These Thurston maps are NET maps for every choice of translation term.
They have degree 25. They are imprimitive, each factoring as a NET map
with degree 5 followed by a Euclidean NET map with degree 5.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/5, 1/5, 2/5, 3/5, 4/5, 5/5
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-1.000000)
(-1.000000,-0.900263)
(-0.899735,-0.889205)
(-0.888571,-0.875000)
(-0.874249,-0.867195)
(-0.866191,-0.858067)
(-0.856248,-0.850271)
(-0.849707,-0.846443)
(-0.846154,-0.842646)
(-0.841961,-0.840086)
(-0.839440,-0.834440)
(-0.830870,-0.828864)
(-0.776030,-0.775220)
(-0.771259,-0.770060)
(-0.768354,-0.766895)
(-0.766535,-0.765065)
(-0.764096,-0.762337)
(-0.761786,-0.760085)
(-0.759424,-0.750000)
(-0.750000,-0.733565)
(-0.733095,-0.727701)
(-0.726851,-0.714286)
(-0.714286,-0.700522)
(-0.699467,-0.666667)
(-0.666667,-0.601053)
(-0.600000,-0.500000)
(-0.500000,0.000000 )
( 0.000000,infinity )
5/4 is the slope of a Thurston obstruction with c = 5 and d = 5.
These NET maps are not rational.
SLOPE FUNCTION INFORMATION
EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
5/4 5 5 No No No No
(5N+1)/(4N+1) 4 5 No No No No
(10N+7)/(8N+6) 3 5 No No No No
(15N+8)/(12N+7) 2 5 No No No No
(15N+13)/(12N+11) 2 5 No No No No
(20N+9)/(16N+8) 1 5 No No No No
(20N+19)/(16N+16) 1 5 No No No No
The fixed point finder is unable to determine whether
there are any more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 34661
There are no equators because both elementary divisors are greater than 1.
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 5/4 is n, then
the intersection pairing of s' with 5/4 is at most n.
The slope function orbit of every slope whose intersection
pairing with 5/4 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=(2,8)(3,22)(4,10)(5,24)(6,21)(7,13)(9,15)(11,16)(12,18)(14,20)(17,23)(19,25)",
"b=**(1,21)(2,3)(4,5)(6,16)(7,8)(9,10)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"c=<1,1,1,1,c^-1,1,1,c,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(5,25)(6,7)(8,9)(10,20)(11,12)(13,14)(16,17)(18,19)(21,22)(23,24)",
"d=(1,22)(2,6)(3,24)(4,8)(7,11)(9,13)(10,25)(12,16)(14,18)(15,20)(17,21)(19,23)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,6)(2,8)(3,22)(4,10)(5,24)(7,13)(9,15)(11,21)(12,18)(14,20)(17,23)(19,25)",
"b=(2,3)(4,5)(6,21)(7,8)(9,10)(11,16)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"c=<1,1,1,1,d,c,c^-1,1,1,c^-1,1,1,1,1,c^-1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(6,7)(8,9)(10,25)(11,12)(13,14)(15,20)(16,17)(18,19)(21,22)(23,24)",
"d=(1,22)(2,6)(3,24)(4,8)(5,10)(7,11)(9,13)(12,16)(14,18)(15,25)(17,21)(19,23)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,7)(2,21)(3,9)(4,23)(5,20)(6,12)(8,14)(10,15)(11,17)(13,19)(16,22)(18,24)",
"b=<1,1,1,1,c^-1,1,1,c,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(5,25)(6,7)(8,9)(10,20)(11,12)(13,14)(16,17)(18,19)(21,22)(23,24)",
"c=****(1,21)(2,3)(4,5)(6,16)(7,8)(9,10)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"d=(1,16)(2,23)(3,7)(4,25)(5,9)(6,11)(8,12)(10,14)(13,17)(15,19)(18,22)(20,24)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,a*b,1,a*b,c^-1,1,1,c^-1,1,c^-1,1,1,1,c,1,1,1,1,1,c,c*d,1,c*d,1,c>(1,7)(2,21)(3,9)(4,23)(5,25)(6,12)(8,14)(10,20)(11,17)(13,19)(16,22)(18,24)",
"b=<1,1,1,1,d,c,c^-1,1,1,c^-1,1,1,1,1,c^-1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(6,7)(8,9)(10,25)(11,12)(13,14)(15,20)(16,17)(18,19)(21,22)(23,24)",
"c=(2,3)(4,5)(6,21)(7,8)(9,10)(11,16)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"d=****(1,21)(2,23)(3,7)(4,25)(5,9)(6,16)(8,12)(10,14)(13,17)(15,19)(18,22)(20,24)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -15504641/18221365.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -15504641/18221365.
Imminent integer overflow halted evaluation of the slope function at
slope 71515584/58984613 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 71835941/59248837 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 79471216/65357057 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 79116809/65065593 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 48713343/39961238 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 48891257/40107187 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 60468697/49369139 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 60248653/49189486 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 45106542/36781295 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 45271283/36915630 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 115819229/94427529 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 116338046/94850521 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 123973321/100958741 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 123420454/100508509 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 49040203/39930766 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 48861747/39785459 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 73477433/59772510 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 73745792/59990815 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 85323232/69252767 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 85012743/69000758 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 62508077/50702523 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 62736373/50887702 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 160122874/129870445 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 160840151/130452205 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 46968529/38085475 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 47140196/38224675 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope 47502054/38512295 during the search for all slope function fixed points.
Imminent integer overflow caused the modular group computation to abort.
**