12a
0852
(K12a
0852
)
A knot diagram
1
Linearized knot diagam
4 5 9 10 3 11 12 1 2 8 7 6
Solving Sequence
6,11
7 12 8
1,3
5 2 10 4 9
c
6
c
11
c
7
c
12
c
5
c
2
c
10
c
4
c
9
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h2.17522 × 10
33
u
103
2.37686 × 10
33
u
102
+ ··· + 1.19004 × 10
34
b + 7.34507 × 10
33
,
1.83944 × 10
33
u
103
+ 7.61714 × 10
33
u
102
+ ··· + 1.19004 × 10
34
a + 1.97168 × 10
34
, u
104
2u
103
+ ··· + u + 1i
I
u
2
= hb 1, a, u 1i
* 2 irreducible components of dim
C
= 0, with total 105 representations.
1
The image of knot diagram is generated by the software Draw programme developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h2.18 × 10
33
u
103
2.38 × 10
33
u
102
+ · · · + 1.19 × 10
34
b + 7.35 ×
10
33
, 1.84 × 10
33
u
103
+ 7.62 × 10
33
u
102
+ · · · + 1.19 × 10
34
a + 1.97 ×
10
34
, u
104
2u
103
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
u
3
2u
u
3
+ u
a
3
=
0.154570u
103
0.640077u
102
+ ··· 8.49712u 1.65682
0.182786u
103
+ 0.199730u
102
+ ··· + 1.15418u 0.617214
a
5
=
0.564505u
103
+ 0.239962u
102
+ ··· + 6.85734u + 1.98992
0.268856u
103
0.201079u
102
+ ··· 1.38328u + 0.531144
a
2
=
0.997344u
103
1.00004u
102
+ ··· 3.56627u 0.283414
0.827859u
103
+ 0.00269680u
102
+ ··· 1.54179u 0.827859
a
10
=
u
5
2u
3
+ u
u
7
3u
5
+ 2u
3
+ u
a
4
=
0.560773u
103
+ 0.239997u
102
+ ··· + 6.85749u + 1.98999
1.30153u
103
1.39251u
102
+ ··· 5.85230u 1.30153
a
9
=
u
10
5u
8
+ 8u
6
3u
4
3u
2
+ 1
u
10
+ 4u
8
5u
6
+ 3u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.780657u
103
+ 6.36032u
102
+ ··· + 24.6150u + 10.1407
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
17u
103
+ ··· 6u + 2
c
2
, c
5
u
104
+ 2u
103
+ ··· 17u 1
c
3
u
104
+ 45u
102
+ ··· 223u + 19
c
4
u
104
+ 2u
103
+ ··· + 89u + 29
c
6
, c
7
, c
11
u
104
+ 2u
103
+ ··· u + 1
c
8
u
104
13u
102
+ ··· + 325815u + 31313
c
9
u
104
+ 4u
103
+ ··· u 1
c
10
, c
12
u
104
3u
103
+ ··· + 1056u 288
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
9y
103
+ ··· 80y + 4
c
2
, c
5
y
104
66y
103
+ ··· 21y + 1
c
3
y
104
+ 90y
103
+ ··· 10893y + 361
c
4
y
104
+ 106y
103
+ ··· + 9595y + 841
c
6
, c
7
, c
11
y
104
86y
103
+ ··· 5y + 1
c
8
y
104
26y
103
+ ··· 64509499981y + 980503969
c
9
y
104
18y
103
+ ··· 5y + 1
c
10
, c
12
y
104
+ 63y
103
+ ··· 965952y + 82944
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.819897 + 0.339888I
a = 0.618092 0.371458I
b = 0.847810 + 0.105674I
0.757428 + 0.259701I 0
u = 0.819897 0.339888I
a = 0.618092 + 0.371458I
b = 0.847810 0.105674I
0.757428 0.259701I 0
u = 1.086970 + 0.359710I
a = 1.360150 0.080546I
b = 1.34875 0.55310I
2.38106 9.69349I 0
u = 1.086970 0.359710I
a = 1.360150 + 0.080546I
b = 1.34875 + 0.55310I
2.38106 + 9.69349I 0
u = 1.105020 + 0.306891I
a = 0.199413 0.213073I
b = 0.016100 + 1.138540I
1.77784 3.79314I 0
u = 1.105020 0.306891I
a = 0.199413 + 0.213073I
