10
104
(K10a
118
)
A knot diagram
1
Linearized knot diagam
8 6 1 9 10 3 4 2 5 7
Solving Sequence
4,9
5 10
2,6
8 1 3 7
c
4
c
9
c
5
c
8
c
1
c
3
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
14
− 11u
13
+ ··· + 4b − 20, 41u
14
+ 221u
13
+ ··· + 8a + 196,
u
15
+ 7u
14
+ 18u
13
+ 20u
12
+ 14u
11
+ 31u
10
+ 55u
9
+ 44u
8
+ 40u
7
+ 54u
6
+ 31u
5
+ 9u
4
+ 7u
3
− 6u
2
+ 8i
I
u
2
= h109a
5
u
4
+ 90a
4
u
4
+ ··· − 83a + 145, −2a
4
u
4
− 5u
4
a
3
+ ··· − 18a − 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
u
3
= h−u
4
+ u
3
+ 2u
2
+ b − u, u
6
+ u
5
− 4u
4
− 4u
3
+ 3u
2
+ a + 3u + 1, u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 52 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
14
− 11u
13
+ · · · + 4b − 20, 41u
14
+ 221u
13
+ · · · + 8a +
196, u
15
+ 7u
14
+ · · · − 6u
2
+ 8i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
−5.12500u
14
− 27.6250u
13
+ ··· + 15.5000u − 24.5000
1
4
u
14
+
11
4
u
13
+ ··· −
9
2
u + 5
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
3u
14
+
33
2
u
13
+ ··· − 10u +
31
2
3
2
u
14
+ 7u
13
+ ··· +
1
2
u + 4
a
1
=
−8u
14
−
179
4
u
13
+ ··· +
125
4
u − 44
17
4
u
14
+
97
4
u
13
+ ··· − 19u + 26
a
3
=
53
8
u
14
+
301
8
u
13
+ ··· − 26u +
77
2
−
15
4
u
14
−
89
4
u
13
+ ··· +
47
2
u − 27
a
7
=
3
2
u
14
+
19
2
u
13
+ ··· −
21
2
u +
23
2
3
2
u
14
+ 7u
13
+ ··· +
1
2
u + 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10u
14
+ 59u
13
+ 113u
12
+ 66u
11
+ 54u
10
+ 245u
9
+ 267u
8
+
113u
7
+ 251u
6
+ 241u
5
+ 11u
4
+ 66u
3
− 7u
2
− 60u + 74
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
15
+ u
14
+ ··· − 3u
3
− 1
c
3
u
15
− 12u
14
+ ··· + 240u − 32
c
4
, c
5
, c
9
u
15
+ 7u
14
+ ··· − 6u
2
+ 8
c
7
, c
10
u
15
− 3u
13
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
15
− 9y
14
+ ··· + 4y
2
− 1
c
3
y
15
− 4y
14
+ ··· − 1280y −1024
c
4
, c
5
, c
9
y
15
− 13y
14
+ ··· + 96y −64
c
7
, c
10
y
15
− 6y
14
+ ··· + 13y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.388466 + 0.947688I
a = 0.050943 − 1.350340I
b = −0.47742 − 1.71628I
−5.82203 + 9.38410I −3.97952 − 7.17475I
u = 0.388466 − 0.947688I
a = 0.050943 + 1.350340I
b = −0.47742 + 1.71628I
−5.82203 − 9.38410I −3.97952 + 7.17475I
u = −0.101121 + 0.829275I
a = 0.467120 + 0.846136I
b = −0.108197 + 1.248190I
−1.32635 + 1.58430I 2.05695 − 3.17357I
u = −0.101121 − 0.829275I
a = 0.467120 − 0.846136I
b = −0.108197 − 1.248190I
−1.32635 − 1.58430I 2.05695 + 3.17357I
u = 0.922792 + 0.829091I
a = −0.839212 + 0.446521I
b = 0.265387 + 1.302840I
−4.34026 − 3.41455I −3.26031 + 4.30453I
u = 0.922792 − 0.829091I
a = −0.839212 − 0.446521I
b = 0.265387 − 1.302840I
−4.34026 + 3.41455I −3.26031 − 4.30453I
u = 0.528410 + 0.302526I
a = 0.715576 + 0.595124I
b = 0.246839 − 0.030877I
1.036950 + 0.848562I 5.31510 − 2.72513I
u = 0.528410 − 0.302526I
a = 0.715576 − 0.595124I
b = 0.246839 + 0.030877I
