10
28
(K10a
44
)
A knot diagram
1
Linearized knot diagam
5 9 8 6 2 1 10 3 4 7
Solving Sequence
1,5
2 6 7 4 10 8 3 9
c
1
c
5
c
6
c
4
c
10
c
7
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
26
− u
25
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 26 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
26
− u
25
+ · · · − u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
−u
3
−u
3
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
10
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
8
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
3
=
−u
23
+ 6u
21
− 16u
19
+ 20u
17
− 4u
15
− 22u
13
+ 26u
11
− 6u
9
− 9u
7
+ 6u
5
−u
23
+ 7u
21
+ ··· − 2u
3
+ u
a
9
=
u
14
− 3u
12
+ 4u
10
− u
8
+ 1
u
16
− 4u
14
+ 8u
12
− 8u
10
+ 4u
8
+ 2u
6
− 4u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
25
− 32u
23
+ 4u
22
+ 116u
21
− 28u
20
− 228u
19
+ 88u
18
+
220u
17
− 144u
16
+ 16u
15
+ 100u
14
− 284u
13
+ 52u
12
+ 268u
11
− 148u
10
− 20u
9
+ 84u
8
−
116u
7
+ 20u
6
+ 60u
5
− 36u
4
+ 4u
3
+ 8u
2
− 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
26
+ u
25
+ ··· + u + 1
c
2
, c
3
, c
8
u
26
− u
25
+ ··· − u + 1
c
4
u
26
+ 15u
25
+ ··· + 3u + 1
c
6
, c
7
, c
10
u
26
+ 3u
25
+ ··· + 11u + 3
c
9
u
26
+ u
25
+ ··· + 13u + 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
26
− 15y
25
+ ··· − 3y + 1
c
2
, c
3
, c
8
y
26
+ 25y
25
+ ··· − 3y + 1
c
4
y
26
− 7y
25
+ ··· + 13y + 1
c
6
, c
7
, c
10
y
26
+ 29y
25
+ ··· + 65y + 9
c
9
y
26
+ 13y
25
+ ··· + 3129y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.932207 + 0.261463I
−1.57798 − 1.00473I −1.82896 + 0.57498I
u = 0.932207 − 0.261463I
−1.57798 + 1.00473I −1.82896 − 0.57498I
u = −0.963114 + 0.429790I
−0.36195 + 3.85582I 3.97718 − 7.89236I
u = −0.963114 − 0.429790I
−0.36195 − 3.85582I 3.97718 + 7.89236I
u = 0.051158 + 0.880772I
−10.59630 + 5.33673I −1.16942 − 2.96646I
u = 0.051158 − 0.880772I
−10.59630 − 5.33673I −1.16942 + 2.96646I
u = −1.098980 + 0.206450I
−7.37246 − 0.32949I −5.60033 − 0.20899I
u = −1.098980 − 0.206450I
−7.37246 + 0.32949I −5.60033 + 0.20899I
u = 1.030410 + 0.480033I
−5.39158 − 6.75127I −1.33497 + 7.43906I
u = 1.030410 − 0.480033I
−5.39158 + 6.75127I −1.33497 − 7.43906I
u = 0.720594 + 0.453573I
−2.18139 − 1.93104I 3.25405 + 4.18474I
u = 0.720594 − 0.453573I
−2.18139 + 1.93104I 3.25405 − 4.18474I
u = −0.027215 + 0.843903I
−4.30846 − 2.13264I 2.18965 + 3.16032I
u = −0.027215 − 0.843903I
−4.30846 + 2.13264I 2.18965 − 3.16032I
u = 1.237150 + 0.448499I
−8.09804 − 2.43962I −1.44223 + 0.17519I
u = 1.237150 − 0.448499I
−8.09804 + 2.43962I −1.44223 − 0.17519I
u = −1.232480 + 0.474736I
−7.90858 + 6.86486I −0.85861 − 6.16378I
u = −1.232480 − 0.474736I
−7.90858 − 6.86486I −0.85861 + 6.16378I
u = −1.260650 + 0.436852I
−14.6036 − 0.7042I −4.80376 − 0.14810I
u = −1.260650 − 0.436852I
−14.6036 + 0.7042I −4.80376 + 0.14810I
u = 0.311125 + 0.584230I
−3.40769 + 2.56217I 2.05300 − 2.97329I
u = 0.311125 − 0.584230I
−3.40769 − 2.56217I 2.05300 + 2.97329I
u = 1.244860 + 0.491994I
−14.1992 − 10.2647I −4.13372 + 5.98641I
u = 1.244860 − 0.491994I
−14.1992 + 10.2647I −4.13372 − 5.98641I
u = −0.445071 + 0.389205I
1.050410 − 0.215716I 9.69812 + 1.13318I
u = −0.445071 − 0.389205I
1.050410 + 0.215716I 9.69812 − 1.13318I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
26
+ u
25
+ ··· + u + 1
c
2
, c
3
, c
8
u
26
− u
25
+ ··· − u + 1
c
4
u
26
+ 15u
25
+ ··· + 3u + 1
c
6
, c
7
, c
10
u
26
+ 3u
25
+ ··· + 11u + 3
c
9
u
26
+ u
25
+ ··· + 13u + 17
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
26
− 15y
25
+ ··· − 3y + 1
c
2
, c
3
, c
8
y
26
+ 25y
25
+ ··· − 3y + 1
c
4
y
26
− 7y
25
+ ··· + 13y + 1
c
6
, c
7
, c
10
y
26
+ 29y
25
+ ··· + 65y + 9
c
9
y
26
+ 13y
25
+ ··· + 3129y + 289
7