b = 0.016100 1.138540I
1.77784 + 3.79314I 0
u = 1.131960 + 0.250386I
a = 0.639350 0.213959I
b = 0.015696 0.221086I
1.278260 0.518432I 0
u = 1.131960 0.250386I
a = 0.639350 + 0.213959I
b = 0.015696 + 0.221086I
1.278260 + 0.518432I 0
u = 0.136123 + 0.826445I
a = 2.34710 0.70307I
b = 1.055580 0.268217I
4.02249 5.82467I 0. + 9.76873I
u = 0.136123 0.826445I
a = 2.34710 + 0.70307I
b = 1.055580 + 0.268217I
4.02249 + 5.82467I 0. 9.76873I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.012968 + 0.834781I
a = 2.87263 + 0.51707I
b = 1.295250 0.298176I
9.32839 4.63448I 4.37030 + 4.68852I
u = 0.012968 0.834781I
a = 2.87263 0.51707I
b = 1.295250 + 0.298176I
9.32839 + 4.63448I 4.37030 4.68852I
u = 1.107320 + 0.388542I
a = 1.317400 0.103258I
b = 1.032010 + 0.213362I
1.05685 + 1.43205I 0
u = 1.107320 0.388542I
a = 1.317400 + 0.103258I
b = 1.032010 0.213362I
1.05685 1.43205I 0
u = 0.144534 + 0.811710I
a = 2.89684 + 0.94833I
b = 1.35719 + 0.57614I
5.2555 + 13.9655I 0. 8.79296I
u = 0.144534 0.811710I
a = 2.89684 0.94833I
b = 1.35719 0.57614I
5.2555 13.9655I 0. + 8.79296I
u = 1.153830 + 0.313248I
a = 1.274740 0.020552I
b = 1.36053 + 0.68227I
2.84442 1.43397I 0
u = 1.153830 0.313248I
a = 1.274740 + 0.020552I
b = 1.36053 0.68227I
2.84442 + 1.43397I 0
u = 0.134940 + 0.785568I
a = 0.90410 + 1.19582I
b = 0.052430 1.189570I
1.14989 + 7.82651I 2.02077 8.17490I
u = 0.134940 0.785568I
a = 0.90410 1.19582I
b = 0.052430 + 1.189570I
1.14989 7.82651I 2.02077 + 8.17490I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.171330 + 0.286191I
a = 3.60617 1.73630I
b = 1.056690 0.074059I
0.890609 0.882288I 0
u = 1.171330 0.286191I
a = 3.60617 + 1.73630I
b = 1.056690 + 0.074059I
0.890609 + 0.882288I 0
u = 0.107809 + 0.782110I
a = 2.98039 0.66950I
b = 1.34008 0.74189I
6.00776 + 5.43570I 4.84361 7.57014I
u = 0.107809 0.782110I
a = 2.98039 + 0.66950I
b = 1.34008 + 0.74189I
6.00776 5.43570I 4.84361 + 7.57014I
u = 0.081733 + 0.774053I
a = 2.92878 1.38458I
b = 1.57005 + 0.30871I
6.79633 + 1.59864I 6.88756 1.28327I
u = 0.081733 0.774053I
a = 2.92878 + 1.38458I
b = 1.57005 0.30871I
6.79633 1.59864I 6.88756 + 1.28327I
u = 0.138651 + 0.759319I
a = 0.351130 0.209085I
b = 0.119000 + 0.310193I
1.63666 3.24838I 2.97188 + 2.12306I
u = 0.138651 0.759319I
a = 0.351130 + 0.209085I
b = 0.119000 0.310193I
1.63666 + 3.24838I 2.97188 2.12306I
u = 0.105697 + 0.761805I
a = 3.83553 + 2.76175I
b = 1.051740 + 0.109936I
4.09016 2.94806I 10.1598 11.5645I
u = 0.105697 0.761805I
a = 3.83553 2.76175I
b = 1.051740 0.109936I
4.09016 + 2.94806I 10.1598 + 11.5645I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.189960 + 0.315903I
a = 1.89639 0.44180I
b = 1.53464 0.36870I
3.42433 + 2.35782I 0
u = 1.189960 0.315903I
a = 1.89639 + 0.44180I
b = 1.53464 + 0.36870I
3.42433 2.35782I 0
u = 1.218850 + 0.280045I
a = 0.58237 + 1.41538I
