12a
0534
(K12a
0534
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 11 2 1 4 12 6 5 9
Solving Sequence
6,10
11 5 12 4 9 1 8 3 2 7
c
10
c
5
c
11
c
4
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
81
+ u
80
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 81 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
81
+ u
80
+ · · · − u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
5
=
−u
u
3
+ u
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
3
− 2u
u
3
+ u
a
9
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
1
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
−u
12
− 6u
10
− 12u
8
− 8u
6
− u
4
− 2u
2
a
8
=
−u
14
− 7u
12
− 18u
10
− 19u
8
− 6u
6
− 2u
4
− 4u
2
+ 1
u
14
+ 6u
12
+ 13u
10
+ 12u
8
+ 6u
6
+ 4u
4
+ u
2
a
3
=
u
25
+ 12u
23
+ ··· + 4u
3
− 3u
−u
25
− 11u
23
+ ··· − 3u
5
+ u
a
2
=
u
62
+ 29u
60
+ ··· − 4u
2
+ 1
−u
62
− 28u
60
+ ··· − 8u
4
− u
2
a
7
=
u
36
+ 17u
34
+ ··· − 7u
2
+ 1
−u
38
− 18u
36
+ ··· + 10u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
79
+ 4u
78
+ ··· + 16u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 37u
80
+ ··· + 5u + 1
c
2
, c
6
u
81
− u
80
+ ··· + u − 1
c
3
, c
8
u
81
+ u
80
+ ··· − 453u − 61
c
4
u
81
− u
80
+ ··· − 1961u − 1237
c
5
, c
10
, c
11
u
81
+ u
80
+ ··· − u − 1
c
7
u
81
− 3u
80
+ ··· + 19u − 1
c
9
, c
12
u
81
+ 13u
80
+ ··· − 5071u − 283
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 15y
80
+ ··· − 7y −1
c
2
, c
6
y
81
− 37y
80
+ ··· + 5y −1
c
3
, c
8
y
81
− 53y
80
+ ··· + 186177y −3721
c
4
y
81
+ 23y
80
+ ··· − 35110083y −1530169
c
5
, c
10
, c
11
y
81
+ 75y
80
+ ··· + 5y −1
c
7
y
81
+ 7y
80
+ ··· + 145y −1
c
9
, c
12
y
81
+ 59y
80
+ ··· − 6263y −80089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.197771 + 1.183570I
0.84481 − 3.23672I 0
u = 0.197771 − 1.183570I
0.84481 + 3.23672I 0
u = 0.046171 + 1.211660I
−2.27651 + 1.93915I 0
u = 0.046171 − 1.211660I
−2.27651 − 1.93915I 0
u = −0.204035 + 1.199890I
2.50774 − 1.86243I 0
u = −0.204035 − 1.199890I
2.50774 + 1.86243I 0
u = −0.688192 + 0.370410I
−0.29265 − 12.11820I 5.45285 + 10.14700I
u = −0.688192 − 0.370410I
−0.29265 + 12.11820I 5.45285 − 10.14700I
u = 0.682734 + 0.364569I
1.77767 + 6.96994I 8.59265 − 6.07951I
u = 0.682734 − 0.364569I
1.77767 − 6.96994I 8.59265 + 6.07951I
u = −0.667182 + 0.376841I
−3.10444 − 4.74353I 1.89111 + 5.31075I
u = −0.667182 − 0.376841I
−3.10444 + 4.74353I 1.89111 − 5.31075I
u = 0.627167 + 0.427079I
−5.80126 + 5.75467I −0.15516 − 7.51536I
u = 0.627167 − 0.427079I
−5.80126 − 5.75467I −0.15516 + 7.51536I
u = 0.669087 + 0.343377I
2.54734 + 4.35898I 9.79953 − 6.09005I
u = 0.669087 − 0.343377I
2.54734 − 4.35898I 9.79953 + 6.09005I
u = −0.220135 + 1.228700I
2.26970 − 4.55930I 0
u = −0.220135 − 1.228700I
2.26970 + 4.55930I 0
u = 0.600027 + 0.450919I
−5.90992 − 1.73415I −0.700518 + 0.546897I
u = 0.600027 − 0.450919I
−5.90992 + 1.73415I −0.700518 − 0.546897I
u = −0.518361 + 0.541766I
−0.99512 + 8.05238I 3.71543 − 4.26648I
u = −0.518361 − 0.541766I
−0.99512 − 8.05238I 3.71543 + 4.26648I
u = 0.186058 + 1.245240I
−2.71415 + 2.87763I 0
u = 0.186058 − 1.245240I
−2.71415 − 2.87763I 0
u = 0.227678 + 1.238350I
0.40246 + 9.70206I 0
u = 0.227678 − 1.238350I
0.40246 − 9.70206I 0
u = −0.661462 + 0.328497I
1.155840 + 0.658240I 7.68128 + 0.74467I
u = −0.661462 − 0.328497I
1.155840 − 0.658240I 7.68128 − 0.74467I
u = 0.504244 + 0.533281I
1.06272 − 2.96937I 6.86213 + 0.09191I
u = 0.504244 − 0.533281I
