12a
0384
(K12a
0384
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 7 2 1 12 11 4 5 8
Solving Sequence
5,10
4 11 12 9 3 8 1 7 6 2
c
4
c
10
c
11
c
9
c
3
c
8
c
12
c
7
c
5
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
75
− u
74
+ ··· − u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 75 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
75
− u
74
+ · · · − u
2
− 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
11
=
−u
u
3
+ u
a
12
=
u
3
u
3
+ u
a
9
=
−u
3
u
5
+ u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
8
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
1
=
u
19
+ 4u
17
+ 8u
15
+ 8u
13
+ 5u
11
+ 2u
9
+ 2u
7
+ u
3
u
19
+ 5u
17
+ 12u
15
+ 15u
13
+ 9u
11
− u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
7
=
−u
27
− 6u
25
+ ··· − 4u
7
− u
3
−u
27
− 7u
25
+ ··· + u
3
+ u
a
6
=
u
54
+ 13u
52
+ ··· − u
4
+ 1
u
54
+ 14u
52
+ ··· + 2u
4
+ u
2
a
2
=
−u
33
− 8u
31
+ ··· + 4u
5
− u
u
35
+ 9u
33
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
73
+ 4u
72
+ ··· + 8u
2
+ 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
75
+ 27u
74
+ ··· − 2u − 1
c
2
, c
6
u
75
− u
74
+ ··· + 2u − 1
c
3
, c
11
u
75
+ u
74
+ ··· + 224u − 37
c
4
, c
10
u
75
− u
74
+ ··· − u
2
− 1
c
7
, c
8
, c
12
u
75
+ 5u
74
+ ··· − 122u − 13
c
9
u
75
− 39u
74
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
75
+ 43y
74
+ ··· − 42y −1
c
2
, c
6
y
75
+ 27y
74
+ ··· − 2y −1
c
3
, c
11
y
75
− 49y
74
+ ··· − 139634y −1369
c
4
, c
10
y
75
+ 39y
74
+ ··· − 2y −1
c
7
, c
8
, c
12
y
75
+ 71y
74
+ ··· + 818y −169
c
9
y
75
− 5y
74
+ ··· + 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.605676 + 0.796769I
−6.04317 + 9.23163I 0. − 8.30449I
u = −0.605676 − 0.796769I
−6.04317 − 9.23163I 0. + 8.30449I
u = 0.434200 + 0.904835I
1.00534 − 6.47824I 4.00000 + 9.67055I
u = 0.434200 − 0.904835I
1.00534 + 6.47824I 4.00000 − 9.67055I
u = −0.357332 + 0.925036I
1.74821 + 1.50345I 6.59382 − 3.63022I
u = −0.357332 − 0.925036I
1.74821 − 1.50345I 6.59382 + 3.63022I
u = 0.596114 + 0.790314I
−4.52032 − 3.81412I 1.55948 + 3.68783I
u = 0.596114 − 0.790314I
−4.52032 + 3.81412I 1.55948 − 3.68783I
u = −0.611709 + 0.774118I
−10.27490 + 2.38694I −4.63689 − 3.32182I
u = −0.611709 − 0.774118I
−10.27490 − 2.38694I −4.63689 + 3.32182I
u = −0.611730 + 0.749244I
−6.17981 − 4.47538I −0.99002 + 1.78684I
u = −0.611730 − 0.749244I
−6.17981 + 4.47538I −0.99002 − 1.78684I
u = 0.599256 + 0.754022I
−4.62446 − 0.87914I 1.19980 + 3.06129I
u = 0.599256 − 0.754022I
−4.62446 + 0.87914I 1.19980 − 3.06129I
u = −0.026354 + 0.944514I
3.78137 + 2.60614I 11.97414 − 3.59156I
u = −0.026354 − 0.944514I
3.78137 − 2.60614I 11.97414 + 3.59156I
u = 0.445777 + 0.744877I
−2.71406 − 1.90275I −3.96566 + 4.94031I
u = 0.445777 − 0.744877I
−2.71406 + 1.90275I −3.96566 − 4.94031I
u = 0.297220 + 1.135960I
0.31557 − 6.14170I 0
u = 0.297220 − 1.135960I
0.31557 + 6.14170I 0
u = 0.792174 + 0.211922I
−3.19444 + 10.59060I 1.16244 − 7.05944I
u = 0.792174 − 0.211922I
−3.19444 − 10.59060I 1.16244 + 7.05944I
u = −0.326975 + 1.136760I
1.78383 + 1.05705I 0
u = −0.326975 − 1.136760I
1.78383 − 1.05705I 0
u = 0.778680 + 0.229580I
−7.67564 + 3.86014I −3.36188 − 2.54547I
u = 0.778680 − 0.229580I
−7.67564 − 3.86014I −3.36188 + 2.54547I
u = −0.783246 + 0.208394I
