12n
0662
(K12n
0662
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 8 10 2 11 3 6 5 4
Solving Sequence
5,12
4
1,9
3 11 8 6 2 7 10
c
4
c
12
c
3
c
11
c
8
c
5
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h3.56429 × 10
66
u
46
+ 1.38822 × 10
67
u
45
+ ··· + 1.35802 × 10
68
b − 1.96080 × 10
67
,
− 2.47131 × 10
68
u
46
− 9.94693 × 10
68
u
45
+ ··· + 1.49382 × 10
69
a + 2.99067 × 10
69
, u
47
+ 4u
46
+ ··· + u + 11i
I
u
2
= h−4u
16
+ 4u
15
+ ··· + b − 4, −2u
17
+ 2u
16
+ ··· + a − 4, u
18
− u
17
+ ··· − 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 65 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
= h3.56×10
66
u
46
+1.39×10
67
u
45
+· · ·+1.36×10
68
b−1.96×10
67
, −2.47×
10
68
u
46
−9.95×10
68
u
45
+· · ·+1.49×10
69
a+2.99×10
69
, u
47
+4u
46
+· · ·+u+11i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
1
=
u
u
3
+ u
a
9
=
0.165436u
46
+ 0.665872u
45
+ ··· + 47.6506u − 2.00203
−0.0262463u
46
− 0.102224u
45
+ ··· + 2.75590u + 0.144387
a
3
=
0.0228210u
46
+ 0.0919063u
45
+ ··· + 22.9291u + 6.98832
−0.0353642u
46
− 0.136035u
45
+ ··· − 1.25538u + 0.587575
a
11
=
−u
u
a
8
=
0.172179u
46
+ 0.702253u
45
+ ··· + 49.1886u − 1.92623
−0.0329894u
46
− 0.138604u
45
+ ··· + 1.21792u + 0.0685910
a
6
=
−0.0344253u
46
− 0.174526u
45
+ ··· + 8.78426u + 2.63038
−0.0166373u
46
− 0.0395220u
45
+ ··· − 0.358128u + 0.921788
a
2
=
−0.0320584u
46
− 0.155060u
45
+ ··· − 31.9101u + 3.00707
−0.0833370u
46
− 0.330300u
45
+ ··· − 4.63638u + 0.105685
a
7
=
−0.0658054u
46
− 0.226720u
45
+ ··· − 5.52898u − 1.15248
0.0661854u
46
+ 0.269634u
45
+ ··· + 2.54666u + 0.0845939
a
10
=
0.103828u
46
+ 0.400441u
45
+ ··· + 14.9287u − 1.57199
−0.0711995u
46
− 0.276077u
45
+ ··· − 0.849870u + 0.420108
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0933045u
46
− 0.348811u
45
+ ··· + 5.64696u + 9.13255
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 56u
46
+ ··· + 13184125u + 534361
c
2
, c
7
u
47
+ 2u
46
+ ··· − 315u + 731
c
3
, c
9
u
47
− u
46
+ ··· − 3782u + 667
c
4
, c
11
, c
12
u
47
+ 4u
46
+ ··· + u + 11
c
5
u
47
+ 8u
46
+ ··· + 151u + 149
c
6
, c
10
u
47
+ u
46
+ ··· + 368u − 103
c
8
u
47
− 4u
45
+ ··· + 23u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
− 124y
46
+ ··· + 5168548507345y −285541678321
c
2
, c
7
y
47
− 56y
46
+ ··· + 13184125y −534361
c
3
, c
9
y
47
− 9y
46
+ ··· + 9199640y −444889
c
4
, c
11
, c
12
y
47
+ 54y
46
+ ··· − 10053y −121
c
5
y
47
+ 32y
46
+ ··· − 1091719y −22201
c
6
, c
10
y
47
+ 5y
46
+ ··· + 92988y −10609
c
8
y
47
− 8y
46
