12a
0376
(K12a
0376
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 12 1 11 5 4 8 7
Solving Sequence
4,11
10
2,5
6 9 3 1 8 12 7
c
10
c
4
c
5
c
9
c
3
c
1
c
8
c
11
c
7
c
2
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
46
− 22u
44
+ ··· + 4b − 4u, u
46
+ 21u
44
+ ··· + 4a + 2, u
49
− 2u
48
+ ··· + 4u − 2i
I
u
2
= h−15a
2
u
2
− 8a
2
u + 29u
2
a − 35a
2
+ 25au + 26u
2
+ 22b + 86a + 8u + 46,
a
3
− 4u
2
a − 2a
2
− 5au − u
2
+ 5u − 3, u
3
+ 2u − 1i
I
u
3
= h11u
3
a
2
− 2a
2
u
2
+ 23u
3
a + 14a
2
u − 18u
2
a − 26u
3
+ 2a
2
+ 31au − 16u
2
+ 19b − a − 40u − 22,
a
3
+ 2a
2
u + u
2
a + 2a
2
+ 5au + 2u
2
− u − 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
I
u
4
= hb − u + 1, 2a + 3u − 2, u
2
+ 2i
I
v
1
= ha, b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 73 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
=
h−u
46
−22u
44
+· · ·+4b−4u, u
46
+21u
44
+· · ·+4a+2, u
49
−2u
48
+· · ·+4u−2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
−
1
4
u
46
−
21
4
u
44
+ ··· −
1
2
u −
1
2
1
4
u
46
+
11
2
u
44
+ ··· + 7u
4
+ u
a
5
=
u
u
3
+ u
a
6
=
−
1
2
u
48
+ u
47
+ ··· + u −
1
2
u
48
− u
47
+ ··· −
3
2
u + 1
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
−
1
2
u
48
+ u
47
+ ··· + 2u −
3
2
3
4
u
45
+
63
4
u
43
+ ··· +
1
2
u − 1
a
8
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
12
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
7
=
−
1
4
u
39
−
9
2
u
37
+ ··· +
1
2
u + 1
−
1
4
u
41
−
19
4
u
39
+ ··· +
5
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
48
− 4u
47
+ ··· − 2u + 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 26u
48
+ ··· + 85u + 9
c
2
, c
5
u
49
+ 2u
48
+ ··· − 5u − 3
c
3
u
49
+ 2u
48
+ ··· + 796u − 202
c
4
, c
9
, c
10
u
49
− 2u
48
+ ··· + 4u − 2
c
6
, c
7
, c
12
u
49
− 2u
48
+ ··· − 9u − 3
c
8
, c
11
u
49
+ 6u
48
+ ··· − 672u − 144
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
− 2y
48
+ ··· + 1321y −81
c
2
, c
5
y
49
− 26y
48
+ ··· + 85y −9
c
3
y
49
+ 22y
48
+ ··· − 274576y −40804
c
4
, c
9
, c
10
y
49
+ 46y
48
+ ··· + 8y −4
c
6
, c
7
, c
12
y
49
− 42y
48
+ ··· − 123y −9
c
8
, c
11
y
49
+ 42y
48
+ ··· − 46080y −20736
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167676 + 1.064370I
a = 0.778944 + 0.169238I
b = −0.470107 + 0.435995I
3.40475 − 2.26424I 9.47951 + 3.87164I
u = −0.167676 − 1.064370I
a = 0.778944 − 0.169238I
b = −0.470107 − 0.435995I
3.40475 + 2.26424I 9.47951 − 3.87164I
u = −0.617073 + 0.561498I
a = −1.89242 + 0.26973I
b = −0.37899 + 2.12914I
−2.80940 + 6.68744I 4.35067 − 3.31669I
u = −0.617073 − 0.561498I
a = −1.89242 − 0.26973I
b = −0.37899 − 2.12914I
−2.80940 − 6.68744I 4.35067 + 3.31669I
u = −0.715606 + 0.424836I
a = 1.350570 − 0.398846I
b = 0.62117 − 2.62903I
−2.31988 − 11.15510I 5.36635 + 8.72298I
u = −0.715606 − 0.424836I
a = 1.350570 + 0.398846I
b = 0.62117 + 2.62903I
−2.31988 + 11.15510I 5.36635 − 8.72298I
u = 0.677267 + 0.437562I
a = −1.279370 − 0.460443I
b = −0.40698 − 2.65012I
−6.72347 + 6.63996I 1.11534 − 6.53780I
u = 0.677267 − 0.437562I
a = −1.279370 + 0.460443I
b = −0.40698 + 2.65012I
