12n
0063
(K12n
0063
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 5 7 8 1 7
Solving Sequence
5,8 9,10 3,11
2 6 1 4 7 12
c
8
c
10
c
2
c
5
c
1
c
4
c
7
c
12
c
3
, c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h211450298892949u
15
− 665970623055347u
14
+ ··· + 44568754122034192d + 9319091588527888,
40959130934865u
15
− 340344314483579u
14
+ ··· + 89137508244068384c − 71636506057825568,
1.48020 × 10
15
u
15
− 5.08467 × 10
15
u
14
+ ··· + 4.45688 × 10
16
b − 3.24669 × 10
16
,
299188489544621u
15
− 2300420730722931u
14
+ ··· + 89137508244068384a + 5859054368972672,
u
16
− 3u
15
+ ··· − 64u + 32i
I
u
2
= h109u
7
c − 121u
7
+ ··· − 2066c + 3882, 9443u
7
c − 4639u
7
+ ··· − 14966c + 1182,
165u
7
+ 651u
6
− 137u
5
− 3762u
4
− 1020u
3
+ 3809u
2
+ 6184b − 3983u − 234,
1393u
7
+ 1111u
6
− 10189u
5
− 3314u
4
+ 26244u
3
− 12555u
2
+ 12368a − 24219u + 1510,
u
8
+ u
7
− 7u
6
− 4u
5
+ 16u
4
− 3u
3
− 9u
2
− 8u − 4i
I
v
1
= ha, d, c − 1, b + v, v
2
− v + 1i
I
v
2
= ha, d + 1, av + c − a, b + v, v
2
− v + 1i
I
v
3
= hc, d + 1, b, a + 1, v + 1i
I
v
4
= hc, d + 1, −v
2
ba + v
3
b − v
2
b + av − v
2
+ c − 1, b
2
v
2
− bv + 1i
* 5 irreducible components of dim
C
= 0, with total 37 representations.
* 1 irreducible components of dim
C
= 1
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
= h2.11 × 10
14
u
15
− 6.66 × 10
14
u
14
+ · · · + 4.46 × 10
16
d + 9.32 ×
10
15
, 4.10 × 10
13
u
15
− 3.40 × 10
14
u
14
+ · · · + 8.91 × 10
16
c − 7.16 × 10
16
, 1.48 ×
10
15
u
15
− 5.08 × 10
15
u
14
+ · · · + 4.46 × 10
16
b − 3.25 × 10
16
, 2.99 × 10
14
u
15
−
2.30 × 10
15
u
14
+ · · · + 8.91 × 10
16
a + 5.86 × 10
15
, u
16
− 3u
15
+ · · · − 64u + 32i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
−0.000459505u
15
+ 0.00381819u
14
+ ··· + 0.107302u + 0.803663
−0.00474436u
15
+ 0.0149425u
14
+ ··· − 0.0874996u − 0.209095
a
3
=
−0.00335648u
15
+ 0.0258076u
14
+ ··· − 1.58963u − 0.0657305
−0.0332117u
15
+ 0.114086u
14
+ ··· − 5.13514u + 0.728469
a
11
=
−0.00520387u
15
+ 0.0187607u
14
+ ··· + 0.0198025u + 0.594568
−0.00474436u
15
+ 0.0149425u
14
+ ··· − 0.0874996u − 0.209095
a
2
=
−0.00335648u
15
+ 0.0258076u
14
+ ··· − 1.58963u − 0.0657305
−0.0222088u
15
+ 0.0813473u
14
+ ··· − 4.02050u + 0.224849
a
6
=
−0.0135509u
15
+ 0.0301119u
14
+ ··· + 0.340570u − 1.37215
−0.0269546u
15
+ 0.0690284u
14
+ ··· + 1.04739u − 1.50134
a
1
=
−0.0142293u
15
+ 0.0443303u
14
+ ··· + 0.947808u − 0.466505
−0.0277802u
15
+ 0.0744421u
14
+ ··· + 1.28838u − 1.83865
a
4
=
u
u
3
+ u
a
7
=
−0.000459505u
15
