10
38
(K10a
29
)
A knot diagram
1
Linearized knot diagam
8 6 5 9 3 10 1 7 4 2
Solving Sequence
5,9
4 10 3 6 7 2 8 1
c
4
c
9
c
3
c
5
c
6
c
2
c
8
c
1
c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
− u
28
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
29
− u
28
+ · · · + u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
2
a
6
=
u
4
+ u
2
+ 1
u
4
a
7
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
10
+ 2u
8
+ 3u
6
+ 4u
4
+ u
2
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
8
=
u
17
+ 2u
15
+ 7u
13
+ 10u
11
+ 15u
9
+ 14u
7
+ 10u
5
+ 4u
3
+ u
u
19
+ 3u
17
+ 8u
15
+ 15u
13
+ 19u
11
+ 21u
9
+ 14u
7
+ 6u
5
+ u
3
+ u
a
1
=
−u
15
− 2u
13
− 6u
11
− 8u
9
− 10u
7
− 8u
5
− 4u
3
−u
15
− u
13
− 4u
11
− 3u
9
− 4u
7
− 2u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
− 12u
26
− 4u
25
− 48u
24
− 12u
23
− 100u
22
− 44u
21
−
208u
20
− 92u
19
− 312u
18
− 172u
17
− 424u
16
− 252u
15
− 456u
14
− 296u
13
− 432u
12
−
288u
11
−328u
10
−216u
9
−216u
8
−128u
7
−120u
6
−56u
5
−48u
4
−32u
3
−16u
2
−12u −10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
29
+ u
28
+ ··· + 3u + 1
c
2
, c
3
, c
5
u
29
+ 7u
28
+ ··· − u − 1
c
4
, c
9
u
29
− u
28
+ ··· + u + 1
c
6
u
29
− u
28
+ ··· + 15u + 25
c
8
, c
10
u
29
+ 9u
28
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
29
− 9y
28
+ ··· − y −1
c
2
, c
3
, c
5
y
29
+ 31y
28
+ ··· + 15y −1
c
4
, c
9
y
29
+ 7y
28
+ ··· − y −1
c
6
y
29
+ 11y
28
+ ··· − 2925y −625
c
8
, c
10
y
29
+ 23y
28
+ ··· − 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438147 + 0.901074I
1.63523 + 2.09123I −4.28547 − 3.54352I
u = 0.438147 − 0.901074I
1.63523 − 2.09123I −4.28547 + 3.54352I
u = −0.409980 + 0.948974I
0.88657 − 7.55674I −6.27529 + 8.69605I
u = −0.409980 − 0.948974I
0.88657 + 7.55674I −6.27529 − 8.69605I
u = −0.273126 + 0.909412I
−3.81512 − 2.50065I −13.4942 + 5.2130I
u = −0.273126 − 0.909412I
−3.81512 + 2.50065I −13.4942 − 5.2130I
u = −0.064282 + 0.911143I
−0.99960 + 2.39368I −10.11411 − 2.65936I
u = −0.064282 − 0.911143I
−0.99960 − 2.39368I −10.11411 + 2.65936I
u = 0.815394 + 0.851135I
2.82194 − 0.04233I −6.03677 + 1.08568I
u = 0.815394 − 0.851135I
2.82194 + 0.04233I −6.03677 − 1.08568I
u = 0.886761 + 0.845005I
9.22437 − 4.97924I −1.18288 + 2.83205I
u = 0.886761 − 0.845005I
9.22437 + 4.97924I −1.18288 − 2.83205I
u = −0.829632 + 0.902432I
5.95691 − 3.09358I −0.04639 + 2.70964I
u = −0.829632 − 0.902432I
5.95691 + 3.09358I −0.04639 − 2.70964I
u = 0.796082 + 0.934420I
2.56729 + 6.08103I −6.75508 − 6.19570I
u = 0.796082 − 0.934420I
2.56729 − 6.08103I −6.75508 + 6.19570I
u = −0.883056 + 0.860857I
9.96021 − 1.00685I 0.05949 + 2.19242I
u = −0.883056 − 0.860857I
9.96021 + 1.00685I 0.05949 − 2.19242I
u = 0.273342 + 0.693824I
−0.332830 + 1.166300I −4.21359 − 5.75923I
u = 0.273342 − 0.693824I
−0.332830 − 1.166300I −4.21359 + 5.75923I
u = 0.610942 + 0.390932I
3.23356 + 1.79478I −0.02040 − 2.96423I
u = 0.610942 − 0.390932I
3.23356 − 1.79478I −0.02040 + 2.96423I
u = −0.840392 + 0.961339I
9.64156 − 5.37662I −0.52039 + 2.73445I
u = −0.840392 − 0.961339I
9.64156 + 5.37662I −0.52039 − 2.73445I
u = 0.833145 + 0.972573I
8.8206 + 11.3493I −1.99701 − 7.67243I
u = 0.833145 − 0.972573I
8.8206 − 11.3493I −1.99701 + 7.67243I
u = −0.627727 + 0.308177I
2.89789 + 3.74340I −0.78236 − 3.16701I
u = −0.627727 − 0.308177I
2.89789 − 3.74340I −0.78236 + 3.16701I
u = −0.451236
−1.36635 −6.67120
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
29
+ u
28
+ ··· + 3u + 1
c
2
, c
3
, c
5
u
29
+ 7u
28
+ ··· − u − 1
c
4
, c
9
u
29
− u
28
+ ··· + u + 1
c
6
u
29
− u
28
+ ··· + 15u + 25
c
8
, c
10
u
29
+ 9u
28
+ ··· − u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
29
− 9y
28
+ ··· − y −1
c
2
, c
3
, c
5
y
29
+ 31y
28
+ ··· + 15y −1
c
4
, c
9
y
29
+ 7y
28
+ ··· − y −1
c
6
y
29
+ 11y
28
+ ··· − 2925y −625
c
8
, c
10
y
29
+ 23y
28
+ ··· − 17y −1
7