1.036950 − 0.848562I 5.31510 + 2.72513I
u = −1.38123 + 0.42191I
a = −0.521626 − 0.558152I
b = 1.14450 − 1.53934I
2.89422 − 6.37595I 2.35312 + 7.90831I
u = −1.38123 − 0.42191I
a = −0.521626 + 0.558152I
b = 1.14450 + 1.53934I
2.89422 + 6.37595I 2.35312 − 7.90831I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48635 + 0.07152I
a = 0.098561 − 0.589973I
b = 0.379744 − 0.426871I
7.67422 − 2.17377I 7.19312 + 2.21789I
u = −1.48635 − 0.07152I
a = 0.098561 + 0.589973I
b = 0.379744 + 0.426871I
7.67422 + 2.17377I 7.19312 − 2.21789I
u = −1.49023 + 0.36505I
a = 0.758806 + 0.630997I
b = −1.13261 + 1.70886I
0.18522 − 14.10710I −0.21037 + 7.77333I
u = −1.49023 − 0.36505I
a = 0.758806 − 0.630997I
b = −1.13261 − 1.70886I
0.18522 + 14.10710I −0.21037 − 7.77333I
u = −1.76149
a = −0.460333
b = 0.363500
5.97579 −5.93620
6
II. I
u
2
= h109a
5
u
4
+ 90a
4
u
4
+ · · · − 83a + 145, −2a
4
u
4
− 5u
4
a
3
+ · · · − 18a −
1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
a
−0.947826a
5
u
4
− 0.782609a
4
u
4
+ ··· + 0.721739a − 1.26087
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
a
2
u
1.56522a
5
u
4
− 0.278261a
4
u
4
+ ··· − 0.547826a + 0.973913
a
1
=
−a
3
u
2
+ a
−0.504348a
5
u
4
− 1.63478a
4
u
4
+ ··· + 0.556522a − 0.278261
a
3
=
1.39130a
5
u
4
+ 0.330435a
4
u
4
+ ··· + 1.71304a + 0.843478
−1.23478a
5
u
4
− 0.678261a
4
u
4
+ ··· + 0.452174a + 0.373913
a
7
=
−1.56522a
5
u
4
+ 0.278261a
4
u
4
+ ··· + 0.547826a − 0.973913
1.56522a
5
u
4
− 0.278261a
4
u
4
+ ··· − 0.547826a + 0.973913
(ii) Obstruction class = −1
(iii) Cusp Shapes =
232
115
a
5
u
4
+
752
115
a
4
u
4
+ ··· −
256
115
a −
102
115
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
30
− u
29
+ ··· − 64u − 7
c
3
(u
3
+ u
2
− 1)
10
c
4
, c
5
, c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
6
c
7
, c
10
u
30
− 3u
29
+ ··· − 14u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
30
− 21y
29
+ ··· − 1884y + 49
c
3
(y
3
− y
2
+ 2y −1)
10
c
4
, c
5
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
6
c
7
, c
10
y
30
+ 7y
29
+ ··· − 116y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = −0.806664 + 0.705849I
b = 0.41170 + 1.41665I
0.49041 + 2.82812I −1.00910 − 2.97945I
u = −1.21774
a = −0.806664 − 0.705849I
b = 0.41170 − 1.41665I
0.49041 − 2.82812I −1.00910 + 2.97945I
u = −1.21774
a = 1.23353
b = −2.05678
−3.64718 −7.53840
u = −1.21774
a = 0.671225 + 0.117277I
b = −0.96834 + 1.96626I
0.49041 + 2.82812I −1.00910 − 2.97945I
u = −1.21774
a = 0.671225 − 0.117277I
b = −0.96834 − 1.96626I
0.49041 − 2.82812I −1.00910 + 2.97945I
u = −1.21774
a = −1.59237
b = 0.582023
−3.64718 −7.53840
u = −0.309916 + 0.549911I
a = −1.25942 + 0.90741I
b = −0.129260 − 0.273797I
−1.58157 − 4.35870I −1.97513 + 7.41010I
u = −0.309916 + 0.549911I
a = 1.21172 + 1.02695I
b = −0.218320 + 1.108690I
−1.58157 + 1.29754I −1.97513 + 1.45120I