+ 0.00381819u
14
+ ··· + 0.107302u + 0.803663
0.00677644u
15
− 0.0186134u
14
+ ··· + 0.258343u + 0.131025
a
12
=
−0.0137698u
15
+ 0.0405121u
14
+ ··· + 0.840506u − 0.270168
−0.0230359u
15
+ 0.0594996u
14
+ ··· + 1.37588u − 1.62956
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
3870228309913117
22284377061017096
u
15
−
2739800330771103
5571094265254274
u
14
+ ··· +
43609984858099500
2785547132627137
u +
900447030377212
2785547132627137
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 9u
15
+ ··· − 24u + 16
c
2
, c
5
u
16
+ u
15
+ ··· − 8u + 4
c
3
u
16
− u
15
+ ··· − 984u + 612
c
4
, c
8
u
16
+ 3u
15
+ ··· + 64u + 32
c
6
, c
7
, c
9
c
10
, c
12
u
16
+ 5u
15
+ ··· + u + 1
c
11
u
16
− u
15
+ ··· + 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 3y
15
+ ··· + 1248y + 256
c
2
, c
5
y
16
+ 9y
15
+ ··· − 24y + 16
c
3
y
16
− 15y
15
+ ··· + 193320y + 374544
c
4
, c
8
y
16
− 15y
15
+ ··· + 5120y + 1024
c
6
, c
7
, c
9
c
10
, c
12
y
16
− y
15
+ ··· + 9y + 1
c
11
y
16
+ 39y
15
+ ··· + 25y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.289911 + 0.801405I
a = 0.044341 + 0.672495I
b = 0.167547 + 0.706079I
c = 0.654021 + 0.248004I
d = −0.336785 + 0.506907I
0.321814 − 1.225450I 4.70206 + 4.90073I
u = 0.289911 − 0.801405I
a = 0.044341 − 0.672495I
b = 0.167547 − 0.706079I
c = 0.654021 − 0.248004I
d = −0.336785 − 0.506907I
0.321814 + 1.225450I 4.70206 − 4.90073I
u = −1.139570 + 0.424244I
a = 0.835279 − 0.536067I
b = −0.871046 − 0.172594I
c = 0.589120 − 0.792720I
d = 0.396064 − 0.812657I
−0.71555 − 3.67228I 1.72542 + 4.33532I
u = −1.139570 − 0.424244I
a = 0.835279 + 0.536067I
b = −0.871046 + 0.172594I
c = 0.589120 + 0.792720I
d = 0.396064 + 0.812657I
−0.71555 + 3.67228I 1.72542 − 4.33532I
u = 0.575594 + 0.321074I
a = −0.193970 + 1.376780I
b = 0.333506 + 0.445900I
c = 1.017480 + 0.434986I
d = 0.169050 + 0.355242I
0.11872 − 1.44911I −0.36516 + 2.80335I
u = 0.575594 − 0.321074I
a = −0.193970 − 1.376780I
b = 0.333506 − 0.445900I
c = 1.017480 − 0.434986I
d = 0.169050 − 0.355242I
0.11872 + 1.44911I −0.36516 − 2.80335I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.067191 + 0.531573I
a = −1.65593 − 0.85713I
b = −3.05755 − 2.07892I
c = 0.547892 + 0.020957I
d = −0.822510 + 0.069711I
2.85279 − 2.27613I 11.67196 + 3.94896I
u = −0.067191 − 0.531573I
a = −1.65593 + 0.85713I
b = −3.05755 + 2.07892I
c = 0.547892 − 0.020957I
d = −0.822510 − 0.069711I
2.85279 + 2.27613I 11.67196 − 3.94896I
u = −0.33229 + 1.72297I
a = −0.700117 + 0.318420I
b = 1.01451 + 1.11512I