+ ··· − 113y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230731 + 1.086340I
a = 0.094144 − 1.313970I
b = 0.243008 + 0.226914I
2.98236 + 2.61578I 1.41474 − 2.87187I
u = 0.230731 − 1.086340I
a = 0.094144 + 1.313970I
b = 0.243008 − 0.226914I
2.98236 − 2.61578I 1.41474 + 2.87187I
u = 0.903444 + 0.695127I
a = 0.0854529 − 0.0543974I
b = 0.609527 + 0.047815I
0.73075 + 3.15581I −8.86017 − 6.34037I
u = 0.903444 − 0.695127I
a = 0.0854529 + 0.0543974I
b = 0.609527 − 0.047815I
0.73075 − 3.15581I −8.86017 + 6.34037I
u = −0.818444
a = 0.271814
b = −1.18073
−3.88729 1.39940
u = −0.315844 + 0.740860I
a = 0.67860 − 1.93996I
b = −0.053790 + 1.035250I
−7.17929 − 3.64393I −6.03198 + 2.78404I
u = −0.315844 − 0.740860I
a = 0.67860 + 1.93996I
b = −0.053790 − 1.035250I
−7.17929 + 3.64393I −6.03198 − 2.78404I
u = 0.660176 + 0.415759I
a = −0.815252 − 0.503616I
b = −0.269834 + 0.274621I
0.54494 + 2.07931I −3.70506 − 3.58771I
u = 0.660176 − 0.415759I
a = −0.815252 + 0.503616I
b = −0.269834 − 0.274621I
0.54494 − 2.07931I −3.70506 + 3.58771I
u = −0.259697 + 1.247040I
a = 1.70284 − 1.07261I
b = −1.80846 + 0.76841I
−7.62776 − 3.97997I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.259697 − 1.247040I
a = 1.70284 + 1.07261I
b = −1.80846 − 0.76841I
−7.62776 + 3.97997I 0
u = −1.048870 + 0.734928I
a = −0.199629 + 0.382583I
b = −0.707111 − 0.228325I
−6.81414 − 8.86603I 0
u = −1.048870 − 0.734928I
a = −0.199629 − 0.382583I
b = −0.707111 + 0.228325I
−6.81414 + 8.86603I 0
u = 0.101342 + 1.311880I
a = −0.412441 + 0.121949I
b = 0.688238 + 1.091370I
−1.93463 − 1.62052I 0
u = 0.101342 − 1.311880I
a = −0.412441 − 0.121949I
b = 0.688238 − 1.091370I
−1.93463 + 1.62052I 0
u = −0.16958 + 1.41249I
a = −1.68224 + 0.29426I
b = 2.51973 + 0.29584I
−4.53442 − 4.80175I 0
u = −0.16958 − 1.41249I
a = −1.68224 − 0.29426I
b = 2.51973 − 0.29584I
−4.53442 + 4.80175I 0
u = 0.009774 + 0.569826I
a = −0.14382 + 2.50997I
b = −1.11181 − 1.45066I
−6.39394 + 2.76050I −5.07909 − 4.30524I
u = 0.009774 − 0.569826I
a = −0.14382 − 2.50997I
b = −1.11181 + 1.45066I
−6.39394 − 2.76050I −5.07909 + 4.30524I
u = 0.24676 + 1.41083I
a = −0.974844 + 0.134792I
b = 1.208570 − 0.117394I
−1.56923 + 2.42458I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24676 − 1.41083I
a = −0.974844 − 0.134792I
b = 1.208570 + 0.117394I
−1.56923 − 2.42458I 0
u = 0.360762 + 0.434634I
a = 0.637654 − 0.160116I
b = 0.121281 − 1.284990I
5.11013 − 0.60703I 1.28346 − 3.49418I
u = 0.360762 − 0.434634I
a = 0.637654 + 0.160116I
b = 0.121281 + 1.284990I
