12a
0595
(K12a
0595
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 2 1 6 12 5 4 8
Solving Sequence
3,7
2 1 8 6 9 4 12 10 5 11
c
2
c
1
c
7
c
6
c
8
c
3
c
12
c
9
c
5
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
69
+ u
68
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 69 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
69
+ u
68
+ · · · − u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
8
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
6
=
u
−u
3
+ u
a
9
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
4
=
−u
20
+ 5u
18
− 11u
16
+ 10u
14
+ 2u
12
− 13u
10
+ 9u
8
− 3u
4
+ u
2
+ 1
u
22
− 6u
20
+ 17u
18
− 26u
16
+ 20u
14
− 13u
10
+ 10u
8
− u
6
− 2u
4
+ u
2
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
10
=
−u
27
+ 8u
25
+ ··· + 4u
5
− u
3
−u
27
+ 7u
25
+ ··· − u
3
+ u
a
5
=
u
57
− 16u
55
+ ··· − u
5
+ u
u
57
− 15u
55
+ ··· − u
5
+ u
a
11
=
u
50
− 13u
48
+ ··· + u
2
+ 1
−u
52
+ 14u
50
+ ··· − 6u
8
− u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
67
+ 72u
65
+ ··· − 8u
3
+ 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
69
+ 37u
68
+ ··· − u + 1
c
2
, c
6
u
69
− u
68
+ ··· − u + 1
c
3
u
69
− u
68
+ ··· − 4205u + 841
c
4
, c
5
, c
10
c
11
u
69
− u
68
+ ··· − u + 1
c
7
, c
12
u
69
− 3u
68
+ ··· + u + 1
c
8
u
69
− 9u
68
+ ··· − 183u + 13
c
9
u
69
− 19u
68
+ ··· + 4845u − 283
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
69
− 9y
68
+ ··· + 3y −1
c
2
, c
6
y
69
− 37y
68
+ ··· − y −1
c
3
y
69
− 29y
68
+ ··· + 24176227y −707281
c
4
, c
5
, c
10
c
11
y
69
+ 79y
68
+ ··· − y −1
c
7
, c
12
y
69
+ 55y
68
+ ··· − 85y −1
c
8
y
69
− 5y
68
+ ··· + 1535y −169
c
9
y
69
− 13y
68
+ ··· + 1486623y −80089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.007650 + 0.064350I
−3.60184 + 2.81733I −9.32476 − 5.48757I
u = −1.007650 − 0.064350I
−3.60184 − 2.81733I −9.32476 + 5.48757I
u = 0.863362 + 0.530746I
0.35930 − 6.77991I −0.61658 + 10.23881I
u = 0.863362 − 0.530746I
0.35930 + 6.77991I −0.61658 − 10.23881I
u = −0.835974 + 0.511530I
1.64738 + 3.32051I 3.54071 − 4.43827I
u = −0.835974 − 0.511530I
1.64738 − 3.32051I 3.54071 + 4.43827I
u = −0.879803 + 0.544272I
−7.29269 + 9.02370I −3.47414 − 8.26985I
u = −0.879803 − 0.544272I
−7.29269 − 9.02370I −3.47414 + 8.26985I
u = 0.859864 + 0.398364I
−1.45583 − 1.56617I −5.75209 + 2.95981I
u = 0.859864 − 0.398364I
−1.45583 + 1.56617I −5.75209 − 2.95981I
u = 1.050990 + 0.067740I
−11.48740 − 4.67055I −10.85743 + 3.45107I
u = 1.050990 − 0.067740I
−11.48740 + 4.67055I −10.85743 − 3.45107I
u = 0.763010 + 0.535883I
−3.25699 − 2.16890I 0.53836 + 3.82901I
u = 0.763010 − 0.535883I
−3.25699 + 2.16890I 0.53836 − 3.82901I
u = 0.931899
−1.68818 −4.45100
u = −0.983730 + 0.422361I
−9.02531 + 0.64002I −6.52857 + 0.I
u = −0.983730 − 0.422361I
−9.02531 − 0.64002I −6.52857 + 0.I
u = −0.689201 + 0.500960I
2.07105 + 0.85287I 5.34302 − 3.58736I
u = −0.689201 − 0.500960I
2.07105 − 0.85287I 5.34302 + 3.58736I
u = −0.614253 + 0.561310I
−6.54819 − 4.59342I −1.49782 + 1.94707I
u = −0.614253 − 0.561310I
−6.54819 + 4.59342I −1.49782 − 1.94707I
u = 0.637725 + 0.530123I
0.99322 + 2.46697I 1.50189 − 3.71848I
u = 0.637725 − 0.530123I
0.99322 − 2.46697I 1.50189 + 3.71848I
u = −1.107000 + 0.388573I
