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 3 points if b = 0.
The postcritical set has 4 points if b = lambda1.
The postcritical set has 4 points if b = lambda2.
The postcritical set has 3 points if b = lambda1+lambda2.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{lambda1,lambda2}
This pure modular group Hurwitz class contains only
finitely many Thurston equivalence classes.
However, this 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
Every NET map in this pure modular group Hurwitz class is
rational because the mod 2 slope correspondence graph has no loops.
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,infinity)
SLOPE FUNCTION INFORMATION
There are no slope function fixed points because
the mod 2 slope correspondence graph has no loops.
NONTRIVIAL CYCLES
1/0 -> 0/1 -> 1/1 -> 1/0
The slope function maps some slope to the nonslope.
The slope function orbit of every slope p/q with |p| <= 50 and
|q| <= 50 ends in either one of the above cycles or the nonslope.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=<1,a>(1,2)",
"b=<1,c>",
"c=<1,d>",
"d=(1,2)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=<1,d>",
"b=(1,2)",
"c=<1,a>(1,2)",
"d=<1,c>",
"a*b*c*d");