u = −0.309916 + 0.549911I
a = 0.048773 + 0.350100I
b = −0.820174 + 0.651930I
−1.58157 + 1.29754I −1.97513 + 1.45120I
u = −0.309916 + 0.549911I
a = −0.37583 − 1.80799I
b = 0.54889 − 1.72674I
−1.58157 − 4.35870I −1.97513 + 7.41010I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309916 + 0.549911I
a = −0.96996 − 1.69646I
b = −0.67455 − 1.32965I
−5.71916 − 1.53058I −8.50440 + 4.43065I
u = −0.309916 + 0.549911I
a = 0.47350 + 2.32765I
b = −0.145272 + 1.011820I
−5.71916 − 1.53058I −8.50440 + 4.43065I
u = −0.309916 − 0.549911I
a = −1.25942 − 0.90741I
b = −0.129260 + 0.273797I
−1.58157 + 4.35870I −1.97513 − 7.41010I
u = −0.309916 − 0.549911I
a = 1.21172 − 1.02695I
b = −0.218320 − 1.108690I
−1.58157 − 1.29754I −1.97513 − 1.45120I
u = −0.309916 − 0.549911I
a = 0.048773 − 0.350100I
b = −0.820174 − 0.651930I
−1.58157 − 1.29754I −1.97513 − 1.45120I
u = −0.309916 − 0.549911I
a = −0.37583 + 1.80799I
b = 0.54889 + 1.72674I
−1.58157 + 4.35870I −1.97513 − 7.41010I
u = −0.309916 − 0.549911I
a = −0.96996 + 1.69646I
b = −0.67455 + 1.32965I
−5.71916 + 1.53058I −8.50440 − 4.43065I
u = −0.309916 − 0.549911I
a = 0.47350 − 2.32765I
b = −0.145272 − 1.011820I
−5.71916 + 1.53058I −8.50440 − 4.43065I
u = 1.41878 + 0.21917I
a = −0.837994 + 0.477676I
b = 1.48326 + 1.70876I
3.96189 + 7.22895I 2.25407 − 6.47803I
u = 1.41878 + 0.21917I
a = −0.265271 − 0.909026I
b = −0.218527 − 0.470543I
3.96189 + 7.22895I 2.25407 − 6.47803I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41878 + 0.21917I
a = 0.772271 − 0.730462I
b = −0.335807 − 1.278970I
−0.17569 + 4.40083I −4.27520 − 3.49859I
u = 1.41878 + 0.21917I
a = 0.696565 − 0.364337I
b = −1.33013 − 0.90847I
3.96189 + 1.57271I 2.25407 − 0.51914I
u = 1.41878 + 0.21917I
a = −0.666236 + 0.232053I
b = −0.10143 + 1.90226I
−0.17569 + 4.40083I −4.27520 − 3.49859I
u = 1.41878 + 0.21917I
a = 0.486743 + 0.419449I
b = −0.264664 + 0.140760I
3.96189 + 1.57271I 2.25407 − 0.51914I
u = 1.41878 − 0.21917I
a = −0.837994 − 0.477676I
b = 1.48326 − 1.70876I
3.96189 − 7.22895I 2.25407 + 6.47803I
u = 1.41878 − 0.21917I
a = −0.265271 + 0.909026I
b = −0.218527 + 0.470543I
3.96189 − 7.22895I 2.25407 + 6.47803I
u = 1.41878 − 0.21917I
a = 0.772271 + 0.730462I
b = −0.335807 + 1.278970I
−0.17569 − 4.40083I −4.27520 + 3.49859I
u = 1.41878 − 0.21917I
a = 0.696565 + 0.364337I
b = −1.33013 + 0.90847I
3.96189 − 1.57271I 2.25407 + 0.51914I
u = 1.41878 − 0.21917I
a = −0.666236 − 0.232053I
b = −0.10143 − 1.90226I
−0.17569 − 4.40083I −4.27520 + 3.49859I
u = 1.41878 − 0.21917I
a = 0.486743 − 0.419449I
b = −0.264664 − 0.140760I
3.96189 − 1.57271I 2.25407 + 0.51914I
12
III. I
u
3
= h−u
4
+ u
3
+ 2u
2
+ b − u, u
6
+ u
5
− 4u
4
− 4u
3
+ 3u
2
+ a + 3u +
1, u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
2
=
−u
6
− u
5
+ 4u
4
+ 4u
3
− 3u
2
− 3u − 1
u
4
− u
3
− 2u
2
+ u
a
6
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
