These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 10.
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
0/5, 0/10, 1/10, 1/5, 1/2, 1/1, 2/2, 3/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-0.013739)
( 0.013830,infinity )
1/0 is the slope of a Thurston obstruction with c = 3 and d = 1.
These NET maps are not rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS: 1 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
1/0 3 1 No No No No
NUMBER OF EQUATORS: 0 0 0 0
There are no more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 287
No nontrivial cycles were found.
The slope function maps some slope 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 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=<1,a*b,b,c^-1*b,1,1,1,c,b^-1,b^-1>(2,10)(3,9)(4,8)(5,7)",
"b=(1,10)(2,9)(3,8)(4,7)(5,6)",
"c=(1,10)(2,9)(3,8)(4,7)(5,6)",
"d=<1,c^-1,c^-1,c^-1,1,1,1,c,c,c*d>(2,10)(3,9)(4,8)(5,7)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=<1,1,b,b,1,1,1,1,b^-1*c,b^-1>(1,2)(3,10)(4,9)(5,8)(6,7)",
"b=<1,a*b,b,c^-1*b,1,1,1,c,b^-1,b^-1>(2,10)(3,9)(4,8)(5,7)",
"c=<1,c^-1,c^-1,c^-1,1,1,1,c,c,c*d>(2,10)(3,9)(4,8)(5,7)",
"d=<1,1,c^-1,c^-1,1,1,1,1,c,c>(1,2)(3,10)(4,9)(5,8)(6,7)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,9)(2,8)(3,7)(4,6)",
"b=(1,10)(2,9)(3,8)(4,7)(5,6)",
"c=(1,10)(2,9)(3,8)(4,7)(5,6)",
"d=(1,9)(2,8)(3,7)(4,6)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,10)(2,9)(3,8)(4,7)(5,6)",
"b=<1,c^-1,c^-1,c^-1,1,1,1,c,c,c*d>(2,10)(3,9)(4,8)(5,7)",
"c=<1,a*b,b,c^-1*b,1,1,1,c,b^-1,b^-1>(2,10)(3,9)(4,8)(5,7)",
"d=(1,10)(2,9)(3,8)(4,7)(5,6)",
"a*b*c*d");