10
17
(K10a
107
)
A knot diagram
1
Linearized knot diagam
6 7 1 9 10 2 3 4 5 8
Solving Sequence
2,6
7 3 8 1 4 10 5 9
c
6
c
2
c
7
c
1
c
3
c
10
c
5
c
9
c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
+ u
19
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 20 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
20
+ u
19
− 11u
18
− 10u
17
+ 49u
16
+ 38u
15
− 114u
14
− 66u
13
+ 152u
12
+
47u
11
− 125u
10
− 4u
9
+ 67u
8
− 8u
7
− 20u
6
+ 10u
5
+ 5u
4
− 3u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
u
a
4
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
10
=
u
7
− 4u
5
+ 4u
3
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
5
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 37u
8
− 12u
6
+ 4u
4
+ 1
u
18
− 10u
16
+ 39u
14
− 74u
12
+ 71u
10
− 38u
8
+ 18u
6
− 4u
4
+ u
2
a
9
=
−u
14
+ 7u
12
− 16u
10
+ 11u
8
+ 2u
6
+ 1
−u
14
+ 8u
12
− 23u
10
+ 28u
8
− 14u
6
+ 4u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
18
− 44u
16
+ 192u
14
− 4u
13
− 420u
12
+ 32u
11
+ 484u
10
−
92u
9
− 296u
8
+ 112u
7
+ 100u
6
− 56u
5
− 4u
4
+ 20u
3
− 4u
2
− 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
20
− u
19
+ ··· − u
2
+ 1
c
3
u
20
− 5u
19
+ ··· + 4u + 1
c
4
, c
5
, c
8
c
9
u
20
+ u
19
+ ··· − u
2
+ 1
c
10
u
20
+ 5u
19
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
y
20
− 23y
19
+ ··· − 2y + 1
c
3
, c
10
y
20
+ y
19
+ ··· − 46y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886444
4.43265 −0.716390
u = 0.653943 + 0.534643I
7.54354 − 5.98288I 2.92800 + 5.90364I
u = 0.653943 − 0.534643I
7.54354 + 5.98288I 2.92800 − 5.90364I
u = −0.638615 + 0.441759I
3.91005I 0. − 8.23335I
u = −0.638615 − 0.441759I
− 3.91005I 0. + 8.23335I
u = 0.613121 + 0.271451I
−1.152210 − 0.756271I −5.04397 + 1.60900I
u = 0.613121 − 0.271451I
−1.152210 + 0.756271I −5.04397 − 1.60900I
u = 0.265798 + 0.599404I
8.68051 + 2.11373I 5.79765 − 0.04379I
u = 0.265798 − 0.599404I
8.68051 − 2.11373I 5.79765 + 0.04379I
u = −1.38695
3.92816 1.96120
u = −0.232031 + 0.442395I
1.152210 − 0.756271I 5.04397 + 1.60900I
u = −0.232031 − 0.442395I
1.152210 + 0.756271I 5.04397 − 1.60900I
u = 1.51222
−4.43265 0.716390
u = −1.58303 + 0.08477I
−8.68051 + 2.11373I −5.79765 − 0.04379I
u = −1.58303 − 0.08477I
−8.68051 − 2.11373I −5.79765 + 0.04379I
u = 1.58517 + 0.12489I
−7.54354 − 5.98288I −2.92800 + 5.90364I
u = 1.58517 − 0.12489I
−7.54354 + 5.98288I −2.92800 − 5.90364I
u = −1.58631 + 0.15748I
8.53676I 0. − 4.57594I
u = −1.58631 − 0.15748I
− 8.53676I 0. + 4.57594I
u = 1.60509
−3.92816 −1.96120
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
20
− u
19
+ ··· − u
2
+ 1
c
3
u
20
− 5u
19
+ ··· + 4u + 1
c
4
, c
5
, c
8
c
9
u
20
+ u
19
+ ··· − u
2
+ 1
c
10
u
20
+ 5u
19
+ ··· − 4u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
y
20
− 23y
19
+ ··· − 2y + 1
c
3
, c
10
y
20
+ y
19
+ ··· − 46y + 1
7