c = 0.412801 − 0.282825I
d = −0.648602 − 1.129520I
−4.26031 + 4.58330I 1.71878 − 4.05752I
u = −0.33229 − 1.72297I
a = −0.700117 − 0.318420I
b = 1.01451 − 1.11512I
c = 0.412801 + 0.282825I
d = −0.648602 + 1.129520I
−4.26031 − 4.58330I 1.71878 + 4.05752I
u = −1.81588 + 0.68377I
a = −0.560451 − 0.078372I
b = 0.088006 − 0.453655I
c = −0.227904 + 0.980118I
d = 1.22507 + 0.96795I
−6.64229 + 8.00732I 6.00576 − 3.88395I
u = −1.81588 − 0.68377I
a = −0.560451 + 0.078372I
b = 0.088006 + 0.453655I
c = −0.227904 − 0.980118I
d = 1.22507 − 0.96795I
−6.64229 − 8.00732I 6.00576 + 3.88395I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.72439 + 0.95526I
a = −0.028668 − 0.723076I
b = −0.46994 − 2.77688I
c = −0.389017 − 0.972862I
d = 1.35436 − 0.88620I
−9.8252 − 14.1242I 4.39428 + 6.97100I
u = 1.72439 − 0.95526I
a = −0.028668 + 0.723076I
b = −0.46994 + 2.77688I
c = −0.389017 + 0.972862I
d = 1.35436 + 0.88620I
−9.8252 + 14.1242I 4.39428 − 6.97100I
u = 2.26504 + 0.41669I
a = 0.259518 + 0.593001I
b = −0.70502 + 2.50841I
c = −0.104392 − 0.792584I
d = 1.16335 − 1.24018I
−12.28130 − 3.00558I 2.14690 + 1.40998I
u = 2.26504 − 0.41669I
a = 0.259518 − 0.593001I
b = −0.70502 − 2.50841I
c = −0.104392 + 0.792584I
d = 1.16335 + 1.24018I
−12.28130 + 3.00558I 2.14690 − 1.40998I
7
II. I
u
2
= h109cu
7
− 121u
7
+ · · · − 2066c + 3882, 9443cu
7
− 4639u
7
+ · · · −
1.50 × 10
4
c + 1182, 165u
7
+ 651u
6
+ · · · + 6184b − 234, 1393u
7
+ 1111u
6
+
· · · + 1.24 × 10
4
a + 1510, u
8
+ u
7
+ · · · − 8u − 4i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
10
=
c
−0.0352523cu
7
+ 0.0391332u
7
+ ··· + 0.668176c − 1.25550
a
3
=
−0.112629u
7
− 0.0898286u
6
+ ··· + 1.95820u − 0.122089
−0.0266818u
7
− 0.105272u
6
+ ··· + 0.644082u + 0.0378396
a
11
=
−0.0352523cu
7
+ 0.0391332u
7
+ ··· + 1.66818c − 1.25550
−0.0352523cu
7
+ 0.0391332u
7
+ ··· + 0.668176c − 1.25550
a
2
=
−0.112629u
7
− 0.0898286u
6
+ ··· + 1.95820u − 0.122089
−0.0140686u
7
− 0.128234u
6
+ ··· + 0.375970u + 0.129043
a
6
=
0.0257924u
7
− 0.0982374u
6
+ ··· + 0.310721u + 0.763422
0.0556274u
7
+ 0.00129366u
6
+ ··· − 0.900388u − 0.751617
a
1
=
0.0133409u
7
+ 0.0526358u
6
+ ··· − 0.322041u − 1.01892
0.0391332u
7
− 0.0456016u
6
+ ··· − 0.0113195u − 0.255498
a
4
=
u
u
3
+ u
a
7
=
c
0.0352523cu
7
− 0.0391332u
7
+ ··· − 0.668176c + 1.25550
a
12
=
−0.0391332cu
7
+ 0.0133409u
7
+ ··· + 1.25550c − 2.01892
−0.0595084cu
7
+ 0.0430142u
7
+ ··· + 0.338939c − 0.842820
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
933
1546
u
7
+
561
1546
u
6
−
7043
1546
u