b = 0.570636 + 0.091864I
0.11833 1.76625I 0
u = 1.218850 0.280045I
a = 0.58237 1.41538I
b = 0.570636 0.091864I
0.11833 + 1.76625I 0
u = 0.039221 + 0.746787I
a = 0.167152 1.170260I
b = 0.567779 + 0.817936I
3.96566 1.29839I 2.18497 + 4.02972I
u = 0.039221 0.746787I
a = 0.167152 + 1.170260I
b = 0.567779 0.817936I
3.96566 + 1.29839I 2.18497 4.02972I
u = 0.238724 + 0.696600I
a = 1.41097 0.43554I
b = 0.893342 0.279263I
1.03956 4.10317I 5.12667 + 9.90639I
u = 0.238724 0.696600I
a = 1.41097 + 0.43554I
b = 0.893342 + 0.279263I
1.03956 + 4.10317I 5.12667 9.90639I
u = 0.082721 + 0.731305I
a = 0.256759 1.035700I
b = 0.714652 0.132439I
3.33458 1.87793I 2.57613 + 6.72386I
u = 0.082721 0.731305I
a = 0.256759 + 1.035700I
b = 0.714652 + 0.132439I
3.33458 + 1.87793I 2.57613 6.72386I
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.235630 + 0.311765I
a = 0.410613 0.014767I
b = 0.439261 0.886111I
0.28138 + 5.13012I 0
u = 1.235630 0.311765I
a = 0.410613 + 0.014767I
b = 0.439261 + 0.886111I
0.28138 5.13012I 0
u = 0.604637 + 0.377946I
a = 1.43689 + 1.33325I
b = 1.289030 + 0.537727I
1.23076 + 9.78607I 3.55004 8.76671I
u = 0.604637 0.377946I
a = 1.43689 1.33325I
b = 1.289030 0.537727I
1.23076 9.78607I 3.55004 + 8.76671I
u = 1.247190 + 0.379009I
a = 1.92688 + 0.79547I
b = 1.311450 + 0.333163I
5.51009 + 8.99383I 0
u = 1.247190 0.379009I
a = 1.92688 0.79547I
b = 1.311450 0.333163I
5.51009 8.99383I 0
u = 1.269870 + 0.379706I
a = 1.36939 1.14885I
b = 1.275090 + 0.263970I
5.34644 + 0.27299I 0
u = 1.269870 0.379706I
a = 1.36939 + 1.14885I
b = 1.275090 0.263970I
5.34644 0.27299I 0
u = 1.32911
a = 0.752093
b = 1.50687
1.93259 0
u = 0.294200 + 0.595315I
a = 1.26888 + 0.93132I
b = 1.237090 0.501458I
2.26017 6.27429I 1.37179 + 2.81174I
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.294200 0.595315I
a = 1.26888 0.93132I
b = 1.237090 + 0.501458I
2.26017 + 6.27429I 1.37179 2.81174I
u = 0.497394 + 0.439590I
a = 1.36564 0.72878I
b = 0.802243 0.161085I
0.66419 1.68719I 11.39599 + 8.12073I
u = 0.497394 0.439590I
a = 1.36564 + 0.72878I
b = 0.802243 + 0.161085I
0.66419 + 1.68719I 11.39599 8.12073I
u = 1.301770 + 0.309962I
a = 1.097610 + 0.496242I
b = 0.710921 0.827783I
0.22651 2.50873I 0
u = 1.301770 0.309962I
a = 1.097610 0.496242I
b = 0.710921 + 0.827783I
0.22651 + 2.50873I 0
u = 1.320810 + 0.229375I
a = 0.168377 0.148303I
b = 0.496393 0.597888I
4.96158 + 3.74028I 0
u = 1.320810 0.229375I
a = 0.168377 + 0.148303I
b = 0.496393 + 0.597888I
4.96158 3.74028I 0
u = 1.357340 + 0.036829I
a = 0.64481 + 1.79711I
b = 1.121420 + 0.753763I
3.40531 3.28760I 0
u = 1.357340 0.036829I
a = 0.64481 1.79711I
b = 1.121420 0.753763I
3.40531 + 3.28760I 0
u = 0.586602 + 0.257849I
a = 0.522102 0.255402I
b = 0.106387 1.029130I
2.46224 + 4.23705I 7.70872 7.47519I
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.586602 0.257849I
