10
30
(K10a
34
)
A knot diagram
1
Linearized knot diagam
8 9 6 10 1 3 2 7 5 4
Solving Sequence
1,4
10 5 6 3 7 9 2 8
c
10
c
4
c
5
c
3
c
6
c
9
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
− u
32
+ ··· + 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 33 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
33
− u
32
+ · · · + 3u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
10
=
1
−u
2
a
5
=
−u
u
3
+ u
a
6
=
−u
3
− 2u
u
3
+ u
a
3
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
−u
11
− 6u
9
− 12u
7
− 8u
5
− u
3
− 2u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
u
13
+ 6u
11
+ 13u
9
+ 12u
7
+ 6u
5
+ 4u
3
+ u
−u
15
− 7u
13
− 18u
11
− 19u
9
− 6u
7
− 2u
5
− 4u
3
+ u
a
8
=
−u
26
− 13u
24
+ ··· + 3u
2
+ 1
u
26
+ 12u
24
+ ··· + 4u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
32
+ 4u
31
− 64u
30
+ 56u
29
− 448u
28
+ 340u
27
− 1788u
26
+
1156u
25
− 4432u
24
+ 2356u
23
− 6940u
22
+ 2804u
21
− 6652u
20
+ 1616u
19
− 3660u
18
+
8u
17
− 1380u
16
− 364u
15
− 932u
14
− 156u
13
− 380u
12
− 360u
11
+ 224u
10
− 328u
9
+
40u
8
− 4u
7
− 56u
6
+ 4u
5
+ 48u
4
− 32u
3
− 12u
2
+ 20u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
33
− u
32
+ ··· − u + 1
c
2
u
33
+ u
32
+ ··· + u + 1
c
3
, c
6
u
33
− 5u
32
+ ··· − 31u + 3
c
4
, c
9
, c
10
u
33
+ u
32
+ ··· + 3u + 1
c
5
u
33
− u
32
+ ··· + 61u + 17
c
8
u
33
+ 15u
32
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
33
+ 15y
32
+ ··· + y −1
c
2
y
33
− y
32
+ ··· + 33y −1
c
3
, c
6
y
33
+ 27y
32
+ ··· + y −9
c
4
, c
9
, c
10
y
33
+ 31y
32
+ ··· + y −1
c
5
y
33
+ 11y
32
+ ··· − 3011y −289
c
8
y
33
+ 7y
32
+ ··· + 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.138722 + 1.178260I
−0.390154 − 0.572456I −8.31906 + 0.48605I
u = −0.138722 − 1.178260I
−0.390154 + 0.572456I −8.31906 − 0.48605I
u = 0.679432 + 0.391507I
1.46905 − 8.41845I −5.65597 + 8.08731I
u = 0.679432 − 0.391507I
1.46905 + 8.41845I −5.65597 − 8.08731I
u = −0.649750 + 0.407780I
3.38108 + 3.30675I −2.44424 − 3.71770I
u = −0.649750 − 0.407780I
3.38108 − 3.30675I −2.44424 + 3.71770I
u = 0.552937 + 0.519363I
1.99857 + 4.30723I −4.15179 − 2.03529I
u = 0.552937 − 0.519363I
1.99857 − 4.30723I −4.15179 + 2.03529I
u = −0.578988 + 0.474023I
3.67259 + 0.72831I −1.49015 − 3.12560I
u = −0.578988 − 0.474023I
3.67259 − 0.72831I −1.49015 + 3.12560I
u = −0.214004 + 1.270020I
0.50606 + 6.56196I −6.35976 − 7.19745I
u = −0.214004 − 1.270020I
0.50606 − 6.56196I −6.35976 + 7.19745I
u = 0.150986 + 1.283520I
2.96939 − 2.39560I −2.36922 + 3.31266I
u = 0.150986 − 1.283520I
2.96939 + 2.39560I −2.36922 − 3.31266I
u = 0.596688 + 0.315979I
−1.43040 − 1.50384I −9.59059 + 3.60616I
u = 0.596688 − 0.315979I
−1.43040 + 1.50384I −9.59059 − 3.60616I
u = −0.632184 + 0.066503I
−3.60742 + 3.47782I −12.61515 − 4.95314I
u = −0.632184 − 0.066503I
−3.60742 − 3.47782I −12.61515 + 4.95314I
u = 0.036115 + 1.379920I
4.95997 − 2.19825I 0.55384 + 3.61625I
u = 0.036115 − 1.379920I
4.95997 + 2.19825I 0.55384 − 3.61625I
u = 0.22801 + 1.42935I
4.19152 − 4.53523I −6.00000 + 3.09222I
u = 0.22801 − 1.42935I
4.19152 + 4.53523I −6.00000 − 3.09222I
u = −0.24113 + 1.46019I
9.39642 + 6.56751I 0. − 3.41838I
u = −0.24113 − 1.46019I
9.39642 − 6.56751I 0. + 3.41838I
u = 0.25408 + 1.45840I
7.42465 − 11.82880I 0. + 7.75337I
u = 0.25408 − 1.45840I
7.42465 + 11.82880I 0. − 7.75337I
u = −0.20598 + 1.46844I
9.92249 + 3.59396I 0. − 3.03909I
u = −0.20598 − 1.46844I
9.92249 − 3.59396I 0. + 3.03909I
u = 0.18821 + 1.47294I
8.40124 + 1.63491I 0
u = 0.18821 − 1.47294I
8.40124 − 1.63491I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514867
−1.00604 −9.72740
u = 0.216864 + 0.450093I
−0.54661 − 1.45331I −5.02647 + 4.36257I
u = 0.216864 − 0.450093I
−0.54661 + 1.45331I −5.02647 − 4.36257I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
33
− u
32
+ ··· − u + 1
c
2
u
33
+ u
32
+ ··· + u + 1
c
3
, c
6
u
33
− 5u
32
+ ··· − 31u + 3
c
4
, c
9
, c
10
u
33
+ u
32
+ ··· + 3u + 1
c
5
u
33
− u
32
+ ··· + 61u + 17
c
8
u
33
+ 15u
32
+ ··· + u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
33
+ 15y
32
+ ··· + y −1
c
2
y
33
− y
32
+ ··· + 33y −1
c
3
, c
6
y
33
+ 27y
32
+ ··· + y −9
c
4
, c
9
, c
10
y
33
+ 31y
32
+ ··· + y −1
c
5
y
33
+ 11y
32
+ ··· − 3011y −289
c
8
y
33
+ 7y
32
+ ··· + 17y −1
8