1.06272 + 2.96937I 6.86213 − 0.09191I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599806 + 0.419570I
−2.86954 − 1.93751I 3.68977 + 3.76519I
u = −0.599806 − 0.419570I
−2.86954 + 1.93751I 3.68977 − 3.76519I
u = −0.528049 + 0.500416I
−3.65675 + 0.77452I 0.180179 + 1.063801I
u = −0.528049 − 0.500416I
−3.65675 − 0.77452I 0.180179 − 1.063801I
u = 0.445960 + 0.514360I
1.74475 − 0.56616I 7.81141 − 0.32467I
u = 0.445960 − 0.514360I
1.74475 + 0.56616I 7.81141 + 0.32467I
u = 0.090833 + 1.321820I
−3.48103 + 1.92013I 0
u = 0.090833 − 1.321820I
−3.48103 − 1.92013I 0
u = 0.664571 + 0.032433I
4.28824 + 6.44063I 11.37631 − 5.73427I
u = 0.664571 − 0.032433I
4.28824 − 6.44063I 11.37631 + 5.73427I
u = −0.660958 + 0.017589I
6.06487 − 1.33192I 14.4027 + 0.6799I
u = −0.660958 − 0.017589I
6.06487 + 1.33192I 14.4027 − 0.6799I
u = −0.394768 + 0.518007I
0.25427 − 4.31628I 4.96258 + 5.88678I
u = −0.394768 − 0.518007I
0.25427 + 4.31628I 4.96258 − 5.88678I
u = −0.042555 + 1.365360I
−6.77977 + 0.65328I 0
u = −0.042555 − 1.365360I
−6.77977 − 0.65328I 0
u = −0.110213 + 1.375120I
−5.52185 − 6.10195I 0
u = −0.110213 − 1.375120I
−5.52185 + 6.10195I 0
u = 0.601777
1.08479 8.90280
u = −0.541617 + 0.228507I
−0.25287 − 3.77283I 7.91061 + 8.40043I
u = −0.541617 − 0.228507I
−0.25287 + 3.77283I 7.91061 − 8.40043I
u = −0.19013 + 1.41345I
−5.52475 − 6.36348I 0
u = −0.19013 − 1.41345I
−5.52475 + 6.36348I 0
u = 0.17372 + 1.43625I
−4.34343 + 1.67894I 0
u = 0.17372 − 1.43625I
−4.34343 − 1.67894I 0
u = −0.25166 + 1.43227I
−4.49351 − 2.67497I 0
u = −0.25166 − 1.43227I
−4.49351 + 2.67497I 0
u = 0.25453 + 1.43844I
−3.17261 + 7.73200I 0
u = 0.25453 − 1.43844I
−3.17261 − 7.73200I 0
u = 0.25853 + 1.44805I
−4.04746 + 10.40670I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25853 − 1.44805I
−4.04746 − 10.40670I 0
u = 0.17326 + 1.46090I
−5.28963 − 0.54466I 0
u = 0.17326 − 1.46090I
−5.28963 + 0.54466I 0
u = −0.25138 + 1.45103I
−8.98223 − 8.10218I 0
u = −0.25138 − 1.45103I
−8.98223 + 8.10218I 0
u = −0.22226 + 1.45599I
−8.89843 − 4.95649I 0
u = −0.22226 − 1.45599I
−8.89843 + 4.95649I 0
u = −0.18698 + 1.46218I
−9.93180 − 1.82433I 0
u = −0.18698 − 1.46218I
−9.93180 + 1.82433I 0
u = −0.26014 + 1.45096I
−6.1479 − 15.5799I 0
u = −0.26014 − 1.45096I
−6.1479 + 15.5799I 0
u = −0.17307 + 1.46742I
−7.42202 + 5.58777I 0
u = −0.17307 − 1.46742I
−7.42202 − 5.58777I 0
u = 0.22921 + 1.46252I
−11.8872 + 8.8870I 0
u = 0.22921 − 1.46252I
−11.8872 − 8.8870I 0
u = 0.21649 + 1.46473I
−12.07490 + 1.25015I 0
u = 0.21649 − 1.46473I
−12.07490 − 1.25015I 0
u = 0.469947 + 0.071920I
0.851920 + 0.071772I 12.35395 − 1.18798I
u = 0.469947 − 0.071920I
0.851920 − 0.071772I 12.35395 + 1.18798I
u = −0.145910 + 0.409235I
−1.47601 + 1.33170I 0.709363 − 0.772030I
u = −0.145910 − 0.409235I
−1.47601 − 1.33170I 0.709363 + 0.772030I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
81
+ 37u
80
+ ··· + 5u + 1
c
2
, c
6
u
81
− u
80
+ ··· + u − 1
c
3
, c
8
u
81
+ u
80
+ ··· − 453u − 61
c
4
u
81
− u
80
+ ··· − 1961u − 1237
c
5
, c
10
, c
11
u
81
+ u
80
+ ··· − u − 1
c
7
u
81
− 3u
80
+ ··· + 19u − 1
c
9
, c
12
u
81
+ 13u
80
+ ··· − 5071u − 283
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 15y
80
+ ··· − 7y −1
c
2
, c
6
y
81
− 37y
80
+ ··· + 5y −1
c
3
, c
8
y
81
− 53y
80
+ ··· + 186177y −3721
c
4
y
81
+ 23y
80
+ ··· − 35110083y −1530169
c
5
, c
10
, c
11
y
81
+ 75y
80
+ ··· + 5y −1
c
7
y
81
+ 7y
80
+ ··· + 145y −1
c
9
, c
12
y
81
+ 59y
80
+ ··· − 6263y −80089
9