−6.72347 − 6.63996I 1.11534 + 6.53780I
u = 0.252222 + 0.762976I
a = 0.970740 − 0.162669I
b = −0.393396 + 1.056380I
3.14407 − 2.16679I 8.11057 + 2.63992I
u = 0.252222 − 0.762976I
a = 0.970740 + 0.162669I
b = −0.393396 − 1.056380I
3.14407 + 2.16679I 8.11057 − 2.63992I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.619485 + 0.505792I
a = 2.02337 + 0.19994I
b = 0.63493 + 2.03020I
−6.98732 − 2.33424I 0.197314 + 0.287759I
u = 0.619485 − 0.505792I
a = 2.02337 − 0.19994I
b = 0.63493 − 2.03020I
−6.98732 + 2.33424I 0.197314 − 0.287759I
u = 0.678594 + 0.396938I
a = −0.306907 − 0.562427I
b = 0.588764 − 0.054642I
0.90488 + 6.19501I 8.65458 − 5.85948I
u = 0.678594 − 0.396938I
a = −0.306907 + 0.562427I
b = 0.588764 + 0.054642I
0.90488 − 6.19501I 8.65458 + 5.85948I
u = 0.555271 + 0.515337I
a = −0.193065 − 0.411686I
b = 0.636055 + 0.278393I
0.40390 − 2.07527I 7.58708 − 0.16558I
u = 0.555271 − 0.515337I
a = −0.193065 + 0.411686I
b = 0.636055 − 0.278393I
0.40390 + 2.07527I 7.58708 + 0.16558I
u = 0.004497 + 1.254000I
a = −1.19737 − 0.79732I
b = 1.006470 + 0.945825I
−2.64701 + 1.46809I 0
u = 0.004497 − 1.254000I
a = −1.19737 + 0.79732I
b = 1.006470 − 0.945825I
−2.64701 − 1.46809I 0
u = 0.693958 + 0.185476I
a = −1.059550 + 0.036670I
b = −0.487962 − 1.323070I
5.18309 + 5.73272I 11.27016 − 7.28979I
u = 0.693958 − 0.185476I
a = −1.059550 − 0.036670I
b = −0.487962 + 1.323070I
5.18309 − 5.73272I 11.27016 + 7.28979I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233838 + 1.278280I
a = −0.114835 − 0.343745I
b = 0.465963 + 0.494287I
2.08059 − 4.29919I 0
u = −0.233838 − 1.278280I
a = −0.114835 + 0.343745I
b = 0.465963 − 0.494287I
2.08059 + 4.29919I 0
u = −0.670778 + 0.090636I
a = 0.695159 − 0.378048I
b = 0.035918 + 0.211766I
6.30803 − 1.01693I 14.2364 + 0.8419I
u = −0.670778 − 0.090636I
a = 0.695159 + 0.378048I
b = 0.035918 − 0.211766I
6.30803 + 1.01693I 14.2364 − 0.8419I
u = −0.196767 + 1.339410I
a = 1.98113 + 1.52913I
b = −0.93410 − 1.43004I
−4.92180 − 6.08417I 0
u = −0.196767 − 1.339410I
a = 1.98113 − 1.52913I
b = −0.93410 + 1.43004I
−4.92180 + 6.08417I 0
u = 0.265708 + 1.335960I
a = −1.24758 + 1.71469I
b = −0.054082 − 1.297110I
0.40943 + 9.20745I 0
u = 0.265708 − 1.335960I
a = −1.24758 − 1.71469I
b = −0.054082 + 1.297110I
0.40943 − 9.20745I 0
u = −0.565566 + 0.178039I
a = 0.847644 − 0.080313I
b = −0.168017 − 1.386940I
−0.16483 − 3.30304I 6.58993 + 8.73893I
u = −0.565566 − 0.178039I
a = 0.847644 + 0.080313I
b = −0.168017 + 1.386940I
−0.16483 + 3.30304I 6.58993 − 8.73893I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.075529 + 1.409520I
a = −0.06668 − 2.20376I
b = −0.56477 + 1.41957I
−7.18390 − 0.26810I 0
u = −0.075529 − 1.409520I
a = −0.06668 + 2.20376I
b = −0.56477 − 1.41957I
−7.18390 + 0.26810I 0
u = 0.25245 + 1.46110I
a = −0.594045 − 0.560678I
b = 0.440686 + 0.137021I
−5.08167 + 9.59602I 0
u = 0.25245 − 1.46110I
a = −0.594045 + 0.560678I
b = 0.440686 − 0.137021I
−5.08167 − 9.59602I 0
u = 0.19236 + 1.47058I
a = −0.541758 − 0.828898I
b = 0.550975 + 0.570094I
−5.96591 + 0.62329I 0