a = 0.522102 + 0.255402I
b = 0.106387 + 1.029130I
2.46224 4.23705I 7.70872 + 7.47519I
u = 1.323900 + 0.311663I
a = 0.497700 + 0.855032I
b = 0.766085 + 0.188074I
1.09041 + 5.66082I 0
u = 1.323900 0.311663I
a = 0.497700 0.855032I
b = 0.766085 0.188074I
1.09041 5.66082I 0
u = 1.320340 + 0.332094I
a = 0.84342 + 1.93940I
b = 1.60232 0.26907I
2.39939 5.59260I 0
u = 1.320340 0.332094I
a = 0.84342 1.93940I
b = 1.60232 + 0.26907I
2.39939 + 5.59260I 0
u = 1.364830 + 0.013621I
a = 0.14110 2.80359I
b = 0.944317 0.153085I
4.84420 + 0.57804I 0
u = 1.364830 0.013621I
a = 0.14110 + 2.80359I
b = 0.944317 + 0.153085I
4.84420 0.57804I 0
u = 1.340460 + 0.271297I
a = 1.19962 1.01951I
b = 0.322997 0.951799I
5.64992 2.03615I 0
u = 1.340460 0.271297I
a = 1.19962 + 1.01951I
b = 0.322997 + 0.951799I
5.64992 + 2.03615I 0
u = 0.158685 + 0.610936I
a = 1.300790 0.327447I
b = 0.228459 + 0.869260I
0.96137 1.25908I 4.98451 + 0.66680I
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.158685 0.610936I
a = 1.300790 + 0.327447I
b = 0.228459 0.869260I
0.96137 + 1.25908I 4.98451 0.66680I
u = 1.333430 + 0.326258I
a = 2.27280 3.29785I
b = 1.051820 0.133392I
0.43475 + 6.88567I 0
u = 1.333430 0.326258I
a = 2.27280 + 3.29785I
b = 1.051820 + 0.133392I
0.43475 6.88567I 0
u = 1.334910 + 0.336617I
a = 1.73924 + 2.18490I
b = 1.32785 + 0.78054I
1.47378 9.47675I 0
u = 1.334910 0.336617I
a = 1.73924 2.18490I
b = 1.32785 0.78054I
1.47378 + 9.47675I 0
u = 0.621098
a = 0.599919
b = 0.141868
1.24720 8.65320
u = 1.365160 + 0.233330I
a = 0.375504 0.313013I
b = 1.183030 + 0.536242I
2.91793 + 3.29629I 0
u = 1.365160 0.233330I
a = 0.375504 + 0.313013I
b = 1.183030 0.536242I
2.91793 3.29629I 0
u = 1.350210 + 0.324204I
a = 0.0340088 0.0616224I
b = 0.161165 0.365219I
3.05646 + 7.17585I 0
u = 1.350210 0.324204I
a = 0.0340088 + 0.0616224I
b = 0.161165 + 0.365219I
3.05646 7.17585I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.349480 + 0.336718I
a = 1.50306 + 0.13604I
b = 0.076257 + 1.214800I
3.52490 11.88240I 0
u = 1.349480 0.336718I
a = 1.50306 0.13604I
b = 0.076257 1.214800I
3.52490 + 11.88240I 0
u = 1.392200 + 0.040896I
a = 0.41176 + 1.35567I
b = 0.189123 + 1.116580I
8.55437 5.02075I 0
u = 1.392200 0.040896I
a = 0.41176 1.35567I
b = 0.189123 1.116580I
8.55437 + 5.02075I 0
u = 1.393450 + 0.083248I
a = 0.382891 + 0.981947I
b = 0.847847 + 0.366478I
6.65127 + 3.23336I 0
u = 1.393450 0.083248I
a = 0.382891 0.981947I
b = 0.847847 0.366478I
6.65127 3.23336I 0
u = 1.371250 + 0.280465I
a = 0.453878 + 1.001390I
b = 0.850252 + 0.379510I
4.02838 + 7.63331I 0
u = 1.371250 0.280465I
a = 0.453878 1.001390I
b = 0.850252 0.379510I
4.02838 7.63331I 0
u = 1.354630 + 0.357246I
a = 1.37123 + 1.50720I
b = 1.063730 + 0.305774I
0.67161 + 10.08760I 0
u = 1.354630 0.357246I
a = 1.37123 1.50720I
b = 1.063730 0.305774I
0.67161 10.08760I 0
13
