10
10
(K10a
64
)
A knot diagram
1
Linearized knot diagam
6 10 9 8 7 2 1 4 3 5
Solving Sequence
1,6
2 7 8 5 4 10 3 9
c
1
c
6
c
7
c
5
c
4
c
10
c
2
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
22
− u
21
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 22 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
22
− u
21
− 5u
20
+ 6u
19
+ 12u
18
− 17u
17
− 15u
16
+ 28u
15
+ 8u
14
−
28u
13
+ 4u
12
+ 16u
11
− 8u
10
− 5u
9
+ 5u
8
+ 2u
7
− u
6
− 3u
5
+ u
4
+ 2u
3
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
8
=
−u
3
−u
3
+ u
a
5
=
u
3
u
5
− u
3
+ u
a
4
=
−u
11
+ 2u
9
− 2u
7
+ u
3
−u
11
+ 3u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
10
=
u
8
− u
6
+ u
4
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
3
=
u
16
− 3u
14
+ 5u
12
− 4u
10
+ 3u
8
− 2u
6
+ 2u
4
+ 1
u
18
− 4u
16
+ 9u
14
− 12u
12
+ 11u
10
− 6u
8
+ 2u
6
+ u
2
a
9
=
−u
19
+ 4u
17
− 8u
15
+ 8u
13
− 3u
11
− 2u
9
+ 2u
7
− u
3
−u
19
+ 5u
17
− 12u
15
+ 17u
13
− 15u
11
+ 9u
9
− 4u
7
+ 2u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
20
− 20u
18
+ 4u
17
+ 52u
16
− 16u
15
− 76u
14
+ 32u
13
+ 68u
12
−
32u
11
− 32u
10
+ 16u
9
+ 12u
8
− 4u
7
− 8u
6
+ 8u
5
+ 12u
4
− 8u
3
− 4u
2
+ 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
22
− u
21
+ ··· − u + 1
c
2
, c
3
, c
4
c
8
, c
9
u
22
+ u
21
+ ··· + u + 1
c
5
u
22
+ 11u
21
+ ··· + u + 1
c
7
u
22
− 3u
21
+ ··· − 9u + 8
c
10
u
22
+ u
21
+ ··· + 4u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
22
− 11y
21
+ ··· − y + 1
c
2
, c
3
, c
4
c
8
, c
9
y
22
+ 29y
21
+ ··· − y + 1
c
5
y
22
+ y
21
+ ··· + 11y + 1
c
7
y
22
+ 9y
21
+ ··· + 239y + 64
c
10
y
22
+ 5y
21
+ ··· − 40y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771950 + 0.627160I
−9.01082 − 2.42790I 0.88720 + 3.18483I
u = 0.771950 − 0.627160I
−9.01082 + 2.42790I 0.88720 − 3.18483I
u = −1.013800 + 0.421442I
−1.60921 + 1.77285I 0.315441 + 0.247623I
u = −1.013800 − 0.421442I
−1.60921 − 1.77285I 0.315441 − 0.247623I
u = 1.113890 + 0.304376I
−6.14010 − 0.06031I −5.06623 − 0.22454I
u = 1.113890 − 0.304376I
−6.14010 + 0.06031I −5.06623 + 0.22454I
u = 0.254770 + 0.794582I
−11.59400 + 4.17420I −0.08704 − 2.12766I
u = 0.254770 − 0.794582I
−11.59400 − 4.17420I −0.08704 + 2.12766I
u = −0.660123 + 0.489854I
−0.62516 + 1.83614I 2.06876 − 5.29489I
u = −0.660123 − 0.489854I
−0.62516 − 1.83614I 2.06876 + 5.29489I
u = 1.069940 + 0.505718I
−0.85422 − 4.78547I 3.13676 + 6.89182I
u = 1.069940 − 0.505718I
−0.85422 + 4.78547I 3.13676 − 6.89182I
u = −1.185860 + 0.285971I
−16.0637 − 0.8225I −5.38923 − 0.37902I
u = −1.185860 − 0.285971I
−16.0637 + 0.8225I −5.38923 + 0.37902I
u = −1.124840 + 0.532465I
−4.60646 + 7.61506I −2.18846 − 7.28240I
u = −1.124840 − 0.532465I
−4.60646 − 7.61506I −2.18846 + 7.28240I
u = −0.271243 + 0.702058I
−2.15136 − 2.90283I 0.96971 + 3.73642I
u = −0.271243 − 0.702058I
−2.15136 + 2.90283I 0.96971 − 3.73642I
u = 1.158640 + 0.550804I
−14.2580 − 9.1806I −3.12638 + 5.65206I
u = 1.158640 − 0.550804I
−14.2580 + 9.1806I −3.12638 − 5.65206I
u = 0.386678 + 0.542882I
1.115750 + 0.498475I 8.47948 − 1.93150I
u = 0.386678 − 0.542882I
1.115750 − 0.498475I 8.47948 + 1.93150I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
22
− u
21
+ ··· − u + 1
c
2
, c
3
, c
4
c
8
, c
9
u
22
+ u
21
+ ··· + u + 1
c
5
u
22
+ 11u
21
+ ··· + u + 1
c
7
u
22
− 3u
21
+ ··· − 9u + 8
c
10
u
22
+ u
21
+ ··· + 4u + 4
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
22
− 11y
21
+ ··· − y + 1
c
2
, c
3
, c
4
c
8
, c
9
y
22
+ 29y
21
+ ··· − y + 1
c
5
y
22
+ y
21
+ ··· + 11y + 1
c
7
y
22
+ 9y
21
+ ··· + 239y + 64
c
10
y
22
+ 5y
21
+ ··· − 40y + 16
7