u = 0.19236 − 1.47058I
a = −0.541758 + 0.828898I
b = 0.550975 − 0.570094I
−5.96591 − 0.62329I 0
u = 0.04361 + 1.49144I
a = 0.26431 − 2.05562I
b = 0.16481 + 1.98787I
−3.91948 − 1.38659I 0
u = 0.04361 − 1.49144I
a = 0.26431 + 2.05562I
b = 0.16481 − 1.98787I
−3.91948 + 1.38659I 0
u = 0.24647 + 1.47591I
a = −1.23308 + 3.23255I
b = −0.78225 − 3.64550I
−12.9040 + 10.0134I 0
u = 0.24647 − 1.47591I
a = −1.23308 − 3.23255I
b = −0.78225 + 3.64550I
−12.9040 − 10.0134I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.26382 + 1.47698I
a = 1.05482 + 3.15508I
b = 1.08638 − 3.45807I
−8.4594 − 14.7285I 0
u = −0.26382 − 1.47698I
a = 1.05482 − 3.15508I
b = 1.08638 + 3.45807I
−8.4594 + 14.7285I 0
u = 0.21115 + 1.48782I
a = 0.15274 − 2.56686I
b = 1.82838 + 2.31454I
−13.44400 + 0.67957I 0
u = 0.21115 − 1.48782I
a = 0.15274 + 2.56686I
b = 1.82838 − 2.31454I
−13.44400 − 0.67957I 0
u = −0.19310 + 1.50554I
a = −0.22564 − 2.54437I
b = −1.59683 + 2.50677I
−9.54977 + 3.78347I 0
u = −0.19310 − 1.50554I
a = −0.22564 + 2.54437I
b = −1.59683 − 2.50677I
−9.54977 − 3.78347I 0
u = −0.202679 + 0.413695I
a = −1.41900 − 1.17309I
b = −0.167114 + 0.794243I
−1.52088 + 0.82300I −1.75933 − 1.01274I
u = −0.202679 − 0.413695I
a = −1.41900 + 1.17309I
b = −0.167114 − 0.794243I
−1.52088 − 0.82300I −1.75933 + 1.01274I
u = 0.418775
a = −0.496253
b = 0.688205
0.773938 13.3940
9
II. I
u
2
=
h−15a
2
u
2
+29u
2
a+· · ·+86a+46, a
3
−4u
2
a−2a
2
−5au−u
2
+5u−3, u
3
+2u−1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
a
0.681818a
2
u
2
− 1.31818au
2
+ ··· − 3.90909a − 2.09091
a
5
=
u
−u + 1
a
6
=
−0.409091a
2
u
2
+ 0.590909au
2
+ ··· + 1.54545a + 0.454545
1
2
a
2
u
2
−
3
2
u
2
a + ··· − 4a − 1
a
9
=
u
2
+ 1
u
a
3
=
−u
2
− u
u
2
a
1
=
0.0454545a
2
u
2
+ 0.0454545au
2
+ ··· − 0.727273a − 0.272727
0.818182a
2
u
2
− 1.68182au
2
+ ··· − 3.59091a − 1.90909
a
8
=
u
2
− u + 1
u
a
12
=
u
2
+ u
−u
2
a
7
=
−0.227273a
2
u
2
+ 0.272727au
2
+ ··· + 0.136364a + 0.363636
0.545455a
2
u
2
− 1.45455au
2
+ ··· − 3.72727a − 1.27273
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 4u + 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 6u
8
+ 15u
7
+ 16u
6
− u
5
− 18u
4
− 11u
3
+ 4u
2
+ 4u + 1
c
2
, c
5
, c
6
c
7
, c
12
u
9
− 3u
7
+ 3u
5
+ u
3
− 2u + 1
c
3
(u
3
− 3u
2
+ 5u − 2)
3
c
4
, c
8
, c
9
c
10
, c
11
(u
3
+ 2u − 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 6y
8
+ 31y
7
− 92y
6
+ 207y
5
− 322y
4
+ 225y
3
− 68y
2
+ 8y −1
c
2
, c
5
, c
6
c
7
, c
12
y
9
− 6y
8
+ 15y
7
− 16y
6
− y
5
+ 18y
4
− 11y
3
− 4y
2
+ 4y −1
c
3
(y
3
+ y
2
+ 13y −4)
3
c
4
, c
8
, c
9
c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.583843 − 0.678582I
b = −0.519013 + 0.319210I
−9.44074 − 5.13794I 0.68207 + 3.20902I
u = −0.22670 + 1.46771I
a = −0.07989 − 2.57481I
b = −2.01693 + 2.08171I
−9.44074 − 5.13794I 0.68207 + 3.20902I
u = −0.22670 + 1.46771I
a = 1.49604 + 3.25339I
b = 0.33038 − 3.73184I
−9.44074 − 5.13794I 0.68207 + 3.20902I
u = −0.22670 − 1.46771I
a = 0.583843 + 0.678582I
b = −0.519013 − 0.319210I
−9.44074 + 5.13794I 0.68207 − 3.20902I
