These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 34.
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
0/17, 0/34, 1/34, 1/17, 1/2, 1/1, 2/2, 3/2, 4/2, 5/2, 3/1, 6/2, 7/2, 8/2
5/1, 11/2, 7/1, 14/2, 9/1, 11/1, 13/1, 15/1, 19/1, 25/1, 31/1, 32/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.000000)
( 0.000000,0.030769)
( 0.033800,infinity)
The half-space computation does not determine rationality.
EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION
INTERVAL COMPUTED FOR HST OR EXTENDED HST
(-0.008052,0.006403) 0/1 EXTENDED HST
( 0.030748,0.030959) 2/65 HST
( 0.030923,0.030981) 10/323 HST
( 0.030967,0.030980) 7/226 HST
( 0.030980,0.030992) 11/355 HST
( 0.030944,0.031038) 15/484 HST
( 0.030993,0.031075) 4/129 HST
( 0.031065,0.031097) 17/547 HST
( 0.031086,0.031117) 6/193 HST
( 0.031105,0.031132) 22/707 HST
( 0.031119,0.031122) 15/482 HST
( 0.031128,0.031129) 8/257 EXTENDED HST
( 0.031123,0.031142) 25/803 HST
( 0.031134,0.031137) 17/546 HST
( 0.031139,0.031145) 9/289 HST
( 0.031141,0.031174) 10/321 HST
( 0.031174,0.031176) 13/417 HST
( 0.031171,0.031182) 53/1700 HST
( 0.031177,0.031177) 40/1283 EXTENDED HST
( 0.031177,0.031178) 27/866 HST
( 0.031180,0.031180) 14/449 EXTENDED HST
( 0.031178,0.031197) 15/481 HST
( 0.031187,0.031203) 19/609 HST
( 0.031194,0.031212) 62/1987 HST
( 0.031203,0.031204) 21/673 HST
( 0.031211,0.031215) 26/833 HST
( 0.031208,0.031221) 28/897 HST
( 0.031194,0.031250) 34/1089 HST
( 0.031248,0.031252) 1/32 EXTENDED HST
( 0.031250,0.031306) 32/1023 HST
( 0.031281,0.031282) 31/991 HST
( 0.031282,0.031295) 26/831 HST
( 0.031288,0.031292) 24/767 HST
( 0.031292,0.031309) 20/639 HST
( 0.031301,0.031302) 19/607 HST
( 0.031302,0.031323) 16/511 HST
( 0.031313,0.031331) 13/415 HST
( 0.031331,0.031355) 10/319 HST
( 0.031348,0.031381) 9/287 HST
( 0.031363,0.031405) 8/255 HST
( 0.031385,0.031395) 7/223 HST
( 0.031399,0.031415) 25/796 HST
( 0.031413,0.031414) 6/191 EXTENDED HST
( 0.031402,0.031443) 17/541 HST
( 0.031426,0.031431) 11/350 HST
( 0.031436,0.031450) 61/1940 HST
( 0.031446,0.031447) 5/159 EXTENDED HST
( 0.031434,0.031496) 9/286 HST
( 0.031496,0.031497) 4/127 EXTENDED HST
( 0.031496,0.031501) 123/3905 HST
( 0.031498,0.031499) 103/3270 HST
( 0.031499,0.031526) 11/349 HST
( 0.031525,0.031539) 7/222 HST
( 0.031520,0.031596) 10/317 HST
( 0.031554,0.031608) 3/95 HST
( 0.031584,0.031630) 11/348 HST
( 0.031615,0.031671) 5/158 HST
( 0.031630,0.031700) 7/221 HST
( 0.031690,0.031711) 11/347 HST
( 0.031701,0.031714) 15/473 HST
( 0.031713,0.031720) 17/536 HST
( 0.031715,0.031729) 21/662 HST
( 0.031728,0.031734) 31/977 HST
( 0.031732,0.031736) 41/1292 HST
( 0.031734,0.031739) 51/1607 HST
( 0.031737,0.031740) 69/2174 HST
( 0.031739,0.031741) 89/2804 HST
( 0.031741,0.031742) 109/3434 HST
( 0.031742,0.031743) 133/4190 HST
( 0.031742,0.031744) 161/5072 HST
( 0.031743,0.031744) 201/6332 HST
( 0.031743,0.031744) 243/7655 HST
( 0.031744,0.031748) 2/63 EXTENDED HST
( 0.031748,0.031748) 241/7591 HST
( 0.031748,0.031749) 201/6331 HST
( 0.031749,0.031750) 167/5260 HST
( 0.031749,0.031751) 125/3937 HST
( 0.031750,0.031752) 103/3244 HST
( 0.031751,0.031754) 77/2425 HST
( 0.031753,0.031754) 67/2110 HST
( 0.031754,0.031757) 57/1795 HST
( 0.031755,0.031758) 49/1543 HST
( 0.031757,0.031763) 37/1165 HST
( 0.031760,0.031820) 7/220 HST
( 0.031819,0.031878) 5/157 HST
( 0.031878,0.031879) 268/8407 HST
( 0.031878,0.031956) 3/94 HST
( 0.031939,0.031990) 7/219 HST
( 0.031985,0.031996) 27/844 HST
( 0.031965,0.032023) 59/1844 HST
( 0.031999,0.032001) 4/125 EXTENDED HST
( 0.032008,0.032051) 9/281 HST
( 0.032039,0.032067) 5/156 HST
( 0.032065,0.032072) 38/1185 HST
( 0.032068,0.032072) 11/343 HST
( 0.032067,0.032084) 17/530 HST
( 0.032083,0.032115) 6/187 HST
( 0.032113,0.032163) 8/249 HST
( 0.032146,0.032181) 11/342 HST
( 0.032180,0.032199) 14/435 HST
( 0.032192,0.032214) 18/559 HST
( 0.032211,0.032222) 24/745 HST
( 0.032219,0.032230) 30/931 HST
( 0.032228,0.032290) 1/31 EXTENDED HST
( 0.032289,0.032304) 27/836 HST
( 0.032297,0.032303) 25/774 HST
( 0.032301,0.032345) 18/557 HST
( 0.032318,0.032337) 16/495 HST
( 0.032325,0.032351) 14/433 HST
( 0.032335,0.032371) 12/371 HST
( 0.032346,0.032408) 10/309 HST
( 0.032362,0.032432) 8/247 HST
( 0.032392,0.032421) 7/216 HST
( 0.032422,0.032476) 5/154 HST
( 0.032468,0.032513) 9/277 HST
( 0.032505,0.032756) 3/92 HST
( 0.032753,0.032764) 19/580 HST
( 0.032763,0.032771) 25/763 HST
( 0.032758,0.032785) 33/1007 HST
( 0.032780,0.032794) 2/61 EXTENDED HST
( 0.032793,0.032805) 47/1433 HST
( 0.032799,0.032827) 23/701 HST
( 0.032812,0.032825) 15/457 HST
( 0.032825,0.032846) 13/396 HST
( 0.032832,0.033127) 3/91 HST
( 0.032945,0.033525) 6/181 HST
( 0.033318,0.033349) 1/30 EXTENDED HST
( 0.033404,0.034539) 3/89 HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 11 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-32/1 1 34 Yes Yes No No
-30/1 1 34 Yes Yes No No
-22/1 1 34 Yes Yes No No
0/1 1 34 Yes Yes No No
-286/9 1 34 Yes Yes No No
-662/21 1 34 Yes Yes No No
-220/7 1 34 Yes Yes No No
-154/5 1 34 Yes Yes No No
-396/13 1 34 Yes Yes No No
-88/3 1 34 Yes Yes No No
-132/5 1 34 Yes Yes No No
NUMBER OF EQUATORS FOUND: 11 11 0 0