5.11013 + 0.60703I 1.28346 + 3.49418I
u = 0.26561 + 1.41132I
a = 1.54991 − 0.05070I
b = −2.44053 + 0.39781I
−5.19455 + 5.50491I 0
u = 0.26561 − 1.41132I
a = 1.54991 + 0.05070I
b = −2.44053 − 0.39781I
−5.19455 − 5.50491I 0
u = −0.125509 + 0.520647I
a = −0.765539 − 0.405108I
b = −0.309014 + 0.532780I
−0.839180 + 0.890051I −6.16723 − 4.38006I
u = −0.125509 − 0.520647I
a = −0.765539 + 0.405108I
b = −0.309014 − 0.532780I
−0.839180 − 0.890051I −6.16723 + 4.38006I
u = −0.435533 + 0.178866I
a = 1.50551 − 0.63819I
b = 0.574481 − 0.251116I
0.66530 − 2.58665I −6.41102 + 3.60115I
u = −0.435533 − 0.178866I
a = 1.50551 + 0.63819I
b = 0.574481 + 0.251116I
0.66530 + 2.58665I −6.41102 − 3.60115I
u = −0.08203 + 1.58782I
a = 1.268210 − 0.226418I
b = −1.97982 − 0.29031I
−8.01777 − 0.17418I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08203 − 1.58782I
a = 1.268210 + 0.226418I
b = −1.97982 + 0.29031I
−8.01777 + 0.17418I 0
u = −0.11259 + 1.60042I
a = 0.729677 − 0.296946I
b = −1.135860 + 0.762303I
−4.00355 + 1.63505I 0
u = −0.11259 − 1.60042I
a = 0.729677 + 0.296946I
b = −1.135860 − 0.762303I
−4.00355 − 1.63505I 0
u = 0.03550 + 1.61092I
a = 1.29442 + 0.57703I
b = −1.86006 + 0.22479I
−14.1356 + 3.0975I 0
u = 0.03550 − 1.61092I
a = 1.29442 − 0.57703I
b = −1.86006 − 0.22479I
−14.1356 − 3.0975I 0
u = −0.12802 + 1.62058I
a = −1.292130 − 0.127233I
b = 2.04273 − 0.55165I
−15.2468 − 5.5387I 0
u = −0.12802 − 1.62058I
a = −1.292130 + 0.127233I
b = 2.04273 + 0.55165I
−15.2468 + 5.5387I 0
u = 0.25028 + 1.64833I
a = −1.240380 + 0.010109I
b = 1.92318 − 0.59872I
−7.20599 + 7.37595I 0
u = 0.25028 − 1.64833I
a = −1.240380 − 0.010109I
b = 1.92318 + 0.59872I
−7.20599 − 7.37595I 0
u = −1.40824 + 0.91175I
a = −0.059175 − 0.279970I
b = 0.184771 − 0.022624I
−6.49736 + 1.06394I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40824 − 0.91175I
a = −0.059175 + 0.279970I
b = 0.184771 + 0.022624I
−6.49736 − 1.06394I 0
u = −0.35417 + 1.64601I
a = 1.48951 + 0.08896I
b = −2.26832 − 0.64624I
−14.5107 − 14.0705I 0
u = −0.35417 − 1.64601I
a = 1.48951 − 0.08896I
b = −2.26832 + 0.64624I
−14.5107 + 14.0705I 0
u = −0.25743 + 1.76322I
a = −1.194790 − 0.225335I
b = 1.92781 + 0.54097I
−16.0072 − 4.6010I 0
u = −0.25743 − 1.76322I
a = −1.194790 + 0.225335I
b = 1.92781 − 0.54097I
−16.0072 + 4.6010I 0
u = 0.042363 + 0.155552I
a = −4.48250 + 6.51526I
b = −0.008354 + 0.583528I
2.00944 + 2.36150I 6.99099 + 1.74215I
u = 0.042363 − 0.155552I
a = −4.48250 − 6.51526I
b = −0.008354 − 0.583528I
2.00944 − 2.36150I 6.99099 − 1.74215I
9
II.