u = −0.22670 − 1.46771I
a = −0.07989 + 2.57481I
b = −2.01693 − 2.08171I
−9.44074 + 5.13794I 0.68207 − 3.20902I
u = −0.22670 − 1.46771I
a = 1.49604 − 3.25339I
b = 0.33038 + 3.73184I
−9.44074 + 5.13794I 0.68207 − 3.20902I
u = 0.453398
a = −0.547908 + 0.054538I
b = 0.637390 − 0.369377I
0.787199 12.6360
u = 0.453398
a = −0.547908 − 0.054538I
b = 0.637390 + 0.369377I
0.787199 12.6360
u = 0.453398
a = 3.09582
b = 1.13636
0.787199 12.6360
13
III. I
u
3
= h11u
3
a
2
+ 23u
3
a + · · · − a − 22, a
3
+ 2a
2
u + u
2
a + 2a
2
+ 5au +
2u
2
− u − 1, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
2
=
a
−0.578947a
2
u
3
− 1.21053au
3
+ ··· + 0.0526316a + 1.15789
a
5
=
u
u
3
+ u
a
6
=
0.315789a
2
u
3
+ 0.842105au
3
+ ··· + 1.78947a − 0.631579
−0.947368a
2
u
3
− 0.526316au
3
+ ··· + 0.631579a + 1.89474
a
9
=
u
2
+ 1
−u
3
− 2u − 1
a
3
=
−u
3
− 2u − 1
−u
3
− u
2
− u − 2
a
1
=
0.789474a
2
u
3
+ 0.105263au
3
+ ··· − 0.526316a − 1.57895
0.789474a
2
u
3
+ 1.10526au
3
+ ··· + 2.47368a − 1.57895
a
8
=
u
3
+ u
2
+ 2u + 2
−u
3
− 2u − 1
a
12
=
u
3
+ 2u + 1
u
3
+ u
2
+ u + 2
a
7
=
0.263158a
2
u
3
+ 1.36842au
3
+ ··· + 1.15789a − 0.526316
−0.105263a
2
u
3
+ 1.05263au
3
+ ··· + 2.73684a + 0.210526
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 4u + 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ 8u
11
+ ··· + 2u
2
+ 1
c
2
, c
5
, c
6
c
7
, c
12
u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 2u
6
− 3u
5
− 3u
4
− u
3
+ 2u
2
+ 2u + 1
c
3
(u
2
+ u + 1)
6
c
4
, c
8
, c
9
c
10
, c
11
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 8y
11
+ ··· + 4y + 1
c
2
, c
5
, c
6
c
7
, c
12
y
12
− 8y
11
+ ··· + 2y
2
+ 1
c
3
(y
2
+ y + 1)
6
c
4
, c
8
, c
9
c
10
, c
11
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 1.164420 − 0.511133I
b = 0.14782 − 2.60434I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = 0.253508 − 0.493412I
b = −0.619418 + 0.097186I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.621744 + 0.440597I
a = −2.17444 + 0.12335I
b = −0.91328 + 1.87086I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = −0.621744 − 0.440597I
a = 1.164420 + 0.511133I
b = 0.14782 + 2.60434I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = 0.253508 + 0.493412I
b = −0.619418 − 0.097186I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −2.17444 − 0.12335I
b = −0.91328 − 1.87086I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = 0.276849 − 0.783184I
b = −0.361992 + 0.876949I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = −0.07790 − 2.21669I
b = 0.939408 + 0.575735I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 + 1.306620I
a = −2.44244 + 0.38663I
b = 1.80746 − 0.35693I
−3.28987 + 2.02988I 4.00000 − 3.46410I
u = 0.121744 − 1.306620I
a = 0.276849 + 0.783184I
b = −0.361992 − 0.876949I
−3.28987 − 2.02988I 4.00000 + 3.46410I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.121744 − 1.306620I
a = −0.07790 + 2.21669I
b = 0.939408 − 0.575735I
−3.28987 − 2.02988I 4.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = −2.44244 − 0.38663I
b = 1.80746 + 0.35693I
