10
33
(K10a
109
)
A knot diagram
1
Linearized knot diagam
7 6 1 10 9 2 3 4 5 8
Solving Sequence
3,6
2 7 8 1 4 9 5 10
c
2
c
6
c
7
c
1
c
3
c
8
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
32
− u
31
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 32 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
32
− u
31
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
7
=
−u
u
3
+ u
a
8
=
−u
3
− 2u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
9
=
−u
17
− 8u
15
− 25u
13
− 36u
11
− 19u
9
+ 4u
7
+ 2u
5
− 4u
3
− u
u
19
+ 9u
17
+ 32u
15
+ 55u
13
+ 43u
11
+ 9u
9
+ 4u
5
+ u
3
+ u
a
5
=
u
28
+ 13u
26
+ ··· − u
2
+ 1
−u
28
− 12u
26
+ ··· − 2u
6
+ 3u
4
a
10
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
−u
10
− 4u
8
− 5u
6
− 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
31
−4u
30
+60u
29
−52u
28
+392u
27
−292u
26
+1448u
25
−908u
24
+3260u
23
−1640u
22
+
4412u
21
− 1548u
20
+ 3076u
19
− 248u
18
+ 220u
17
+ 888u
16
− 924u
15
+ 580u
14
+ 60u
13
−
204u
12
+616u
11
−212u
10
+144u
9
+72u
8
−108u
7
+60u
6
−12u
5
−8u
4
+20u
3
−8u
2
+8u−6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
32
+ u
31
+ ··· + 2u + 1
c
3
u
32
− 7u
31
+ ··· − 104u + 17
c
4
, c
5
, c
9
u
32
− u
31
+ ··· − 2u + 1
c
7
u
32
− u
31
+ ··· + 20u
3
+ 1
c
8
u
32
+ u
31
+ ··· − 20u
3
+ 1
c
10
u
32
+ 7u
31
+ ··· + 104u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
y
32
+ 29y
31
+ ··· + 4y
2
+ 1
c
3
, c
10
y
32
+ 9y
31
+ ··· + 3056y + 289
c
7
, c
8
y
32
+ y
31
+ ··· + 56y
2
+ 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.209460 + 1.051390I
−4.41658 + 4.25629I −3.47389 − 4.09777I
u = −0.209460 − 1.051390I
−4.41658 − 4.25629I −3.47389 + 4.09777I
u = 0.089089 + 1.108640I
1.25663 − 1.65846I 0.43981 + 4.42001I
u = 0.089089 − 1.108640I
1.25663 + 1.65846I 0.43981 − 4.42001I
u = 0.714631 + 0.281038I
−5.41367 − 7.91274I −4.55825 + 6.96002I
u = 0.714631 − 0.281038I
−5.41367 + 7.91274I −4.55825 − 6.96002I
u = 0.339557 + 0.664733I
−3.94538 + 4.07051I −1.91410 − 1.89651I
u = 0.339557 − 0.664733I
−3.94538 − 4.07051I −1.91410 + 1.89651I
u = −0.672202 + 0.282270I
4.49550I 0. − 7.21172I
u = −0.672202 − 0.282270I
− 4.49550I 0. + 7.21172I
u = −0.694439 + 0.142847I
−7.11727 − 0.78256I −7.62681 − 0.59259I
u = −0.694439 − 0.142847I
−7.11727 + 0.78256I −7.62681 + 0.59259I
u = 0.515560 + 0.370610I
−1.25663 − 1.65846I −0.43981 + 4.42001I
u = 0.515560 − 0.370610I
−1.25663 + 1.65846I −0.43981 − 4.42001I
u = 0.598306 + 0.209645I
−1.19944 − 1.01594I −3.95412 + 1.45531I
u = 0.598306 − 0.209645I
−1.19944 + 1.01594I −3.95412 − 1.45531I
u = −0.265495 + 1.341380I
−2.44890 + 2.68301I −2.52130 − 2.36594I
u = −0.265495 − 1.341380I
−2.44890 − 2.68301I −2.52130 + 2.36594I
u = −0.323417 + 0.508294I
1.19944 − 1.01594I 3.95412 + 1.45531I
u = −0.323417 − 0.508294I
1.19944 + 1.01594I 3.95412 − 1.45531I
u = 0.235723 + 1.392280I
3.94538 − 4.07051I 1.91410 + 1.89651I
u = 0.235723 − 1.392280I
3.94538 + 4.07051I 1.91410 − 1.89651I
u = −0.14428 + 1.41797I
7.11727 + 0.78256I 7.62681 + 0.59259I
u = −0.14428 − 1.41797I
7.11727 − 0.78256I 7.62681 − 0.59259I
u = 0.19271 + 1.41648I
4.41658 − 4.25629I 3.47389 + 4.09777I
u = 0.19271 − 1.41648I
4.41658 + 4.25629I 3.47389 − 4.09777I
u = 0.10594 + 1.42756I
2.44890 + 2.68301I 2.52130 − 2.36594I
u = 0.10594 − 1.42756I
2.44890 − 2.68301I 2.52130 + 2.36594I
u = −0.26371 + 1.41237I
5.41367 + 7.91274I 4.55825 − 6.96002I
u = −0.26371 − 1.41237I
5.41367 − 7.91274I 4.55825 + 6.96002I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.28148 + 1.41481I
− 11.5357I 0. + 7.26982I
u = 0.28148 − 1.41481I
11.5357I 0. − 7.26982I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
32
+ u
31
+ ··· + 2u + 1
c
3
u
32
− 7u
31
+ ··· − 104u + 17
c
4
, c
5
, c
9
u
32
− u
31
+ ··· − 2u + 1
c
7
u
32
− u
31
+ ··· + 20u
3
+ 1
c
8
u
32
+ u
31
+ ··· − 20u
3
+ 1
c
10
u
32
+ 7u
31
+ ··· + 104u + 17
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
y
32
+ 29y
31
+ ··· + 4y
2
+ 1
c
3
, c
10
y
32
+ 9y
31
+ ··· + 3056y + 289
c
7
, c
8
y
32
+ y
31
+ ··· + 56y
2
+ 1
8
