These Thurston maps all have degree 2.
There are choices of translation term b for
which the resulting Thurston map is not a NET map.
The postcritical set has 4 points if b = 0.
The postcritical set has 2 points if b = lambda1.
The postcritical set has 4 points if b = lambda2.
The postcritical set has 2 points if b = lambda1+lambda2.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0,lambda2}
This pure 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 4.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/1, 1/2, 1/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-0.019079)
( 0.019836,infinity )
1/0 is the slope of a Thurston obstruction with c = 1 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 1 1 No * No *
NUMBER OF EQUATORS: 0 * 0 *
There are no more slope function fixed points because every
loop multiplier of the mod 2 slope correspondence graph is
at least 1 and there can be at most one obstruction.
No nontrivial cycles were found.
"INFINITE CYCLES"
-> N/1 -> (N-1)/1 ->
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=**",
"b=(1,2)",
"c=(1,2)",
"d=****",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=<1,c>",
"b=(1,2)",
"c=(1,2)",
"d=<1,c*b*c^-1>",
"a*b*c*d");
**