5
−
278
773
u
4
+
8922
773
u
3
−
11743
1546
u
2
−
10913
1546
u +
2838
773
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
8
+ 6u
7
+ 15u
6
+ 14u
5
− 9u
4
− 31u
3
− 26u
2
− 8u + 1)
2
c
2
, c
5
(u
8
+ 2u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 7u
3
+ 4u
2
+ 4u + 1)
2
c
3
(u
8
− 2u
7
− 7u
6
+ 12u
5
+ 5u
4
+ 3u
3
− 2u
2
+ 2u + 1)
2
c
4
, c
8
(u
8
− u
7
− 7u
6
+ 4u
5
+ 16u
4
+ 3u
3
− 9u
2
+ 8u − 4)
2
c
6
, c
7
, c
9
c
10
, c
12
u
16
+ 3u
15
+ ··· − 40u − 16
c
11
u
16
− 3u
15
+ ··· − 2336u + 256
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
8
− 6y
7
+ 39y
6
− 146y
5
+ 267y
4
− 239y
3
+ 162y
2
− 116y + 1)
2
c
2
, c
5
(y
8
+ 6y
7
+ 15y
6
+ 14y
5
− 9y
4
− 31y
3
− 26y
2
− 8y + 1)
2
c
3
(y
8
− 18y
7
+ 107y
6
− 206y
5
− 9y
4
− 91y
3
+ 2y
2
− 8y + 1)
2
c
4
, c
8
(y
8
− 15y
7
+ 89y
6
− 252y
5
+ 366y
4
− 305y
3
− 95y
2
+ 8y + 16)
2
c
6
, c
7
, c
9
c
10
, c
12
y
16
− 3y
15
+ ··· − 2336y + 256
c
11
y
16
+ 17y
15
+ ··· − 2843136y + 65536
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.170290 + 0.725937I
a = 0.534878 + 0.687758I
b = −0.30552 + 1.93634I
c = 0.508470 + 0.631641I
d = 0.226676 + 0.960653I
−1.14222 + 1.62541I 1.41499 − 1.42555I
u = 1.170290 + 0.725937I
a = 0.534878 + 0.687758I
b = −0.30552 + 1.93634I
c = 0.406912 − 0.059872I
d = −1.40546 − 0.35393I
−1.14222 + 1.62541I 1.41499 − 1.42555I
u = 1.170290 − 0.725937I
a = 0.534878 − 0.687758I
b = −0.30552 − 1.93634I
c = 0.508470 − 0.631641I
d = 0.226676 − 0.960653I
−1.14222 − 1.62541I 1.41499 + 1.42555I
u = 1.170290 − 0.725937I
a = 0.534878 − 0.687758I
b = −0.30552 − 1.93634I
c = 0.406912 + 0.059872I
d = −1.40546 + 0.35393I
−1.14222 − 1.62541I 1.41499 + 1.42555I
u = −0.195492 + 0.552709I
a = −1.19398 + 1.11168I
b = 0.116024 + 0.545126I
c = 0.527146 + 0.046214I
d = −0.882537 + 0.165040I
2.92647 + 1.66195I 9.38368 − 3.48117I
u = −0.195492 + 0.552709I
a = −1.19398 + 1.11168I
b = 0.116024 + 0.545126I
c = −5.82950 + 3.76506I
d = 1.121050 + 0.078180I
2.92647 + 1.66195I 9.38368 − 3.48117I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.195492 − 0.552709I
a = −1.19398 − 1.11168I
b = 0.116024 − 0.545126I
c = 0.527146 − 0.046214I
d = −0.882537 − 0.165040I
2.92647 − 1.66195I 9.38368 + 3.48117I
u = −0.195492 − 0.552709I
a = −1.19398 − 1.11168I
b = 0.116024 − 0.545126I
c = −5.82950 − 3.76506I
d = 1.121050 − 0.078180I
2.92647 − 1.66195I 9.38368 + 3.48117I
u = −0.580387
a = −0.526601
b = −0.511567
c = 0.467644
d = −1.13838
2.18625 3.21290
u = −0.580387
a = −0.526601
b = −0.511567
c = 1.67123
d = 0.401639