−3.28987 − 2.02988I 4.00000 + 3.46410I
18
IV. I
u
4
= hb − u + 1, 2a + 3u − 2, u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
−2
a
2
=
−
3
2
u + 1
u − 1
a
5
=
u
−u
a
6
=
−
1
2
u + 1
−1
a
9
=
−1
0
a
3
=
−u
u
a
1
=
−
1
2
u + 1
−1
a
8
=
−1
0
a
12
=
1
0
a
7
=
−
1
2
u
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
(u − 1)
2
c
2
, c
12
(u + 1)
2
c
3
, c
4
, c
9
c
10
u
2
+ 2
c
8
, c
11
u
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y − 1)
2
c
3
, c
4
, c
9
c
10
(y + 2)
2
c
8
, c
11
y
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 1.00000 − 2.12132I
b = −1.00000 + 1.41421I
−4.93480 0
u = − 1.414210I
a = 1.00000 + 2.12132I
b = −1.00000 − 1.41421I
−4.93480 0
22
V. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
1
0
a
10
=
1
0
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
9
=
1
0
a
3
=
1
0
a
1
=
−1
−1
a
8
=
1
0
a
12
=
1
0
a
7
=
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
u
c
5
, c
6
, c
7
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
y − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
9
+ 6u
8
+ ··· + 4u + 1)
· (u
12
+ 8u
11
+ ··· + 2u
2
+ 1)(u
49
+ 26u
48
+ ··· + 85u + 9)
c
2
(u − 1)(u + 1)
2
(u
9
− 3u
7
+ 3u
5
+ u
3
− 2u + 1)
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 2u
6
− 3u
5
− 3u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
49
+ 2u
48
+ ··· − 5u − 3)
c
3
u(u
2
+ 2)(u
2
+ u + 1)
6
(u
3
− 3u
2
+ 5u − 2)
3
· (u
49
+ 2u
48
+ ··· + 796u − 202)
c
4
, c
9
, c
10
u(u
2
+ 2)(u
3
+ 2u − 1)
3
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
3
· (u
49
− 2u
48
+ ··· + 4u − 2)
c
5
(u − 1)
2
(u + 1)(u
9
− 3u
7
+ 3u
5
+ u
3
− 2u + 1)
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 2u
6
− 3u
5
− 3u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
49
+ 2u
48
+ ··· − 5u − 3)
c
6
, c
7
(u − 1)
2
(u + 1)(u
9
− 3u
7
+ 3u
5
+ u
3
− 2u + 1)
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 2u
6
− 3u
5
− 3u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
49
− 2u
48
+ ··· − 9u − 3)
c
8
, c
11
u
3
(u
3
+ 2u − 1)
3
(u
4
+ u
3
+ 2u
2
+ 2u + 1)
3
· (u
49
+ 6u
48
+ ··· − 672u − 144)
c
12
(u − 1)(u + 1)
2
(u
9
− 3u
7
+ 3u
5
+ u
3
− 2u + 1)
· (u
12
− 4u
10
− u
9
+ 6u
8
+ 3u
7
− 2u
6
− 3u
5
− 3u
4
− u
3
+ 2u
2
+ 2u + 1)
· (u
49
− 2u
48
+ ··· − 9u − 3)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
3
· (y
9
− 6y
8
+ 31y
7
− 92y
6
+ 207y
5
− 322y
4
+ 225y
3
− 68y
2
+ 8y − 1)
· (y
12
− 8y
11
+ ··· + 4y + 1)(y
49
− 2y
48
+ ··· + 1321y − 81)
c
2
, c
5
((y − 1)
3
)(y
9
− 6y
8
+ ··· + 4y − 1)
· (y
12
− 8y
11
+ ··· + 2y
2
+ 1)(y
49
− 26y
48
+ ··· + 85y − 9)
c
3
y(y + 2)
2
(y
2
+ y + 1)
6
(y
3
+ y
2
+ 13y − 4)
3
· (y
49
+ 22y
48
+ ··· − 274576y − 40804)
c
4
, c
9
, c
10
y(y + 2)
2
(y
3
+ 4y
2
+ 4y − 1)
3
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· (y
49
+ 46y
48
+ ··· + 8y − 4)
c
6
, c
7
, c
12
((y − 1)
3
)(y
9
− 6y
8
+ ··· + 4y − 1)
· (y
12
− 8y
11
+ ··· + 2y
2
+ 1)(y
49
− 42y
48
+ ··· − 123y − 9)
c
8
, c
11
y
3
(y
3
+ 4y
2
+ 4y − 1)
3
(y
4
+ 3y
3
+ 2y
2
+ 1)
3
· (y
49
+ 42y
48
+ ··· − 46080y − 20736)
28
