10
12
(K10a
43
)
A knot diagram
1
Linearized knot diagam
6 9 7 10 1 4 3 2 8 5
Solving Sequence
3,9
2 8 10 7 4 5 6 1
c
2
c
8
c
9
c
7
c
3
c
4
c
6
c
1
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ u
22
+ ··· + 2u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 23 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
23
+ u
22
+ · · · + 2u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
2
=
1
−u
2
a
8
=
u
−u
3
+ u
a
10
=
−u
3
u
5
− u
3
+ u
a
7
=
u
3
−u
3
+ u
a
4
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
5
=
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
a
6
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
1
=
u
20
− 5u
18
+ 11u
16
− 10u
14
− 2u
12
+ 13u
10
− 9u
8
+ 3u
4
− u
2
+ 1
−u
20
+ 6u
18
− 16u
16
+ 22u
14
− 13u
12
− 4u
10
+ 10u
8
− 4u
6
− u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
22
− 28u
20
− 4u
19
+ 88u
18
+ 24u
17
− 144u
16
− 64u
15
+ 100u
14
+ 84u
13
+ 52u
12
−
36u
11
− 148u
10
− 44u
9
+ 84u
8
+ 60u
7
+ 20u
6
− 16u
5
− 36u
4
− 12u
3
+ 8u
2
+ 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
23
+ u
22
+ ··· + 2u
2
− 1
c
2
, c
8
u
23
+ u
22
+ ··· + 2u
2
− 1
c
3
, c
6
, c
7
u
23
+ 3u
22
+ ··· + 8u + 1
c
9
u
23
+ 13u
22
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
23
− 25y
22
+ ··· + 4y −1
c
2
, c
8
y
23
− 13y
22
+ ··· + 4y −1
c
3
, c
6
, c
7
y
23
+ 23y
22
+ ··· + 44y −1
c
9
y
23
− 5y
22
+ ··· − 12y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943991 + 0.417010I
−0.32248 − 3.66903I 4.65447 + 8.36170I
u = 0.943991 − 0.417010I
−0.32248 + 3.66903I 4.65447 − 8.36170I
u = −0.925645 + 0.242794I
−1.56228 + 0.94741I −1.84899 − 0.66530I
u = −0.925645 − 0.242794I
−1.56228 − 0.94741I −1.84899 + 0.66530I
u = 1.06813
3.34151 2.11920
u = −0.941020 + 0.526196I
6.90346 + 5.14882I 7.72787 − 5.87498I
u = −0.941020 − 0.526196I
6.90346 − 5.14882I 7.72787 + 5.87498I
u = −0.096630 + 0.838348I
2.71524 − 4.94630I 6.58652 + 2.90766I
u = −0.096630 − 0.838348I
2.71524 + 4.94630I 6.58652 − 2.90766I
u = 0.032467 + 0.825255I
−3.91327 + 2.09016I 2.84908 − 3.29724I
u = 0.032467 − 0.825255I
−3.91327 − 2.09016I 2.84908 + 3.29724I
u = −0.514598 + 0.582714I
8.10021 − 0.74106I 10.45548 − 0.11519I
u = −0.514598 − 0.582714I
8.10021 + 0.74106I 10.45548 + 0.11519I
u = 1.234440 + 0.405346I
−1.31438 + 0.65510I 2.52162 + 0.18366I
u = 1.234440 − 0.405346I
−1.31438 − 0.65510I 2.52162 − 0.18366I
u = −1.227460 + 0.443418I
−7.66398 + 2.39421I −0.836170 − 0.236041I
u = −1.227460 − 0.443418I
−7.66398 − 2.39421I −0.836170 + 0.236041I
u = 1.222590 + 0.473871I
−7.44486 − 6.76579I −0.10985 + 6.36717I
u = 1.222590 − 0.473871I
−7.44486 + 6.76579I −0.10985 − 6.36717I
u = −1.217040 + 0.502393I
−0.62159 + 9.81750I 3.52842 − 5.98024I
u = −1.217040 − 0.502393I
−0.62159 − 9.81750I 3.52842 + 5.98024I
u = 0.454832 + 0.348349I
0.985778 + 0.157850I 10.41194 − 1.08803I
u = 0.454832 − 0.348349I
0.985778 − 0.157850I 10.41194 + 1.08803I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
23
+ u
22
+ ··· + 2u
2
− 1
c
2
, c
8
u
23
+ u
22
+ ··· + 2u
2
− 1
c
3
, c
6
, c
7
u
23
+ 3u
22
+ ··· + 8u + 1
c
9
u
23
+ 13u
22
+ ··· + 4u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
23
− 25y
22
+ ··· + 4y −1
c
2
, c
8
y
23
− 13y
22
+ ··· + 4y −1
c
3
, c
6
, c
7
y
23
+ 23y
22
+ ··· + 44y −1
c
9
y
23
− 5y
22
+ ··· − 12y −1
7
