10
97
(K10a
12
)
A knot diagram
1
Linearized knot diagam
6 9 7 3 10 4 1 5 2 8
Solving Sequence
3,7
4
5,9
2 10 6 1 8
c
3
c
4
c
2
c
9
c
6
c
1
c
8
c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2736614u
16
+ 18940720u
15
+ ··· + 188712037b − 172998039,
178471267u
16
+ 26934984u
15
+ ··· + 754848148a + 1554469489,
u
17
+ 3u
15
+ 7u
13
+ u
12
+ 10u
11
+ 2u
10
+ 11u
9
+ 4u
8
+ 22u
7
− 12u
6
+ 38u
5
− 21u
4
+ 36u
3
− 18u
2
+ 17u − 4i
I
u
2
= hu
13
a − u
13
+ ··· + b − 3, 2u
13
a − u
13
+ ··· + 2a − 5,
u
14
− u
13
+ 3u
12
− 2u
11
+ 6u
10
− 3u
9
+ 7u
8
− 2u
7
+ 6u
6
+ 4u
4
+ 2u
2
+ u + 1i
I
u
3
= hb + 1, 2a − 2u − 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 47 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
= h2.74 × 10
6
u
16
+ 1 .89 × 10
7
u
15
+ · · · + 1.89 × 10
8
b − 1.73 × 10
8
, 1.78 ×
10
8
u
16
+2.69×10
7
u
15
+· · ·+7.55×10
8
a+1.55×10
9
, u
17
+3u
15
+· · ·+17u−4i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
u
2
+ 1
−u
2
a
9
=
−0.236433u
16
− 0.0356827u
15
+ ··· + 3.37770u − 2.05931
−0.0145015u
16
− 0.100368u
15
+ ··· − 1.37842u + 0.916730
a
2
=
0.252945u
16
+ 0.0144309u
15
+ ··· − 3.32958u + 2.37418
0.0316855u
16
+ 0.201926u
15
+ ··· + 2.11952u − 0.917967
a
10
=
−0.475929u
16
+ 0.0117484u
15
+ ··· + 7.44839u − 3.87934
−0.0117484u
16
− 0.307312u
15
+ ··· − 4.21145u + 1.90371
a
6
=
−u
u
3
+ u
a
1
=
0.229183u
16
− 0.0145015u
15
+ ··· − 3.56691u + 2.51768
−0.0356827u
16
+ 0.0837041u
15
+ ··· + 1.96005u − 0.945733
a
8
=
−0.229492u
16
+ 0.0316855u
15
+ ··· + 3.85585u − 1.78184
0.0144309u
16
− 0.191499u
15
+ ··· − 1.92588u + 1.01178
(ii) Obstruction class = −1
(iii) Cusp Shapes =
153304973
188712037
u
16
−
89774747
754848148
u
15
+ ··· −
9028153643
754848148
u −
1460399043
188712037
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
4(4u
17
+ 2u
16
+ ··· + u
2
+ 1)
c
2
, c
7
, c
9
c
10
u
17
+ 2u
16
+ ··· − 2u + 1
c
3
, c
6
u
17
+ 3u
15
+ ··· + 17u + 4
c
4
u
17
+ 6u
16
+ ··· + 145u − 16
c
5
u
17
− 3u
16
+ ··· − 24u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
16(16y
17
+ 132y
16
+ ··· − 2y −1)
c
2
, c
7
, c
9
c
10
y
17
+ 10y
16
+ ··· + 8y −1
c
3
, c
6
y
17
+ 6y
16
+ ··· + 145y −16
c
4
y
17
+ 10y
16
+ ··· + 44449y −256
c
5
y
17
+ 5y
16
+ ··· − 6976y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.417221 + 0.885126I
a = −0.476552 + 0.009774I
b = −0.222604 + 0.163997I
−0.34103 − 1.75255I −2.16634 + 2.85736I
u = −0.417221 − 0.885126I
a = −0.476552 − 0.009774I
b = −0.222604 − 0.163997I
−0.34103 + 1.75255I −2.16634 − 2.85736I
u = 0.597620 + 0.869356I
a = −0.334759 + 0.962950I
b = 1.335870 + 0.125893I
−1.15632 + 2.35456I 2.48228 − 6.50501I
u = 0.597620 − 0.869356I
a = −0.334759 − 0.962950I