u
6
− 4u
4
− 2u
3
+ 4u
2
+ 4u + 1
u
6
− 3u
4
− u
3
+ 2u
2
+ u
a
1
=
u
6
+ u
5
− 3u
4
− 4u
3
+ 3u + 2
−u
3
+ 2u
a
3
=
−u
6
− u
5
+ 4u
4
+ 4u
3
− 3u
2
− 3u
−u
6
+ 4u
4
− 4u
2
a
7
=
−u
4
− u
3
+ 2u
2
+ 3u + 1
u
6
− 3u
4
− u
3
+ 2u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
6
+ u
5
+ 3u
4
+ 3u
3
+ 7u
2
− 5u − 8
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
7
− u
6
− 3u
5
+ 3u
4
+ 2u
3
− 3u
2
− u + 1
c
2
, c
8
u
7
+ u
6
− 3u
5
− 3u
4
+ 2u
3
+ 3u
2
− u − 1
c
3
u
7
+ 3u
6
+ 3u
5
− u
4
− 4u
3
− 2u
2
+ 1
c
4
, c
5
u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1
c
7
, c
10
u
7
+ u
4
− 2u
3
− 1
c
9
u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
7
− 7y
6
+ 19y
5
− 29y
4
+ 30y
3
− 19y
2
+ 7y −1
c
3
y
7
− 3y
6
+ 7y
5
− 13y
4
+ 6y
3
− 2y
2
+ 4y −1
c
4
, c
5
, c
9
y
7
− 8y
6
+ 24y
5
− 33y
4
+ 20y
3
− 6y
2
+ 4y −1
c
7
, c
10
y
7
− 4y
5
− y
4
+ 4y
3
+ 2y
2
− 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.25920
a = 1.35619
b = −1.39446
−2.88904 5.52810
u = −0.401963 + 0.546430I
a = 1.019580 + 0.650467I
b = −0.59726 + 1.44367I
−2.11479 + 2.13385I −6.73578 − 5.40456I
u = −0.401963 − 0.546430I
a = 1.019580 − 0.650467I
b = −0.59726 − 1.44367I
−2.11479 − 2.13385I −6.73578 + 5.40456I
u = −1.346460 + 0.204423I
a = −0.556014 − 0.539828I
b = 0.21748 − 1.74792I
1.45010 − 4.82255I 1.50641 + 5.81707I
u = −1.346460 − 0.204423I
a = −0.556014 + 0.539828I
b = 0.21748 + 1.74792I
1.45010 + 4.82255I 1.50641 − 5.81707I
u = 0.552010
a = −2.60549
b = −0.132774
−5.57629 −7.84920
u = 1.68564
a = 0.322173
b = −0.713207
6.50483 9.77980
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
7
− u
6
+ ··· − u + 1)(u
15
+ u
14
+ ··· − 3u
3
− 1)
· (u
30
− u
29
+ ··· − 64u − 7)
c
2
, c
8
(u
7
+ u
6
+ ··· − u − 1)(u
15
+ u
14
+ ··· − 3u
3
− 1)
· (u
30
− u
29
+ ··· − 64u − 7)
c
3
(u
3
+ u
2
− 1)
10
(u
7
+ 3u
6
+ 3u
5
− u
4
− 4u
3
− 2u
2
+ 1)
· (u
15
− 12u
14
+ ··· + 240u − 32)
c
4
, c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
6
(u
7
− 4u
5
− u
4
+ 4u
3
+ 2u
2
− 1)
· (u
15
+ 7u
14
+ ··· − 6u
2
+ 8)
c
7
, c
10
(u
7
+ u
4
− 2u
3
− 1)(u
15
− 3u
13
+ ··· + u + 1)(u
30
− 3u
29
+ ··· − 14u − 1)
c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
6
(u
7
− 4u
5
+ u
4
+ 4u
3
− 2u
2
+ 1)
· (u
15
+ 7u
14
+ ··· − 6u
2
+ 8)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
7
− 7y
6
+ 19y
5
− 29y
4
+ 30y
3
− 19y
2
+ 7y −1)
· (y
15
− 9y
14
+ ··· + 4y
2
− 1)(y
30
− 21y
29
+ ··· − 1884y + 49)
c
3
(y
3
− y
2
+ 2y −1)
10
(y
7
− 3y
6
+ 7y
5
− 13y
4
+ 6y
3
− 2y
2
+ 4y −1)
· (y
15
− 4y
14
+ ··· − 1280y −1024)
c
4
, c
5
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
6
· (y
7
− 8y
6
+ 24y
5
− 33y
4
+ 20y
3
− 6y
2
+ 4y −1)
· (y
15
− 13y
14
+ ··· + 96y −64)
c
7
, c
10
(y
7
− 4y
5
− y
4
+ 4y
3
+ 2y
2
− 1)(y
15
− 6y
14
+ ··· + 13y −1)
· (y
30
+ 7y
29
+ ··· − 116y + 1)
18
