12a
0550
(K12a
0550
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 10 2 1 6 12 5 4 9
Solving Sequence
4,11
5 12 10 6 9 1 8 3 2 7
c
4
c
11
c
10
c
5
c
9
c
12
c
8
c
3
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
74
+ u
73
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 74 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
74
+ u
73
+ · · · + u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
12
=
u
u
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
u
5
+ 2u
3
− u
u
5
+ 3u
3
+ u
a
1
=
u
9
+ 4u
7
+ 3u
5
− 2u
3
+ u
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
8
=
−u
11
− 6u
9
− 12u
7
− 8u
5
− u
3
− 2u
u
13
+ 7u
11
+ 17u
9
+ 16u
7
+ 6u
5
+ 5u
3
+ u
a
3
=
−u
24
− 13u
22
+ ··· − 2u
2
+ 1
u
26
+ 14u
24
+ ··· + 10u
4
+ u
2
a
2
=
−u
59
− 32u
57
+ ··· + 28u
5
+ u
3
u
61
+ 33u
59
+ ··· + u
3
+ u
a
7
=
−u
31
− 16u
29
+ ··· − 4u
3
− 2u
−u
31
− 17u
29
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
73
+ 4u
72
+ ··· + 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 35u
73
+ ··· − u + 1
c
2
, c
6
u
74
− u
73
+ ··· − u + 1
c
3
u
74
+ u
73
+ ··· − 879u + 481
c
4
, c
5
, c
10
c
11
u
74
− u
73
+ ··· − u + 1
c
7
u
74
− 3u
73
+ ··· − 325u + 175
c
8
u
74
+ 9u
73
+ ··· + 169u + 13
c
9
, c
12
u
74
− 13u
73
+ ··· − 2717u + 283
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 9y
73
+ ··· + 5y + 1
c
2
, c
6
y
74
− 35y
73
+ ··· + y + 1
c
3
y
74
− 19y
73
+ ··· − 9331555y + 231361
c
4
, c
5
, c
10
c
11
y
74
+ 81y
73
+ ··· + y + 1
c
7
y
74
+ 17y
73
+ ··· + 1185525y + 30625
c
8
y
74
+ 5y
73
+ ··· + 4433y + 169
c
9
, c
12
y
74
+ 45y
73
+ ··· + 403241y + 80089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.581679 + 0.588687I
1.14751 − 12.21490I 2.00000 + 10.62461I
u = −0.581679 − 0.588687I
1.14751 + 12.21490I 2.00000 − 10.62461I
u = 0.579078 + 0.579968I
3.39034 + 7.17138I 4.72098 − 6.80374I
u = 0.579078 − 0.579968I
3.39034 − 7.17138I 4.72098 + 6.80374I
u = −0.558960 + 0.584212I
−1.22103 − 4.59999I −1.85198 + 5.42057I
u = −0.558960 − 0.584212I
−1.22103 + 4.59999I −1.85198 − 5.42057I
u = 0.580042 + 0.552186I
4.60737 + 4.92092I 6.44482 − 6.98206I
u = 0.580042 − 0.552186I
4.60737 − 4.92092I 6.44482 + 6.98206I
u = −0.581910 + 0.533281I
3.51551 − 0.09713I 4.79421 + 0.95551I
u = −0.581910 − 0.533281I
3.51551 + 0.09713I 4.79421 − 0.95551I
u = 0.160664 + 0.764547I
−3.59023 + 7.24183I −4.81965 − 8.01497I
u = 0.160664 − 0.764547I
−3.59023 − 7.24183I −4.81965 + 8.01497I
u = 0.081400 + 0.760927I
−5.25802 − 0.19086I −8.37896 − 0.60569I
u = 0.081400 − 0.760927I
−5.25802 + 0.19086I −8.37896 + 0.60569I
u = 0.475714 + 0.583485I
−2.85675 + 4.95140I −3.45849 − 7.85168I
u = 0.475714 − 0.583485I
−2.85675 − 4.95140I −3.45849 + 7.85168I
u = −0.594230 + 0.443922I
3.77889 − 3.92096I 5.61393 + 5.93891I
u = −0.594230 − 0.443922I
3.77889 + 3.92096I 5.61393 − 5.93891I
u = −0.149812 + 0.724787I
−1.30291 − 2.53624I −1.75249 + 4.49036I
u = −0.149812 − 0.724787I
−1.30291 + 2.53624I −1.75249 − 4.49036I
u = 0.595573 + 0.422112I
4.98992 − 0.90435I 7.85161 + 0.13371I
u = 0.595573 − 0.422112I
4.98992 + 0.90435I 7.85161 − 0.13371I
u = −0.611496 + 0.376425I
1.77025 + 8.14990I 3.28357 − 4.51693I
u = −0.611496 − 0.376425I
1.77025 − 8.14990I 3.28357 + 4.51693I
u = 0.603907 + 0.386844I
3.95690 − 3.13486I 6.57615 + 0.47238I