b = 1.335870 − 0.125893I
−1.15632 − 2.35456I 2.48228 + 6.50501I
u = 0.236791 + 0.896556I
a = 0.903548 + 1.016340I
b = 0.840094 − 0.523489I
−2.94308 + 1.91475I −12.50863 − 1.23884I
u = 0.236791 − 0.896556I
a = 0.903548 − 1.016340I
b = 0.840094 + 0.523489I
−2.94308 − 1.91475I −12.50863 + 1.23884I
u = 0.979244 + 0.594888I
a = 0.26940 + 1.57950I
b = −0.44756 − 1.37873I
9.32990 − 8.56729I 0.17143 + 4.34513I
u = 0.979244 − 0.594888I
a = 0.26940 − 1.57950I
b = −0.44756 + 1.37873I
9.32990 + 8.56729I 0.17143 − 4.34513I
u = −1.198530 + 0.485201I
a = −0.11385 + 1.41682I
b = −0.047500 − 1.229640I
7.90214 − 1.97950I 6.13742 + 2.92595I
u = −1.198530 − 0.485201I
a = −0.11385 − 1.41682I
b = −0.047500 + 1.229640I
7.90214 + 1.97950I 6.13742 − 2.92595I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.745598 + 1.114110I
a = −1.29641 − 1.54585I
b = −0.53774 + 1.38258I
7.7059 + 14.8527I −2.01529 − 8.44038I
u = 0.745598 − 1.114110I
a = −1.29641 + 1.54585I
b = −0.53774 − 1.38258I
7.7059 − 14.8527I −2.01529 + 8.44038I
u = −0.203786 + 1.345170I
a = −0.540937 + 0.304824I
b = −0.347263 − 1.122360I
1.26847 − 6.54787I −3.86293 + 7.90993I
u = −0.203786 − 1.345170I
a = −0.540937 − 0.304824I
b = −0.347263 + 1.122360I
1.26847 + 6.54787I −3.86293 − 7.90993I
u = −0.87723 + 1.18507I
a = 0.723215 − 1.188380I
b = 0.161092 + 1.190930I
5.81019 − 5.32225I 2.45956 + 7.34338I
u = −0.87723 − 1.18507I
a = 0.723215 + 1.188380I
b = 0.161092 − 1.190930I
5.81019 + 5.32225I 2.45956 − 7.34338I
u = 0.275016
a = −1.51732
b = 0.531228
−0.869406 −11.1450
6
II.
I
u
2
= hu
13
a−u
13
+· · · +b−3, 2u
13
a−u
13
+· · · +2a−5, u
14
−u
13
+· · · +u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
5
=
u
2
+ 1
−u
2
a
9
=
a
−u
13
a + u
13
+ ··· − 2u + 3
a
2
=
u
13
a + 6u
13
+ ··· + 3a + 6
−u
13
a − u
13
+ ··· − a + 1
a
10
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
−u
13
+ u
12
− 2u
11
+ 3u
10
− 3u
9
+ 5u
8
− 2u
7
+ 6u
6
+ 4u
4
+ 3u
2
+ u + 1
a
6
=
−u
u
3
+ u
a
1
=
u
12
a + 3u
13
+ ··· + 2a + 6
2u
13
− 2u
12
+ ··· − au + 2
a
8
=
−u
13
a − u
13
+ ··· − a + 1
−u
13
a + 2u
13
+ ··· + a + 4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
12
+ 4u
11
− 8u
10
+ 8u
9
− 16u
8
+ 12u
7
− 12u
6
+ 12u
5
− 8u
4
+ 4u
3
− 4u
2
+ 8u − 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
28
− 3u
27
+ ··· − 1254u + 653
c
2
, c
7
, c
9
c
10
u
28
− 5u
27
+ ··· − 2u + 1
c
3
, c
5
, c
6
(u
14
+ u
13
+ ··· − u + 1)
2
c
4
(u
14
+ 5u
13
+ ··· + 3u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
28
+ 15y
27
+ ··· + 3659320y + 426409
c
2
, c
7
, c
9
c
10
y
28
+ 19y
27
+ ··· − 10y
2
+ 1
c
3
, c
5
, c
6
(y
14
+ 5y
13
+ ··· + 3y + 1)
2
c
4
(y
14
+ 9y
13