2.18625 3.21290
u = 2.05532
a = 0.542487
b = −0.209470
c = 0.059530 + 0.815129I
d = 0.91088 + 1.22029I
−7.78143 4.64060
u = 2.05532
a = 0.542487
b = −0.209470
c = 0.059530 − 0.815129I
d = 0.91088 − 1.22029I
−7.78143 4.64060
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −2.21226 + 0.50002I
a = −0.098844 − 0.650687I
b = 0.55002 − 2.74145I
c = −0.131998 + 0.812425I
d = 1.19484 + 1.19923I
−12.14610 + 5.90409I 2.27459 − 2.82977I
u = −2.21226 + 0.50002I
a = −0.098844 − 0.650687I
b = 0.55002 − 2.74145I
c = 0.140006 − 0.672065I
d = 0.70292 − 1.42606I
−12.14610 + 5.90409I 2.27459 − 2.82977I
u = −2.21226 − 0.50002I
a = −0.098844 + 0.650687I
b = 0.55002 + 2.74145I
c = −0.131998 − 0.812425I
d = 1.19484 − 1.19923I
−12.14610 − 5.90409I 2.27459 + 2.82977I
u = −2.21226 − 0.50002I
a = −0.098844 + 0.650687I
b = 0.55002 + 2.74145I
c = 0.140006 + 0.672065I
d = 0.70292 + 1.42606I
−12.14610 − 5.90409I 2.27459 + 2.82977I
13
III. I
v
1
= ha, d, c − 1, b + v, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
1
0
a
3
=
0
−v
a
11
=
1
0
a
2
=
−1
−v
a
6
=
1
1
a
1
=
−1
−1
a
4
=
v
0
a
7
=
1
0
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u + 1)
2
c
12
(u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
c = 1.00000
d = 0
1.64493 − 2.02988I 3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = 1.00000
d = 0
1.64493 + 2.02988I 3.00000 − 3.46410I
17
IV. I
v
2
= ha, d + 1, av + c − a, b + v, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
−1
a
3
=
0
−v
a
11
=
−1
−1
a
2
=
−1
−v
a
6
=
1
1
a
1
=
−1
−1
a
4
=
v
0
a
7
=
1
1
a
12
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
8
c
11
, c
12
u
2
c
7
(u + 1)
2
c
9
, c
10
(u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
8
c
11
, c
12
y
2
c
7
, c
9
, c
10
(y − 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
c = 0
d = −1.00000
1.64493 − 2.02988I 3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = 0
d = −1.00000
1.64493 + 2.02988I 3.00000 − 3.46410I
21
V. I
v
3
= hc, d + 1, b, a + 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
−1
a
3
=
−1
0
a
11
=
−1
−1
a
2
=
−1
0
a
6
=
−1
0
a
1
=
−1
0
a
4
=
−1
0
a
7
=
1
1
a
12
=
−2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
u
c
6
, c
9
, c
10
u − 1
c
7
, c
11
, c
12
u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
y
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y − 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = −1.00000
b = 0
c = 0
d = −1.00000
3.28987 12.0000
25
VI. I
v
4
= hc, d + 1, −v
2
ba + v
3
b + · · · + c − 1, b
2
v
2
