the nonslope.
If the slope function maps slope s to a slope s' and
if the intersection pairing of s with 1/0 is n, then
the intersection pairing of s' with 1/0 is at most n.
The slope function orbit of every slope whose intersection
pairing with 1/0 is at most 50 either ends in one of the
slopes described above or it has an infinite tail in one of
the infinite sets described above.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=**(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)",
"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=****(1,34)(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)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,2)(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=(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=(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=(1,2)(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=(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=(1,34)(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=(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)",
"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=(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=(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");
**