u = 0.603907 − 0.386844I
3.95690 + 3.13486I 6.57615 − 0.47238I
u = 0.384733 + 0.589181I
−2.15217 − 2.34776I −2.61549 − 0.50712I
u = 0.384733 − 0.589181I
−2.15217 + 2.34776I −2.61549 + 0.50712I
u = −0.457206 + 0.515716I
0.32851 − 1.59321I 1.85928 + 4.31200I
u = −0.457206 − 0.515716I
0.32851 + 1.59321I 1.85928 − 4.31200I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.576050 + 0.370037I
−0.597920 + 0.702387I 0.117490 + 1.017971I
u = −0.576050 − 0.370037I
−0.597920 − 0.702387I 0.117490 − 1.017971I
u = −0.191536 + 0.572330I
−0.30101 − 1.44762I −0.21354 + 6.41359I
u = −0.191536 − 0.572330I
−0.30101 + 1.44762I −0.21354 − 6.41359I
u = −0.13095 + 1.44541I
−4.02653 + 5.58703I 0
u = −0.13095 − 1.44541I
−4.02653 − 5.58703I 0
u = 0.13429 + 1.45675I
−1.94463 − 0.59547I 0
u = 0.13429 − 1.45675I
−1.94463 + 0.59547I 0
u = −0.10830 + 1.47365I
−6.49129 − 1.54826I 0
u = −0.10830 − 1.47365I
−6.49129 + 1.54826I 0
u = 0.14890 + 1.47840I
−1.17433 + 1.68063I 0
u = 0.14890 − 1.47840I
−1.17433 − 1.68063I 0
u = 0.442216 + 0.250522I
−2.00759 − 1.71991I −0.002985 + 0.493302I
u = 0.442216 − 0.250522I
−2.00759 + 1.71991I −0.002985 − 0.493302I
u = −0.15679 + 1.48846I
−2.52069 − 6.55186I 0
u = −0.15679 − 1.48846I
−2.52069 + 6.55186I 0
u = 0.465321 + 0.114222I
−0.77170 + 5.14412I 3.35203 − 6.10091I
u = 0.465321 − 0.114222I
−0.77170 − 5.14412I 3.35203 + 6.10091I
u = −0.16980 + 1.53508I
−3.33883 − 2.79785I 0
u = −0.16980 − 1.53508I
−3.33883 + 2.79785I 0
u = −0.02101 + 1.54796I
−7.42999 − 2.03723I 0
u = −0.02101 − 1.54796I
−7.42999 + 2.03723I 0
u = −0.13143 + 1.54609I
−6.62453 − 3.70192I 0
u = −0.13143 − 1.54609I
−6.62453 + 3.70192I 0
u = 0.17209 + 1.54345I
−2.35401 + 7.64003I 0
u = 0.17209 − 1.54345I
−2.35401 − 7.64003I 0
u = 0.11928 + 1.55708I
−9.35786 − 0.47227I 0
u = 0.11928 − 1.55708I
−9.35786 + 0.47227I 0
u = 0.17433 + 1.55520I
−3.72276 + 9.91652I 0
u = 0.17433 − 1.55520I
−3.72276 − 9.91652I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.13939 + 1.55951I
−10.05520 + 7.19221I 0
u = 0.13939 − 1.55951I
−10.05520 − 7.19221I 0
u = −0.16695 + 1.55795I
−8.37394 − 7.24510I 0
u = −0.16695 − 1.55795I
−8.37394 + 7.24510I 0
u = −0.17594 + 1.55858I
−6.0096 − 14.9821I 0
u = −0.17594 − 1.55858I
−6.0096 + 14.9821I 0
u = −0.412346 + 0.073322I
1.227240 − 0.638691I 7.97254 + 1.54143I
u = −0.412346 − 0.073322I
1.227240 + 0.638691I 7.97254 − 1.54143I
u = −0.02854 + 1.58475I
−9.12688 − 3.11271I 0
u = −0.02854 − 1.58475I
−9.12688 + 3.11271I 0
u = 0.01619 + 1.59177I
−13.22470 + 0.12897I 0
u = 0.01619 − 1.59177I
−13.22470 − 0.12897I 0
u = 0.03179 + 1.59277I
−11.57340 + 7.87379I 0
u = 0.03179 − 1.59277I
−11.57340 − 7.87379I 0
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
74
+ 35u
73
+ ··· − u + 1
c
2
, c
6
u
74
− u
73
+ ··· − u + 1
c
3
u
74
+ u
73
+ ··· − 879u + 481
c
4
, c
5
, c
10
c
11
u
74
− u
73
+ ··· − u + 1
c
7
u
74
− 3u
73
+ ··· − 325u + 175
c
8
u
74
+ 9u
73
+ ··· + 169u + 13
c
9
, c
12
u
74
− 13u
73
+ ··· − 2717u + 283
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 9y
73
+ ··· + 5y + 1
c
2
, c
6
y
74
− 35y
73
+ ··· + y + 1
c
3
y
74
− 19y
73
+ ··· − 9331555y + 231361
c
4
, c
5
, c
10
c
11
y
74
+ 81y
73
+ ··· + y + 1
c
7
y
74
+ 17y
73
+ ··· + 1185525y + 30625
c
8
y
74
+ 5y
73
+ ··· + 4433y + 169
c
9
, c
12
y
74
+ 45y
73
+ ··· + 403241y + 80089
9