−9.04626 + 0.50923I 0
u = −1.107000 − 0.388573I
−9.04626 − 0.50923I 0
u = −0.137752 + 0.815117I
−10.8743 − 9.4349I −5.12264 + 5.41104I
u = −0.137752 − 0.815117I
−10.8743 + 9.4349I −5.12264 − 5.41104I
u = 0.135322 + 0.801855I
−2.99570 + 7.10512I −2.78124 − 7.18886I
u = 0.135322 − 0.801855I
−2.99570 − 7.10512I −2.78124 + 7.18886I
u = −0.073813 + 0.807863I
−12.67980 + 0.44790I −7.20362 + 0.05375I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.073813 − 0.807863I
−12.67980 − 0.44790I −7.20362 − 0.05375I
u = −0.127650 + 0.782006I
−1.37080 − 3.50950I 0.93203 + 2.31314I
u = −0.127650 − 0.782006I
−1.37080 + 3.50950I 0.93203 − 2.31314I
u = 0.087303 + 0.782586I
−4.38416 + 0.86576I −5.85927 + 0.77218I
u = 0.087303 − 0.782586I
−4.38416 − 0.86576I −5.85927 − 0.77218I
u = 1.127960 + 0.449076I
−2.38041 − 2.24656I 0
u = 1.127960 − 0.449076I
−2.38041 + 2.24656I 0
u = −1.142880 + 0.475125I
−2.14308 + 5.59560I 0
u = −1.142880 − 0.475125I
−2.14308 − 5.59560I 0
u = 1.153950 + 0.498640I
−8.24718 − 7.43164I 0
u = 1.153950 − 0.498640I
−8.24718 + 7.43164I 0
u = 1.199180 + 0.389997I
−5.28056 − 0.45902I 0
u = 1.199180 − 0.389997I
−5.28056 + 0.45902I 0
u = −1.209940 + 0.381438I
−7.02202 − 3.10940I 0
u = −1.209940 − 0.381438I
−7.02202 + 3.10940I 0
u = 0.183314 + 0.704841I
−5.44368 + 2.87522I −1.31258 − 3.07627I
u = 0.183314 − 0.704841I
−5.44368 − 2.87522I −1.31258 + 3.07627I
u = −1.205010 + 0.410064I
−8.18209 + 3.26828I 0
u = −1.205010 − 0.410064I
−8.18209 − 3.26828I 0
u = 1.218430 + 0.378071I
−14.9696 + 5.4032I 0
u = 1.218430 − 0.378071I
−14.9696 − 5.4032I 0
u = 1.218030 + 0.415989I
−16.5257 − 4.7100I 0
u = 1.218030 − 0.415989I
−16.5257 + 4.7100I 0
u = 1.194350 + 0.489511I
−7.61719 − 5.52009I 0
u = 1.194350 − 0.489511I
−7.61719 + 5.52009I 0
u = −1.188620 + 0.503633I
−4.47624 + 8.24964I 0
u = −1.188620 − 0.503633I
−4.47624 − 8.24964I 0
u = 1.193800 + 0.510098I
−6.11348 − 11.92620I 0
u = 1.193800 − 0.510098I
−6.11348 + 11.92620I 0
u = −1.206320 + 0.487082I
−16.0195 + 4.2556I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.206320 − 0.487082I
−16.0195 − 4.2556I 0
u = −1.198100 + 0.513816I
−14.0097 + 14.3072I 0
u = −1.198100 − 0.513816I
−14.0097 − 14.3072I 0
u = −0.386946 + 0.563275I
−7.28945 + 3.35761I −1.95583 − 2.56316I
u = −0.386946 − 0.563275I
−7.28945 − 3.35761I −1.95583 + 2.56316I
u = −0.163148 + 0.605619I
0.62850 − 1.34733I 3.35755 + 4.56273I
u = −0.163148 − 0.605619I
0.62850 + 1.34733I 3.35755 − 4.56273I
u = 0.305258 + 0.505306I
0.08963 − 1.59531I 1.18713 + 4.74981I
u = 0.305258 − 0.505306I
0.08963 + 1.59531I 1.18713 − 4.74981I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
69
+ 37u
68
+ ··· − u + 1
c
2
, c
6
u
69
− u
68
+ ··· − u + 1
c
3
u
69
− u
68
+ ··· − 4205u + 841
c
4
, c
5
, c
10
c
11
u
69
− u
68
+ ··· − u + 1
c
7
, c
12
u
69
− 3u
68
+ ··· + u + 1
c
8
u
69
− 9u
68
+ ··· − 183u + 13
c
9
u
69
− 19u
68
+ ··· + 4845u − 283
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
69
− 9y
68
+ ··· + 3y −1
c
2
, c
6
y
69
− 37y
68
+ ··· − y −1
c
3
y
69
− 29y
68
+ ··· + 24176227y −707281
c
4
, c
5
, c
10
c
11
y
69
+ 79y
68
+ ··· − y −1
c
7
, c
12
y
69
+ 55y
68
+ ··· − 85y −1
c
8
y
69
− 5y
68
+ ··· + 1535y −169
c
9
y
69
− 13y
68
+ ··· + 1486623y −80089
9