+ ··· + 15y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772300 + 0.626535I
a = 0.406503 − 0.509972I
b = −1.027090 − 0.175615I
4.48016 − 3.41271I −1.89400 + 2.62516I
u = 0.772300 + 0.626535I
a = −0.59492 − 1.65604I
b = 0.41210 + 1.42136I
4.48016 − 3.41271I −1.89400 + 2.62516I
u = 0.772300 − 0.626535I
a = 0.406503 + 0.509972I
b = −1.027090 + 0.175615I
4.48016 + 3.41271I −1.89400 − 2.62516I
u = 0.772300 − 0.626535I
a = −0.59492 + 1.65604I
b = 0.41210 − 1.42136I
4.48016 + 3.41271I −1.89400 − 2.62516I
u = −0.050221 + 1.076790I
a = −0.752996 − 0.510112I
b = −0.637817 + 0.252286I
−1.35286 − 2.76747I −9.41762 + 3.21377I
u = −0.050221 + 1.076790I
a = 0.315982 + 0.198126I
b = 0.426047 + 1.000290I
−1.35286 − 2.76747I −9.41762 + 3.21377I
u = −0.050221 − 1.076790I
a = −0.752996 + 0.510112I
b = −0.637817 − 0.252286I
−1.35286 + 2.76747I −9.41762 − 3.21377I
u = −0.050221 − 1.076790I
a = 0.315982 − 0.198126I
b = 0.426047 − 1.000290I
−1.35286 + 2.76747I −9.41762 − 3.21377I
u = 0.727524 + 0.860849I
a = 0.715949 + 1.174200I
b = −0.51211 − 1.46812I
7.93259 + 2.76747I 1.41762 − 3.21377I
u = 0.727524 + 0.860849I
a = −1.19732 − 1.74297I
b = −0.64484 + 1.35997I
7.93259 + 2.76747I 1.41762 − 3.21377I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.727524 − 0.860849I
a = 0.715949 − 1.174200I
b = −0.51211 + 1.46812I
7.93259 − 2.76747I 1.41762 + 3.21377I
u = 0.727524 − 0.860849I
a = −1.19732 + 1.74297I
b = −0.64484 − 1.35997I
7.93259 − 2.76747I 1.41762 + 3.21377I
u = −0.494052 + 0.663856I
a = 0.96368 − 1.66194I
b = 0.053811 − 0.680241I
3.26705 − 1.37770I −4.88590 + 4.12207I
u = −0.494052 + 0.663856I
a = −0.95490 − 2.71701I
b = 0.006983 + 1.150230I
3.26705 − 1.37770I −4.88590 + 4.12207I
u = −0.494052 − 0.663856I
a = 0.96368 + 1.66194I
b = 0.053811 + 0.680241I
3.26705 + 1.37770I −4.88590 − 4.12207I
u = −0.494052 − 0.663856I
a = −0.95490 + 2.71701I
b = 0.006983 − 1.150230I
3.26705 + 1.37770I −4.88590 − 4.12207I
u = −0.622207 + 1.001070I
a = 0.372140 + 0.404462I
b = 0.340282 + 0.137082I
2.09958 − 3.41271I −6.10600 + 2.62516I
u = −0.622207 + 1.001070I
a = −1.58493 + 1.41489I
b = −0.136381 − 1.104830I
2.09958 − 3.41271I −6.10600 + 2.62516I
u = −0.622207 − 1.001070I
a = 0.372140 − 0.404462I
b = 0.340282 − 0.137082I
2.09958 + 3.41271I −6.10600 − 2.62516I
u = −0.622207 − 1.001070I
a = −1.58493 − 1.41489I
b = −0.136381 + 1.104830I
2.09958 + 3.41271I −6.10600 − 2.62516I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.683715 + 1.025590I
a = 0.010710 − 0.783806I
b = −1.148810 + 0.016311I
3.28987 + 8.93586I −4.00000 − 7.26077I
u = 0.683715 + 1.025590I
a = 1.32082 + 1.63940I
b = 0.56444 − 1.41873I
3.28987 + 8.93586I −4.00000 − 7.26077I
u = 0.683715 − 1.025590I