I
u
2
= h−4u
16
+4u
15
+· · ·+b−4, −2u
17
+2u
16
+· · ·+a−4, u
18
−u
17
+· · ·−4u+1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
1
=
u
u
3
+ u
a
9
=
2u
17
− 2u
16
+ ··· − 8u + 4
4u
16
− 4u
15
+ ··· − 19u + 4
a
3
=
2u
17
− 6u
16
+ ··· + 30u − 2
4u
16
− 3u
15
+ ··· − 12u + 5
a
11
=
−u
u
a
8
=
5u
17
+ 37u
15
+ ··· − 22u + 8
−3u
17
+ 2u
16
+ ··· + 7u
2
− 5u
a
6
=
u
17
+ 7u
16
+ ··· − 5u + 6
−5u
16
+ 5u
15
+ ··· + 10u − 2
a
2
=
u
17
− 5u
16
+ ··· + 18u + 1
u
17
+ 3u
16
+ ··· − 20u + 6
a
7
=
−3u
17
+ u
16
+ ··· − 3u − 3
2u
17
− u
16
+ ··· + 5u − 2
a
10
=
−6u
17
+ 5u
16
+ ··· + 30u − 8
7u
17
− 7u
16
+ ··· + 15u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
17
+ 15u
16
−6u
15
+ 124u
14
−78u
13
+ 428u
12
−330u
11
+ 860u
10
−
804u
9
+ 1204u
8
− 1198u
7
+ 1236u
6
− 1032u
5
+ 790u
4
− 445u
3
+ 213u
2
− 65u + 14
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 15u
17
+ ··· − 10u + 1
c
2
u
18
− u
17
+ ··· − 5u
2
+ 1
c
3
u
18
+ 6u
16
+ ··· − u + 1
c
4
u
18
− u
17
+ ··· − 4u + 1
c
5
u
18
+ u
17
+ ··· − 2u + 1
c
6
u
18
+ 7u
16
+ ··· − 3u + 1
c
7
u
18
+ u
17
+ ··· − 5u
2
+ 1
c
8
u
18
+ 5u
17
+ ··· + 4u + 1
c
9
u
18
+ 6u
16
+ ··· + u + 1
c
10
u
18
+ 7u
16
+ ··· + 3u + 1
c
11
, c
12
u
18
+ u
17
+ ··· + 4u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 19y
17
+ ··· + 6y + 1
c
2
, c
7
y
18
− 15y
17
+ ··· − 10y + 1
c
3
, c
9
y
18
+ 12y
17
+ ··· + 11y + 1
c
4
, c
11
, c
12
y
18
+ 19y
17
+ ··· + 24y + 1
c
5
y
18
+ 13y
17
+ ··· + 22y + 1
c
6
, c
10
y
18
+ 14y
17
+ ··· + 15y + 1
c
8
y
18
− 11y
17
+ ··· + 12y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.047457 + 1.260530I
a = −0.463361 − 0.372899I
b = 0.75763 + 1.65026I
−1.07422 − 1.82174I 2.53563 + 3.44461I
u = 0.047457 − 1.260530I
a = −0.463361 + 0.372899I
b = 0.75763 − 1.65026I
−1.07422 + 1.82174I 2.53563 − 3.44461I
u = 0.624909 + 0.377226I
a = −1.085780 − 0.083376I
b = −0.359942 + 0.016839I
1.55326 + 2.89712I 3.21609 − 6.87440I
u = 0.624909 − 0.377226I
a = −1.085780 + 0.083376I
b = −0.359942 − 0.016839I
1.55326 − 2.89712I 3.21609 + 6.87440I
u = −0.811576 + 0.982182I
a = −0.203378 − 0.578815I
b = 0.041786 + 0.805202I
−5.97620 + 1.12633I −2.64487 − 2.46137I
u = −0.811576 − 0.982182I
a = −0.203378 + 0.578815I
b = 0.041786 − 0.805202I
−5.97620 − 1.12633I −2.64487 + 2.46137I
u = −0.248975 + 1.257170I
a = −1.70042 + 1.40960I
b = 2.26145 − 1.10023I
−8.03080 − 4.68996I −8.61446 + 8.30623I
u = −0.248975 − 1.257170I
a = −1.70042 − 1.40960I
b = 2.26145 + 1.10023I
−8.03080 + 4.68996I −8.61446 − 8.30623I
u = 0.310491 + 0.635862I
