12a
0380
(K12a
0380
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 1 12 11 5 4 8 7
Solving Sequence
4,11
10 5 9 3 8 12 7 1 2 6
c
10
c
4
c
9
c
3
c
8
c
11
c
7
c
12
c
1
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
38
+ u
37
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 38 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
38
+ u
37
+ · · · + u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
8
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
12
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
7
=
−u
12
− 5u
10
− 7u
8
+ 2u
4
− 3u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
1
=
u
16
+ 7u
14
+ 17u
12
+ 14u
10
− u
8
+ 2u
6
+ 6u
4
− 4u
2
+ 1
−u
16
− 8u
14
− 24u
12
− 32u
10
− 18u
8
− 8u
6
− 8u
4
a
2
=
u
28
+ 13u
26
+ ··· − 5u
2
+ 1
u
30
+ 14u
28
+ ··· − 16u
4
+ u
2
a
6
=
−u
20
− 9u
18
+ ··· − 5u
2
+ 1
u
20
+ 10u
18
+ 40u
16
+ 80u
14
+ 83u
12
+ 50u
10
+ 36u
8
+ 24u
6
+ u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
36
− 4u
35
− 72u
34
− 68u
33
− 580u
32
− 516u
31
− 2748u
30
− 2292u
29
− 8476u
28
−
6576u
27
−17864u
26
−12736u
25
−26568u
24
−17112u
23
−29228u
22
−16736u
21
−26160u
20
−
13388u
19
− 21072u
18
− 9832u
17
− 14636u
16
− 5896u
15
− 7812u
14
− 2336u
13
− 3700u
12
−
856u
11
−1816u
10
−336u
9
−456u
8
+ 80u
7
−56u
6
+ 40u
5
−68u
4
+ 20u
3
+ 24u
2
+ 16u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 23u
37
+ ··· + 5u + 1
c
2
, c
5
u
38
+ u
37
+ ··· + u + 1
c
3
u
38
− u
37
+ ··· + 81u + 317
c
4
, c
9
, c
10
u
38
+ u
37
+ ··· + u + 1
c
6
, c
7
, c
8
c
11
, c
12
u
38
+ 3u
37
+ ··· + 15u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 15y
37
+ ··· + 3y + 1
c
2
, c
5
y
38
− 23y
37
+ ··· − 5y + 1
c
3
y
38
+ 25y
37
+ ··· + 1416135y + 100489
c
4
, c
9
, c
10
y
38
+ 37y
37
+ ··· − 5y + 1
c
6
, c
7
, c
8
c
11
, c
12
y
38
+ 53y
37
+ ··· + 123y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699030 + 0.516783I
−16.5834 + 2.6642I −1.43407 − 0.13323I
u = −0.699030 − 0.516783I
−16.5834 − 2.6642I −1.43407 + 0.13323I
u = −0.709471 + 0.500003I
−16.5259 − 7.3585I −1.27138 + 5.67363I
u = −0.709471 − 0.500003I
−16.5259 + 7.3585I −1.27138 − 5.67363I
u = 0.699159 + 0.504973I
−12.61000 + 2.32929I 1.79922 − 2.79577I
u = 0.699159 − 0.504973I
−12.61000 − 2.32929I 1.79922 + 2.79577I
u = 0.046655 + 1.266040I
−2.65817 + 1.73113I 5.04604 − 4.55747I
u = 0.046655 − 1.266040I
−2.65817 − 1.73113I 5.04604 + 4.55747I
u = 0.617788 + 0.394340I
−5.75531 + 5.89610I −0.12847 − 7.53727I
u = 0.617788 − 0.394340I
−5.75531 − 5.89610I −0.12847 + 7.53727I
u = 0.548294 + 0.475497I
−6.07647 − 2.03534I −1.49342 + 0.25635I
u = 0.548294 − 0.475497I
−6.07647 + 2.03534I −1.49342 − 0.25635I
u = −0.553289 + 0.398678I
−2.61813 − 1.78595I 2.96437 + 4.13592I
u = −0.553289 − 0.398678I
−2.61813 + 1.78595I 2.96437 − 4.13592I
u = 0.108014 + 1.329890I
−3.47258 + 1.99659I 3.63851 − 3.32884I
u = 0.108014 − 1.329890I
−3.47258 − 1.99659I 3.63851 + 3.32884I
u = −0.165337 + 1.349130I
−5.18486 − 5.72137I 0. + 8.45786I
u = −0.165337 − 1.349130I
−5.18486 + 5.72137I 0. − 8.45786I
u = −0.070878 + 1.410250I
−7.16634 − 0.25397I 0
u = −0.070878 − 1.410250I
−7.16634 + 0.25397I 0
u = −0.529018 + 0.191801I
−0.35654 − 3.20662I 5.93778 + 9.20174I
u = −0.529018 − 0.191801I
−0.35654 + 3.20662I 5.93778 − 9.20174I
u = −0.19412 + 1.44071I
−8.51769 − 4.51489I 0
u = −0.19412 − 1.44071I
−8.51769 + 4.51489I 0
u = 0.21879 + 1.44502I
−11.6645 + 8.9374I 0
u = 0.21879 − 1.44502I
−11.6645 − 8.9374I 0
u = 0.18046 + 1.46649I
−12.33810 + 0.59580I 0
u = 0.18046 − 1.46649I
−12.33810 − 0.59580I 0
u = 0.24198 + 1.50771I
−19.1586 + 5.7629I 0
u = 0.24198 − 1.50771I
−19.1586 − 5.7629I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24749 + 1.50794I
16.4216 − 10.8522I 0
u = −0.24749 − 1.50794I
16.4216 + 10.8522I 0
u = −0.23899 + 1.51269I
16.2818 − 0.7569I 0
u = −0.23899 − 1.51269I
16.2818 + 0.7569I 0
u = 0.455694 + 0.048977I
0.826554 + 0.063442I 12.58366 − 0.84901I
u = 0.455694 − 0.048977I
0.826554 − 0.063442I 12.58366 + 0.84901I
u = −0.209212 + 0.399902I
−1.53939 + 0.81265I −1.98721 − 0.48886I
u = −0.209212 − 0.399902I
−1.53939 − 0.81265I −1.98721 + 0.48886I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
38
+ 23u
37
+ ··· + 5u + 1
c
2
, c
5
u
38
+ u
37
+ ··· + u + 1
c
3
u
38
− u
37
+ ··· + 81u + 317
c
4
, c
9
, c
10
u
38
+ u
37
+ ··· + u + 1
c
6
, c
7
, c
8
c
11
, c
12
u
38
+ 3u
37
+ ··· + 15u + 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
38
− 15y
37
+ ··· + 3y + 1
c
2
, c
5
y
38
− 23y
37
+ ··· − 5y + 1
c
3
y
38
+ 25y
37
+ ··· + 1416135y + 100489
c
4
, c
9
, c
10
y
38
+ 37y
37
+ ··· − 5y + 1
c
6
, c
7
, c
8
c
11
, c
12
y
38
+ 53y
37
+ ··· + 123y + 9
8