a = 0.010710 + 0.783806I
b = −1.148810 − 0.016311I
3.28987 − 8.93586I −4.00000 + 7.26077I
u = 0.683715 − 1.025590I
a = 1.32082 − 1.63940I
b = 0.56444 + 1.41873I
3.28987 − 8.93586I −4.00000 + 7.26077I
u = −0.517057 + 0.454483I
a = −0.163546 − 1.319840I
b = −0.212363 − 0.520130I
3.31269 − 1.37770I −3.11410 + 4.12207I
u = −0.517057 + 0.454483I
a = −0.85718 − 1.74842I
b = 0.015745 + 1.176090I
3.31269 − 1.37770I −3.11410 + 4.12207I
u = −0.517057 − 0.454483I
a = −0.163546 + 1.319840I
b = −0.212363 + 0.520130I
3.31269 + 1.37770I −3.11410 − 4.12207I
u = −0.517057 − 0.454483I
a = −0.85718 + 1.74842I
b = 0.015745 − 1.176090I
3.31269 + 1.37770I −3.11410 − 4.12207I
12
III. I
u
3
= hb + 1, 2a − 2u − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u + 1
a
5
=
−u
u + 1
a
9
=
u +
1
2
−1
a
2
=
u +
3
2
−1
a
10
=
2u + 2
−2
a
6
=
−u
u + 1
a
1
=
u + 1
−
1
2
u − 1
a
8
=
u + 1
1
2
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
4
u − 10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
2
− 2u + 1)
c
2
, c
10
(u + 1)
2
c
3
, c
4
u
2
+ u + 1
c
5
u
2
c
6
u
2
− u + 1
c
7
, c
9
(u − 1)
2
c
8
4(4u
2
+ 2u + 1)
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
16(16y
2
+ 4y + 1)
c
2
, c
7
, c
9
c
10
(y −1)
2
c
3
, c
4
, c
6
y
2
+ y + 1
c
5
y
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.866025I
b = −1.00000
−1.64493 − 2.02988I −10.12500 + 0.21651I
u = −0.500000 − 0.866025I
a = − 0.866025I
b = −1.00000
−1.64493 + 2.02988I −10.12500 − 0.21651I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(4u
2
− 2u + 1)(4u
17
+ 2u
16
+ ··· + u
2
+ 1)
· (u
28
− 3u
27
+ ··· − 1254u + 653)
c
2
, c
10
((u + 1)
2
)(u
17
+ 2u
16
+ ··· − 2u + 1)(u
28
− 5u
27
+ ··· − 2u + 1)
c
3
(u
2
+ u + 1)(u
14
+ u
13
+ ··· − u + 1)
2
(u
17
+ 3u
15
+ ··· + 17u + 4)
c
4
(u
2
+ u + 1)(u
14
+ 5u
13
+ ··· + 3u + 1)
2
(u
17
+ 6u
16
+ ··· + 145u − 16)
c
5
u
2
(u
14
+ u
13
+ ··· − u + 1)
2
(u
17
− 3u
16
+ ··· − 24u + 32)
c
6
(u
2
− u + 1)(u
14
+ u
13
+ ··· − u + 1)
2
(u
17
+ 3u
15
+ ··· + 17u + 4)
c
7
, c
9
((u − 1)
2
)(u
17
+ 2u
16
+ ··· − 2u + 1)(u
28
− 5u
27
+ ··· − 2u + 1)
c
8
16(4u
2
+ 2u + 1)(4u
17
+ 2u
16
+ ··· + u
2
+ 1)
· (u
28
− 3u
27
+ ··· − 1254u + 653)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
256(16y
2
+ 4y + 1)(16y
17
+ 132y
16
+ ··· − 2y −1)
· (y
28
+ 15y
27
+ ··· + 3659320y + 426409)
c
2
, c
7
, c
9
c
10
((y −1)
2
)(y
17
+ 10y
16
+ ··· + 8y −1)(y
28
+ 19y
27
+ ··· − 10y
2
+ 1)
c
3
, c
6
(y
2
+ y + 1)(y
14
+ 5y
13
+ ··· + 3y + 1)
2
(y
17
+ 6y
16
+ ··· + 145y −16)
c
4
(y
2
+ y + 1)(y
14
+ 9y
13
+ ··· + 15y + 1)
2
· (y
17
+ 10y
16
+ ··· + 44449y −256)
c
5
y
2
(y
14
+ 5y
13
+ ··· + 3y + 1)
2
(y
17
+ 5y
16
+ ··· − 6976y −1024)
18
