10
20
(K10a
74
)
A knot diagram
1
Linearized knot diagam
4 8 2 1 9 10 3 7 6 5
Solving Sequence
5,9
6 10 7 1 4 2 3 8
c
5
c
9
c
6
c
10
c
4
c
1
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
17
− u
16
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 17 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
= hu
17
− u
16
− 6u
15
+ 5u
14
+ 15u
13
− 9u
12
− 16u
11
+ 2u
10
− u
9
+
13u
8
+ 18u
7
− 12u
6
− 12u
5
− 4u
4
− 2u
3
+ 6u
2
+ 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
10
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
3
− 2u
−u
3
+ u
a
4
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
2
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
3
=
u
12
− 5u
10
+ 9u
8
− 4u
6
− 6u
4
+ 5u
2
+ 1
−u
12
+ 4u
10
− 6u
8
+ 2u
6
+ 3u
4
− 2u
2
a
8
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
15
− 24u
13
− 4u
12
+ 56u
11
+ 20u
10
− 44u
9
− 36u
8
− 40u
7
+
12u
6
+ 84u
5
+ 36u
4
− 12u
3
− 28u
2
− 36u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
u
17
+ 3u
16
+ ··· − 3u − 1
c
2
, c
7
u
17
+ u
16
+ ··· + u + 1
c
5
, c
6
, c
9
u
17
− u
16
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
y
17
+ 23y
16
+ ··· + 9y −1
c
2
, c
7
y
17
+ 3y
16
+ ··· − 3y −1
c
5
, c
6
, c
9
y
17
− 13y
16
+ ··· − 3y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012292 + 0.931569I
13.9525 + 3.3872I 0.08288 − 2.32417I
u = −0.012292 − 0.931569I
13.9525 − 3.3872I 0.08288 + 2.32417I
u = −1.11583
−2.09753 −3.69430
u = −1.164080 + 0.305929I
0.607153 + 1.195370I −3.40206 − 0.58854I
u = −1.164080 − 0.305929I
0.607153 − 1.195370I −3.40206 + 0.58854I
u = 1.261810 + 0.096321I
−4.71727 − 2.28997I −12.30509 + 4.71022I
u = 1.261810 − 0.096321I
−4.71727 + 2.28997I −12.30509 − 4.71022I
u = −0.066401 + 0.709465I
3.89229 + 2.50454I 0.07700 − 3.85927I
u = −0.066401 − 0.709465I
3.89229 − 2.50454I 0.07700 + 3.85927I
u = 1.262700 + 0.297820I
−0.19933 − 6.12281I −5.66204 + 6.84601I
u = 1.262700 − 0.297820I
−0.19933 + 6.12281I −5.66204 − 6.84601I
u = −1.282560 + 0.458780I
10.01240 + 1.56927I −3.08060 − 0.65050I
u = −1.282560 − 0.458780I
10.01240 − 1.56927I −3.08060 + 0.65050I
u = 1.301090 + 0.450240I
9.86681 − 8.31738I −3.35967 + 5.18877I
u = 1.301090 − 0.450240I
9.86681 + 8.31738I −3.35967 − 5.18877I
u = −0.242352 + 0.298895I
−0.289621 + 0.926552I −5.50330 − 7.34204I
u = −0.242352 − 0.298895I
−0.289621 − 0.926552I −5.50330 + 7.34204I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
u
17
+ 3u
16
+ ··· − 3u − 1
c
2
, c
7
u
17
+ u
16
+ ··· + u + 1
c
5
, c
6
, c
9
u
17
− u
16
+ ··· + 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
10
y
17
+ 23y
16
+ ··· + 9y −1
c
2
, c
7
y
17
+ 3y
16
+ ··· − 3y −1
c
5
, c
6
, c
9
y
17
− 13y
16
+ ··· − 3y −1
7
