10
26
(K10a
111
)
A knot diagram
1
Linearized knot diagam
7 8 9 10 1 3 2 6 5 4
Solving Sequence
3,8
2 7 1 6 9 4 5 10
c
2
c
7
c
1
c
6
c
8
c
3
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
+ u
29
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
+ u
29
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
6
=
u
3
− 2u
−u
3
+ u
a
9
=
−u
7
+ 4u
5
− 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
4
=
−u
14
+ 7u
12
− 18u
10
+ 19u
8
− 4u
6
− 4u
4
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
5
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
− u
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
10
=
−u
27
+ 12u
25
+ ··· + 10u
5
− 5u
3
−u
29
+ 13u
27
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
+ 52u
26
− 4u
25
− 292u
24
+ 48u
23
+ 912u
22
− 244u
21
−
1684u
20
+ 672u
19
+ 1752u
18
−1056u
17
−752u
16
+ 896u
15
−212u
14
−332u
13
+ 180u
12
+
64u
11
+ 156u
10
− 112u
9
− 96u
8
+ 64u
7
− 20u
6
− 8u
5
+ 8u
4
+ 20u
3
− 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
30
+ u
29
+ ··· − u + 1
c
3
, c
5
u
30
− u
29
+ ··· − 5u + 5
c
4
, c
9
, c
10
u
30
+ u
29
+ ··· + u + 1
c
6
u
30
− 3u
29
+ ··· − u + 1
c
8
u
30
− 7u
29
+ ··· − 39u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
30
− 27y
29
+ ··· + 3y + 1
c
3
, c
5
y
30
− 19y
29
+ ··· + 115y + 25
c
4
, c
9
, c
10
y
30
+ 25y
29
+ ··· + 3y + 1
c
6
y
30
+ y
29
+ ··· − y + 1
c
8
y
30
+ 5y
29
+ ··· + 383y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.006930 + 0.206480I
1.56161 + 3.89629I −0.45772 − 4.15365I
u = 1.006930 − 0.206480I
1.56161 − 3.89629I −0.45772 + 4.15365I
u = −0.832034 + 0.169903I
−2.20811 + 0.02948I −4.37202 + 0.47071I
u = −0.832034 − 0.169903I
−2.20811 − 0.02948I −4.37202 − 0.47071I
u = 0.266850 + 0.721202I
0.29816 + 7.69168I −2.03043 − 6.90287I
u = 0.266850 − 0.721202I
0.29816 − 7.69168I −2.03043 + 6.90287I
u = 0.703536 + 0.310326I
1.91248 − 3.85600I 0.77500 + 2.05029I
u = 0.703536 − 0.310326I
1.91248 + 3.85600I 0.77500 − 2.05029I
u = −0.228391 + 0.710789I
−4.18456 − 3.64220I −7.10429 + 4.72167I
u = −0.228391 − 0.710789I
−4.18456 + 3.64220I −7.10429 − 4.72167I
u = 0.169829 + 0.699155I
−0.939054 − 0.373325I −4.20674 − 0.53471I
u = 0.169829 − 0.699155I
−0.939054 + 0.373325I −4.20674 + 0.53471I
u = −0.379833 + 0.540597I
5.15123 − 1.73295I 3.31181 + 4.09879I
u = −0.379833 − 0.540597I
5.15123 + 1.73295I 3.31181 − 4.09879I
u = 1.351750 + 0.104838I
3.53116 + 0.39832I −0.06522 + 1.62643I
u = 1.351750 − 0.104838I
3.53116 − 0.39832I −0.06522 − 1.62643I
u = −1.363600 + 0.194579I
4.77317 − 3.51597I 2.79512 + 5.12276I
u = −1.363600 − 0.194579I
4.77317 + 3.51597I 2.79512 − 5.12276I
u = −1.360050 + 0.270550I
3.89598 − 3.12979I 0.91872 + 1.86186I
u = −1.360050 − 0.270550I
3.89598 + 3.12979I 0.91872 − 1.86186I
u = 1.39028 + 0.28253I
0.96260 + 7.24749I −2.00000 − 5.63452I
u = 1.39028 − 0.28253I
0.96260 − 7.24749I −2.00000 + 5.63452I
u = −1.42059 + 0.09196I
8.32515 + 2.69486I 5.41344 − 2.42783I
u = −1.42059 − 0.09196I
8.32515 − 2.69486I 5.41344 + 2.42783I
u = −1.40881 + 0.28598I
5.64069 − 11.35200I 2.55345 + 7.31316I
u = −1.40881 − 0.28598I
5.64069 + 11.35200I 2.55345 − 7.31316I
u = 1.42434 + 0.20546I
10.89310 + 4.47665I 7.02629 − 3.57345I
u = 1.42434 − 0.20546I
10.89310 − 4.47665I 7.02629 + 3.57345I
u = 0.179795 + 0.471439I
−0.135164 + 0.995104I −2.48606 − 6.82295I
u = 0.179795 − 0.471439I
−0.135164 − 0.995104I −2.48606 + 6.82295I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
30
+ u
29
+ ··· − u + 1
c
3
, c
5
u
30
− u
29
+ ··· − 5u + 5
c
4
, c
9
, c
10
u
30
+ u
29
+ ··· + u + 1
c
6
u
30
− 3u
29
+ ··· − u + 1
c
8
u
30
− 7u
29
+ ··· − 39u + 7
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
30
− 27y
29
+ ··· + 3y + 1
c
3
, c
5
y
30
− 19y
29
+ ··· + 115y + 25
c
4
, c
9
, c
10
y
30
+ 25y
29
+ ··· + 3y + 1
c
6
y
30
+ y
29
+ ··· − y + 1
c
8
y
30
+ 5y
29
+ ··· + 383y + 49
7