− bv + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
10
=
0
−1
a
3
=
a
b
a
11
=
−1
−1
a
2
=
−av + v
2
− b + 2a − 2v + 1
b
a
6
=
−a
2
v + 2v
2
a − v
3
− av + v
2
− b + a − 2v
−a
2
v + 2v
2
a − v
3
− av + v
2
− b + a − 2v − 1
a
1
=
a
2
v − 2v
2
a + v
3
+ av − v
2
+ b − a + 2v
a
2
v − 2v
2
a + v
3
+ av − v
2
+ b − a + 2v + 1
a
4
=
v
0
a
7
=
1
1
a
12
=
a
2
v − 2v
2
a + v
3
+ av − v
2
+ b − a + 2v − 1
a
2
v − 2v
2
a + v
3
+ av − v
2
+ b − a + 2v
(ii) Obstruction class = −1
(iii) Cusp Shapes = −a
3
v + 3v
3
a − 2v
4
− 3v
2
a + 3v
3
+ 3av − 5v
2
+ 4b − 7a + 5v + 5
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
26
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
3.28987 − 2.02988I 9.78678 − 2.82138I
27
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
· (u
8
+ 6u
7
+ 15u
6
+ 14u
5
− 9u
4
− 31u
3
− 26u
2
− 8u + 1)
2
· (u
16
+ 9u
15
+ ··· − 24u + 16)
c
2
u(u
2
+ u + 1)
2
(u
8
+ 2u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 7u
3
+ 4u
2
+ 4u + 1)
2
· (u
16
+ u
15
+ ··· − 8u + 4)
c
3
u(u
2
− u + 1)
2
(u
8
− 2u
7
− 7u
6
+ 12u
5
+ 5u
4
+ 3u
3
− 2u
2
+ 2u + 1)
2
· (u
16
− u
15
+ ··· − 984u + 612)
c
4
, c
8
u
5
(u
8
− u
7
− 7u
6
+ 4u
5
+ 16u
4
+ 3u
3
− 9u
2
+ 8u − 4)
2
· (u
16
+ 3u
15
+ ··· + 64u + 32)
c
5
u(u
2
− u + 1)
2
(u
8
+ 2u
7
+ 5u
6
+ 6u
5
+ 7u
4
+ 7u
3
+ 4u
2
+ 4u + 1)
2
· (u
16
+ u
15
+ ··· − 8u + 4)
c
6
u
2
(u − 1)(u + 1)
2
(u
16
+ 3u
15
+ ··· − 40u − 16)(u
16
+ 5u
15
+ ··· + u + 1)
c
7
u
2
(u + 1)
3
(u
16
+ 3u
15
+ ··· − 40u − 16)(u
16
+ 5u
15
+ ··· + u + 1)
c
9
, c
10
u
2
(u − 1)
3
(u
16
+ 3u
15
+ ··· − 40u − 16)(u
16
+ 5u
15
+ ··· + u + 1)
c
11
u
2
(u + 1)
3
(u
16
− 3u
15
+ ··· − 2336u + 256)(u
16
− u
15
+ ··· + 9u + 1)
c
12
u
2
(u − 1)
2
(u + 1)(u
16
+ 3u
15
+ ··· − 40u − 16)(u
16
+ 5u
15
+ ··· + u + 1)
28
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
· (y
8
− 6y
7
+ 39y
6
− 146y
5
+ 267y
4
− 239y
3
+ 162y
2
− 116y + 1)
2
· (y
16
− 3y
15
+ ··· + 1248y + 256)
c
2
, c
5
y(y
2
+ y + 1)
2
· (y
8
+ 6y
7
+ 15y
6
+ 14y
5
− 9y
4
− 31y
3
− 26y
2
− 8y + 1)
2
· (y
16
+ 9y
15
+ ··· − 24y + 16)
c
3
y(y
2
+ y + 1)
2
· (y
8
− 18y
7
+ 107y
6
− 206y
5
− 9y
4
− 91y
3
+ 2y
2
− 8y + 1)
2
· (y
16
− 15y
15
+ ··· + 193320y + 374544)
c
4
, c
8
y
5
(y
8
− 15y
7
+ 89y
6
− 252y
5
+ 366y
4
− 305y
3
− 95y
2
+ 8y + 16)
2
· (y
16
− 15y
15
+ ··· + 5120y + 1024)
c
6
, c
7
, c
9
c
10
, c
12
y
2
(y − 1)
3
(y
16
− 3y
15
+ ··· − 2336y + 256)(y
16
− y
15
+ ··· + 9y + 1)
c
11
y
2
(y − 1)
3
(y
16
+ 17y
15
+ ··· − 2843136y + 65536)
· (y
16
+ 39y
15
+ ··· + 25y + 1)
29