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.357480 + 0.349121I
a = 1.64850 2.17322I
b = 1.35890 0.59148I
0.5224 18.1526I 0
u = 1.357480 0.349121I
a = 1.64850 + 2.17322I
b = 1.35890 + 0.59148I
0.5224 + 18.1526I 0
u = 1.408100 + 0.014929I
a = 0.117428 0.268962I
b = 0.493413 0.253339I
7.53758 + 0.06657I 0
u = 1.408100 0.014929I
a = 0.117428 + 0.268962I
b = 0.493413 + 0.253339I
7.53758 0.06657I 0
u = 1.409240 + 0.065039I
a = 0.12694 1.58323I
b = 1.28505 0.59078I
5.09313 11.01120I 0
u = 1.409240 0.065039I
a = 0.12694 + 1.58323I
b = 1.28505 + 0.59078I
5.09313 + 11.01120I 0
u = 0.435976 + 0.239765I
a = 0.86661 1.89922I
b = 1.191680 0.582430I
2.08857 + 2.52807I 0.32506 8.71630I
u = 0.435976 0.239765I
a = 0.86661 + 1.89922I
b = 1.191680 + 0.582430I
2.08857 2.52807I 0.32506 + 8.71630I
u = 0.449559 + 0.091341I
a = 0.46059 + 4.92050I
b = 0.953699 + 0.055151I
0.728992 0.299030I 7.0296 19.8342I
u = 0.449559 0.091341I
a = 0.46059 4.92050I
b = 0.953699 0.055151I
0.728992 + 0.299030I 7.0296 + 19.8342I
14
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.198188 + 0.402789I
a = 0.984161 0.454357I
b = 0.189920 + 0.365207I
0.424686 1.170030I 5.91811 + 4.92395I
u = 0.198188 0.402789I
a = 0.984161 + 0.454357I
b = 0.189920 0.365207I
0.424686 + 1.170030I 5.91811 4.92395I
u = 0.229242 + 0.271377I
a = 0.49573 1.39916I
b = 1.242340 + 0.280456I
2.66352 0.40407I 2.91521 3.41969I
u = 0.229242 0.271377I
a = 0.49573 + 1.39916I
b = 1.242340 0.280456I
2.66352 + 0.40407I 2.91521 + 3.41969I
15
II. I
u
2
= hb 1, a, u 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
1
a
7
=
1
1
a
12
=
1
0
a
8
=
0
1
a
1
=
1
0
a
3
=
0
1
a
5
=
1
1
a
2
=
1
0
a
10
=
0
1
a
4
=
1
0
a
9
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
12
u
c
2
, c
11
u + 1
c
3
, c
4
, c
5
c
6
, c
7
, c
8
c
9
u 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
y
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
y 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
0 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
104
17u
103
+ ··· 6u + 2)
c
2
(u + 1)(u
104
+ 2u
103
+ ··· 17u 1)
c
3
(u 1)(u
104
+ 45u
102
+ ··· 223u + 19)
c
4
(u 1)(u
104
+ 2u
103
+ ··· + 89u + 29)
c
5
(u 1)(u
104
+ 2u
103
+ ··· 17u 1)
c
6
, c
7
(u 1)(u
104
+ 2u
103
+ ··· u + 1)
c
8
(u 1)(u
104
13u
102
+ ··· + 325815u + 31313)
c
9
(u 1)(u
104
+ 4u
103
+ ··· u 1)
c
10
, c
12
u(u
104
3u
103
+ ··· + 1056u 288)
c
11
(u + 1)(u
104
+ 2u
103
+ ··· u + 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
104
9y
103
+ ··· 80y + 4)
c
2
, c
5
(y 1)(y
104
66y
103
+ ··· 21y + 1)
c
3
(y 1)(y
104
+ 90y
103
+ ··· 10893y + 361)
c
4
(y 1)(y
104
+ 106y
103
+ ··· + 9595y + 841)
c
6
, c
7
, c
11
(y 1)(y
104
86y
103
+ ··· 5y + 1)
c
8
(y 1)(y
104
26y
103
+ ··· 6.45095 × 10
10
y + 9.80504 × 10
8
)
c
9
(y 1)(y
104
18y
103
+ ··· 5y + 1)
c
10
, c
12
y(y
104
+ 63y
103
+ ··· 965952y + 82944)
21