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: 2040
Here is their union. There are no more slope function fixed points
whose negative reciprocals lie in any of the following intervals.
EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION
(-infinity,0.031250)
( 0.031251,0.031261)
( 0.031261,0.031262)
( 0.031262,0.031262)
( 0.031262,0.031264)
( 0.031264,0.031266)
( 0.031267,0.031268)
( 0.031268,0.031270)
( 0.031270,0.031270)
( 0.031270,0.031272)
( 0.031272,0.031272)
( 0.031272,0.031273)
( 0.031273,0.031273)
( 0.031273,0.031276)
( 0.031276,0.031278)
( 0.031278,0.031280)
( 0.031281,0.031281)
( 0.031282,0.031282)
( 0.031282,0.031284)
( 0.031284,0.031287)
( 0.031287,0.031289)
( 0.031291,0.031291)
( 0.031292,0.031295)
( 0.031297,0.031297)
( 0.031299,0.031302)
( 0.031304,0.031304)
( 0.031306,0.031312)
( 0.031315,0.031315)
( 0.031320,0.031320)
( 0.031325,0.031326)
( 0.031332,0.031332)
( 0.031339,0.031339)
( 0.031348,0.031348)
( 0.031358,0.031359)
( 0.031372,0.031373)
( 0.031390,0.031391)
( 0.031414,0.031414)
( 0.031446,0.031447)
( 0.031496,0.031496)
( 0.031576,0.031582)
( 0.031746,0.031746)
( 0.032256,0.032260)
( 0.033331,0.033335)
( 0.034381,0.034591)
( 0.035497,0.035948)
( 0.037011,0.037062)
( 0.038043,0.038915)
( 0.039683,0.040342)
( 0.041371,0.041985)
( 0.043445,0.043512)
( 0.045412,0.045496)
( 0.046667,0.048673)
( 0.049157,0.050926)
( 0.052516,0.052748)
( 0.054348,0.056897)
( 0.057377,0.060440)
( 0.060870,0.064327)
( 0.066465,0.066865)
( 0.068898,0.074324)
( 0.074468,0.087766)
( 0.090521,0.091316)
( 0.094595,0.136364)
( 0.141865,0.143916)
( 0.150862,0.300000)
( 0.328099,0.339080)
( 0.388889,1.833333)
(35.750000,infinity)
No nontrivial cycles were found.
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.
If the slope function maps slope p/q to slope p'/q', then |q'| <= |q|
for every slope p/q with |p| <= 50 and |q| <= 50.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=<1,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*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)",
"d=<1,1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(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 lambda1:
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=**(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)",
"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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*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 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=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*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)",
"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+lambda2:
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=****(1,33)(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)",
"d=****(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(33,34)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -3767342/117721 during the search for all slope function fixed points.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 3529/112931.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 4529/144931.
Imminent integer overflow halted evaluation of the slope function at slope
-1256058/39251 while computing a fixed point excluded interval about 34722/1111127.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1519/48609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1519/48609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1519/48609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1519/48609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 4838/154819.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 4838/154819.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 5054/161731.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 5054/161731.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1710/54721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1778/56897.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1886/60353.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1886/60353.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1886/60353.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1886/60353.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1980/63361.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1980/63361.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1980/63361.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2019/64609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2019/64609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2019/64609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2019/64609.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2080/66561.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 38632/1236241.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 38632/1236241.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2282/73025.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1381/44191.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1381/44191.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1381/44191.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 1381/44191.
Imminent integer overflow caused the modular group computation to abort.
**