8
17
(K8a
14
)
A knot diagram
1
Linearized knot diagam
7 5 1 2 8 3 4 6
Solving Sequence
5,8
6
1,3
2 4 7
c
5
c
8
c
2
c
4
c
7
c
1
, c
3
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= h−11044u
17
− 26768u
16
+ ··· + 654509b − 534698,
− 14404u
17
+ 515530u
16
+ ··· + 654509a − 1200167, u
18
+ u
17
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 18 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−1.10 × 10
4
u
17
− 2.68 × 10
4
u
16
+ · · · + 6.55 × 10
5
b − 5.35 × 10
5
, −1.44 ×
10
4
u
17
+ 5.16× 10
5
u
16
+ · · · + 6.55 × 10
5
a −1.20 × 10
6
, u
18
+ u
17
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
u
2
a
1
=
−u
−u
3
+ u
a
3
=
0.0220073u
17
− 0.787659u
16
+ ··· + 2.49594u + 1.83369
0.0168737u
17
+ 0.0408978u
16
+ ··· − 0.737771u + 0.816945
a
2
=
0.00513362u
17
− 0.828557u
16
+ ··· + 3.23371u + 1.01675
0.0168737u
17
+ 0.0408978u
16
+ ··· − 0.737771u + 0.816945
a
4
=
−0.00366076u
17
− 0.644874u
16
+ ··· + 2.32739u + 1.74996
−0.0674949u
17
− 0.163591u
16
+ ··· − 1.04891u + 0.732219
a
7
=
−0.00251181u
17
− 0.00174176u
16
+ ··· − 1.88221u − 0.722479
0.176743u
17
− 0.811747u
16
+ ··· + 3.33200u + 0.00509084
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2081176
654509
u
17
−
1538700
654509
u
16
+ ··· +
3609404
654509
u +
2997870
654509
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 3u
17
+ ··· + u + 1
c
2
, c
4
u
18
+ u
17
+ ··· + 3u + 1
c
3
u
18
− 3u
17
+ ··· − u + 1
c
5
, c
8
u
18
− u
17
+ ··· − 3u + 1
c
6
u
18
− u
17
+ ··· + 5u + 1
c
7
u
18
+ u
17
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
18
− 3y
17
+ ··· − 3y + 1
c
2
, c
4
, c
5
c
8
y
18
− 11y
17
+ ··· − 3y + 1
c
6
, c
7
y
18
+ 13y
17
+ ··· − 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.912810 + 0.341070I
a = 0.50288 + 1.83925I
b = 1.168300 + 0.720176I
1.46999 + 3.11720I 3.21326 − 6.66243I
u = −0.912810 − 0.341070I
a = 0.50288 − 1.83925I
b = 1.168300 − 0.720176I
1.46999 − 3.11720I 3.21326 + 6.66243I
u = 0.950168 + 0.130449I
a = 0.05948 − 3.09238I
b = 0.950168 − 0.130449I
− 0.520528I 0. − 13.01684I
u = 0.950168 − 0.130449I
a = 0.05948 + 3.09238I
b = 0.950168 + 0.130449I
0.520528I 0. + 13.01684I
u = −0.167072 + 1.125400I
a = 0.300048 + 0.121690I
b = −1.190060 + 0.368733I
3.57267 − 4.95181I 3.31278 + 5.61624I
u = −0.167072 − 1.125400I
a = 0.300048 − 0.121690I
b = −1.190060 − 0.368733I
3.57267 + 4.95181I 3.31278 − 5.61624I
u = −1.190060 + 0.368733I
a = −0.385891 + 1.324270I
b = −0.167072 + 1.125400I
−3.57267 + 4.95181I −3.31278 − 5.61624I
u = −1.190060 − 0.368733I
a = −0.385891 − 1.324270I
b = −0.167072 − 1.125400I
−3.57267 − 4.95181I −3.31278 + 5.61624I
u = 1.342100 + 0.135496I
a = −0.083889 − 0.268734I
b = −0.470709 − 0.243089I
−2.59619 − 0.05903I −5.04488 − 1.45254I
u = 1.342100 − 0.135496I
a = −0.083889 + 0.268734I
b = −0.470709 + 0.243089I
−2.59619 + 0.05903I −5.04488 + 1.45254I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.168300 + 0.720176I
a = 0.337342 + 0.860665I
b = −0.912810 + 0.341070I
−1.46999 − 3.11720I −3.21326 + 6.66243I
u = 1.168300 − 0.720176I
a = 0.337342 − 0.860665I
b = −0.912810 − 0.341070I
−1.46999 + 3.11720I −3.21326 − 6.66243I
u = −1.30098 + 0.59320I
a = −0.11190 − 1.47782I
b = −1.30098 − 0.59320I
10.9859I 0. − 7.09338I
u = −1.30098 − 0.59320I
a = −0.11190 + 1.47782I
b = −1.30098 + 0.59320I
− 10.9859I 0. + 7.09338I
u = 0.081063 + 0.532154I
a = 0.989810 − 0.121474I
b = 0.081063 − 0.532154I
− 1.47534I 0. + 4.20317I
u = 0.081063 − 0.532154I
a = 0.989810 + 0.121474I
b = 0.081063 + 0.532154I
1.47534I 0. − 4.20317I
u = −0.470709 + 0.243089I
a = 0.892107 + 0.422485I
b = 1.342100 − 0.135496I
2.59619 − 0.05903I 5.04488 − 1.45254I
u = −0.470709 − 0.243089I
a = 0.892107 − 0.422485I
b = 1.342100 + 0.135496I
2.59619 + 0.05903I 5.04488 + 1.45254I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
18
+ 3u
17
+ ··· + u + 1
c
2
, c
4
u
18
+ u
17
+ ··· + 3u + 1
c
3
u
18
− 3u
17
+ ··· − u + 1
c
5
, c
8
u
18
− u
17
+ ··· − 3u + 1
c
6
u
18
− u
17
+ ··· + 5u + 1
c
7
u
18
+ u
17
+ ··· − 5u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
18
− 3y
17
+ ··· − 3y + 1
c
2
, c
4
, c
5
c
8
y
18
− 11y
17
+ ··· − 3y + 1
c
6
, c
7
y
18
+ 13y
17
+ ··· − 3y + 1
8