a = −0.93533 + 1.31096I
b = −0.187193 − 0.083340I
1.60805 + 2.77366I −4.09387 − 6.07484I
u = 0.310491 − 0.635862I
a = −0.93533 − 1.31096I
b = −0.187193 + 0.083340I
1.60805 − 2.77366I −4.09387 + 6.07484I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.014631 + 1.305350I
a = 0.630377 − 1.122440I
b = −0.846119 + 0.087531I
1.59046 − 1.08301I −3.32575 + 0.28729I
u = 0.014631 − 1.305350I
a = 0.630377 + 1.122440I
b = −0.846119 − 0.087531I
1.59046 + 1.08301I −3.32575 − 0.28729I
u = 0.20726 + 1.40864I
a = 1.66745 − 0.04254I
b = −2.57675 + 0.57229I
−3.94351 + 5.76224I −0.19696 − 7.32113I
u = 0.20726 − 1.40864I
a = 1.66745 + 0.04254I
b = −2.57675 − 0.57229I
−3.94351 − 5.76224I −0.19696 + 7.32113I
u = 0.29358 + 1.54080I
a = −0.716837 + 0.233224I
b = 1.191490 − 0.331330I
−2.32605 + 2.81106I −7.01886 − 6.08609I
u = 0.29358 − 1.54080I
a = −0.716837 − 0.233224I
b = 1.191490 + 0.331330I
−2.32605 − 2.81106I −7.01886 + 6.08609I
u = 0.062225 + 0.316348I
a = 1.80727 − 1.62985I
b = −0.282355 − 1.294230I
5.08446 + 1.31343I 0.64304 − 6.49722I
u = 0.062225 − 0.316348I
a = 1.80727 + 1.62985I
b = −0.282355 + 1.294230I
5.08446 − 1.31343I 0.64304 + 6.49722I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 15u
17
+ ··· − 10u + 1)
· (u
47
+ 56u
46
+ ··· + 13184125u + 534361)
c
2
(u
18
− u
17
+ ··· − 5u
2
+ 1)(u
47
+ 2u
46
+ ··· − 315u + 731)
c
3
(u
18
+ 6u
16
+ ··· − u + 1)(u
47
− u
46
+ ··· − 3782u + 667)
c
4
(u
18
− u
17
+ ··· − 4u + 1)(u
47
+ 4u
46
+ ··· + u + 11)
c
5
(u
18
+ u
17
+ ··· − 2u + 1)(u
47
+ 8u
46
+ ··· + 151u + 149)
c
6
(u
18
+ 7u
16
+ ··· − 3u + 1)(u
47
+ u
46
+ ··· + 368u − 103)
c
7
(u
18
+ u
17
+ ··· − 5u
2
+ 1)(u
47
+ 2u
46
+ ··· − 315u + 731)
c
8
(u
18
+ 5u
17
+ ··· + 4u + 1)(u
47
− 4u
45
+ ··· + 23u + 3)
c
9
(u
18
+ 6u
16
+ ··· + u + 1)(u
47
− u
46
+ ··· − 3782u + 667)
c
10
(u
18
+ 7u
16
+ ··· + 3u + 1)(u
47
+ u
46
+ ··· + 368u − 103)
c
11
, c
12
(u
18
+ u
17
+ ··· + 4u + 1)(u
47
+ 4u
46
+ ··· + u + 11)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 19y
17
+ ··· + 6y + 1)
· (y
47
− 124y
46
+ ··· + 5168548507345y −285541678321)
c
2
, c
7
(y
18
− 15y
17
+ ··· − 10y + 1)
· (y
47
− 56y
46
+ ··· + 13184125y −534361)
c
3
, c
9
(y
18
+ 12y
17
+ ··· + 11y + 1)(y
47
− 9y
46
+ ··· + 9199640y −444889)
c
4
, c
11
, c
12
(y
18
+ 19y
17
+ ··· + 24y + 1)(y
47
+ 54y
46
+ ··· − 10053y −121)
c
5
(y
18
+ 13y
17
+ ··· + 22y + 1)(y
47
+ 32y
46
+ ··· − 1091719y −22201)
c
6
, c
10
(y
18
+ 14y
17
+ ··· + 15y + 1)(y
47
+ 5y
46
+ ··· + 92988y −10609)
c
8
(y
18
− 11y
17
+ ··· + 12y + 1)(y
47
− 8y
46
+ ··· − 113y −9)
16