−1.76009 − 5.07972I 3.22251 + 2.55358I
u = −0.783246 − 0.208394I
−1.76009 + 5.07972I 3.22251 − 2.55358I
u = −0.416318 + 1.118240I
2.27451 + 1.40801I 0
u = −0.416318 − 1.118240I
2.27451 − 1.40801I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756757 + 0.247164I
−3.87573 − 2.95735I −0.06195 + 2.67044I
u = 0.756757 − 0.247164I
−3.87573 + 2.95735I −0.06195 − 2.67044I
u = 0.312742 + 1.169010I
−3.42309 + 0.45321I 0
u = 0.312742 − 1.169010I
−3.42309 − 0.45321I 0
u = −0.752182 + 0.229843I
−2.28210 − 2.23283I 2.43604 + 2.41048I
u = −0.752182 − 0.229843I
−2.28210 + 2.23283I 2.43604 − 2.41048I
u = −0.331893 + 1.180670I
2.43376 − 1.52363I 0
u = −0.331893 − 1.180670I
2.43376 + 1.52363I 0
u = 0.325952 + 1.187250I
1.06510 + 7.02113I 0
u = 0.325952 − 1.187250I
1.06510 − 7.02113I 0
u = −0.214391 + 0.731240I
0.447274 + 1.029570I 6.61766 − 6.37411I
u = −0.214391 − 0.731240I
0.447274 − 1.029570I 6.61766 + 6.37411I
u = 0.449541 + 1.154810I
4.51193 − 4.07458I 0
u = 0.449541 − 1.154810I
4.51193 + 4.07458I 0
u = −0.482271 + 1.142580I
1.76946 + 6.42913I 0
u = −0.482271 − 1.142580I
1.76946 − 6.42913I 0
u = −0.751767 + 0.088561I
3.83758 − 5.79700I 6.35953 + 6.44372I
u = −0.751767 − 0.088561I
3.83758 + 5.79700I 6.35953 − 6.44372I
u = 0.744452 + 0.066574I
4.31968 + 0.36674I 7.87220 − 0.50275I
u = 0.744452 − 0.066574I
4.31968 − 0.36674I 7.87220 + 0.50275I
u = −0.409035 + 1.184990I
7.51694 − 1.78430I 0
u = −0.409035 − 1.184990I
7.51694 + 1.78430I 0
u = 0.419688 + 1.183890I
7.91319 − 3.70818I 0
u = 0.419688 − 1.183890I
7.91319 + 3.70818I 0
u = 0.533487 + 1.149800I
−1.23150 − 1.88454I 0
u = 0.533487 − 1.149800I
−1.23150 + 1.88454I 0
u = −0.527390 + 1.154690I
0.42284 + 7.03628I 0
u = −0.527390 − 1.154690I
0.42284 − 7.03628I 0
u = 0.474033 + 1.180990I
7.52996 − 4.83567I 0
u = 0.474033 − 1.180990I
7.52996 + 4.83567I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482557 + 1.181340I
6.99960 + 10.33920I 0
u = −0.482557 − 1.181340I
6.99960 − 10.33920I 0
u = 0.535680 + 1.162020I
−4.93464 − 8.76118I 0
u = 0.535680 − 1.162020I
−4.93464 + 8.76118I 0
u = −0.530550 + 1.169690I
1.06556 + 9.96571I 0
u = −0.530550 − 1.169690I
1.06556 − 9.96571I 0
u = 0.534111 + 1.171560I
−0.3673 − 15.5144I 0
u = 0.534111 − 1.171560I
−0.3673 + 15.5144I 0
u = 0.458828 + 0.536244I
−0.03059 + 2.65332I −0.13467 − 2.90348I
u = 0.458828 − 0.536244I
−0.03059 − 2.65332I −0.13467 + 2.90348I
u = −0.646867 + 0.153322I
−1.02159 − 2.08911I −1.37094 + 4.75504I
u = −0.646867 − 0.153322I
−1.02159 + 2.08911I −1.37094 − 4.75504I
u = 0.651127
1.36435 8.10100
u = −0.446014 + 0.404386I
0.26212 + 1.94827I 0.25758 − 3.35365I
u = −0.446014 − 0.404386I
0.26212 − 1.94827I 0.25758 + 3.35365I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
75
+ 27u
74
+ ··· − 2u − 1
c
2
, c
6
u
75
− u
74
+ ··· + 2u − 1
c
3
, c
11
u
75
+ u
74
+ ··· + 224u − 37
c
4
, c
10
u
75
− u
74
+ ··· − u
2
− 1
c
7
, c
8
, c
12
u
75
+ 5u
74
+ ··· − 122u − 13
c
9
u
75
− 39u
74
+ ··· − 2u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
75
+ 43y
74
+ ··· − 42y −1
c
2
, c
6
y
75
+ 27y
74
+ ··· − 2y −1
c
3
, c
11
y
75
− 49y
74
+ ··· − 139634y −1369
c
4
, c
10
y
75
+ 39y
74
+ ··· − 2y −1
c
7
, c
8
, c
12
y
75
+ 71y
74
+ ··· + 818y −169
c
9
y
75
− 5y
74
+ ··· + 6y −1
9
