12a
1203
(K12a
1203
)
A knot diagram
1
Linearized knot diagam
4 11 7 9 10 3 12 1 5 2 6 8
Solving Sequence
7,12
8
1,4
2 9 5 3 6 11 10
c
7
c
12
c
1
c
8
c
4
c
3
c
6
c
11
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
10
− 2u
9
− 23u
8
+ 12u
7
+ 42u
6
− 23u
5
− 20u
4
+ 20u
3
+ b − 16u − 6,
− 24u
10
+ 16u
9
+ 131u
8
− 92u
7
− 215u
6
+ 162u
5
+ 63u
4
− 111u
3
+ 16u
2
+ 7a + 83u + 29,
u
11
− 6u
9
+ 12u
7
− 8u
5
+ 2u
4
+ 3u
3
− 4u
2
− 4u − 1i
I
u
2
= h1.89277 × 10
85
u
59
− 8.97500 × 10
85
u
58
+ ··· + 5.45911 × 10
86
b + 6.16613 × 10
86
,
− 3.98384 × 10
87
u
59
+ 1.21124 × 10
88
u
58
+ ··· + 1.63773 × 10
87
a − 8.06741 × 10
86
, u
60
− 3u
59
+ ··· − 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 71 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
=
h4u
10
−2u
9
+· · ·+b −6, −24u
10
+16u
9
+· · ·+7a +29, u
11
−6u
9
+· · ·−4u −1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
24
7
u
10
−
16
7
u
9
+ ··· −
83
7
u −
29
7
−4u
10
+ 2u
9
+ 23u
8
− 12u
7
− 42u
6
+ 23u
5
+ 20u
4
− 20u
3
+ 16u + 6
a
2
=
−4.48980u
10
+ 4.32653u
9
+ ··· + 17.8367u + 4.73469
30
7
u
10
−
20
7
u
9
+ ··· −
109
7
u −
38
7
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
24
7
u
10
−
16
7
u
9
+ ··· −
76
7
u −
29
7
−4u
10
+ 2u
9
+ 23u
8
− 12u
7
− 42u
6
+ 24u
5
+ 20u
4
− 22u
3
+ 16u + 6
a
3
=
−
4
7
u
10
−
2
7
u
9
+ ··· +
29
7
u +
13
7
−4u
10
+ 2u
9
+ 23u
8
− 12u
7
− 42u
6
+ 23u
5
+ 20u
4
− 20u
3
+ 16u + 6
a
6
=
−1.57143u
10
+ 1.71429u
9
+ ··· + 4.14286u + 1.85714
3u
10
− 2u
9
+ ··· − 12u − 4
a
11
=
−1.65306u
10
+ 2.10204u
9
+ ··· − 0.551020u − 1.02041
33
7
u
10
−
22
7
u
9
+ ··· −
115
7
u −
39
7
a
10
=
16
7
u
10
−
13
7
u
9
+ ··· −
67
7
u −
17
7
−2u
10
+ u
9
+ ··· + 10u + 4
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
68
7
u
10
−
36
7
u
9
−
384
7
u
8
+
228
7
u
7
+
664
7
u
6
−
480
7
u
5
− 32u
4
+
444
7
u
3
−
92
7
u
2
−
276
7
u −
18
7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
7(7u
11
− 57u
10
+ ··· − 288u + 64)
c
2
, c
3
, c
6
c
10
u
11
+ 2u
10
− 2u
9
− 6u
8
+ 6u
6
+ 6u
5
+ 4u
4
− 3u
3
− 2u
2
+ 2u − 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
11
− 6u
9
+ 12u
7
− 8u
5
− 2u
4
+ 3u
3
+ 4u
2
− 4u + 1
c
11
7(7u
11
− 57u
10
+ ··· − 1232u + 160)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
49(49y
11
− 141y
10
+ ··· − 48128y −4096)
c
2
, c
3
, c
6
c
10
y
11
− 8y
10
+ ··· − 8y
2
− 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
11
− 12y
10
+ ··· + 8y −1
c
11
49(49y
11
− 575y
10
+ ··· + 214784y −25600)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478687 + 0.745648I
a = −0.553902 − 0.948598I
b = −1.34136 + 0.45173I
−5.83345 + 8.24192I −1.78003 − 8.25664I
u = 0.478687 − 0.745648I
a = −0.553902 + 0.948598I
b = −1.34136 − 0.45173I
−5.83345 − 8.24192I −1.78003 + 8.25664I
u = −0.658231 + 0.262357I
a = −1.46305 − 1.04015I
b = 1.266780 − 0.115508I
−4.39476 + 0.14427I 2.57188 + 3.97363I
u = −0.658231 − 0.262357I
a = −1.46305 + 1.04015I
b = 1.266780 + 0.115508I
−4.39476 − 0.14427I 2.57188 − 3.97363I
u = 1.33602
a = 2.25023
b = −0.601613
7.19259 15.0510
u = −0.479037 + 0.241898I
a = −0.181635 − 0.272909I
b = −0.259055 + 0.400626I
0.928640 − 0.385456I 9.67201 + 2.53338I
u = −0.479037 − 0.241898I
a = −0.181635 + 0.272909I
b = −0.259055 − 0.400626I
0.928640 + 0.385456I 9.67201 − 2.53338I
u = −1.58856 + 0.17840I
a = −0.206594 + 1.159350I
b = 0.242301 − 0.964246I
15.1584 − 4.3999I 11.24843 + 1.35382I
u = −1.58856 − 0.17840I
a = −0.206594 − 1.159350I
b = 0.242301 + 0.964246I
15.1584 + 4.3999I 11.24843 − 1.35382I
u = 1.57913 + 0.29390I
a = −0.36279 + 1.54535I
b = 1.39214 − 0.58407I
7.8167 + 16.1195I 5.19082 − 7.65707I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57913 − 0.29390I
a = −0.36279 − 1.54535I
b = 1.39214 + 0.58407I
7.8167 − 16.1195I 5.19082 + 7.65707I
6
II.
I
u
2
= h1.89×10
85
u
59
−8.98×10
85
u
58
+· · ·+5.46×10
86
b+6.17×10
86
, −3.98×
10
87
u
59
+1.21×10
88
u
58
+· · ·+1.64×10
87
a−8.07×10
86
, u
60
−3u
59
+· · ·−4u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
2.43253u
59
− 7.39586u
58
+ ··· − 72.0815u + 0.492596
−0.0346718u
59
+ 0.164404u
58
+ ··· − 0.741074u − 1.12951
a
2
=
8.63257u
59
− 26.7187u
58
+ ··· − 207.349u + 18.6317
−0.243987u
59
+ 0.846358u
58
+ ··· + 9.95097u − 2.79898
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
2.76707u
59
− 8.30435u
58
+ ··· − 79.3106u − 0.0929557
−0.0306498u
59
+ 0.143629u
58
+ ··· − 0.263022u − 1.12429
a
3
=
2.39786u
59
− 7.23146u
58
+ ··· − 72.8226u − 0.636916
−0.0346718u
59
+ 0.164404u
58
+ ··· − 0.741074u − 1.12951
a
6
=
3.00540u
59
− 9.41833u
58
+ ··· − 57.5152u − 3.02190
0.197053u
59
− 0.528407u
58
+ ··· + 0.476650u − 1.12091
a
11
=
6.13879u
59
− 20.4327u
58
+ ··· − 157.725u + 8.37417
−0.446686u
59
+ 1.03858u
58
+ ··· + 5.09039u − 2.20303
a
10
=
−0.616946u
59
+ 2.65559u
58
+ ··· + 44.4296u − 20.2992
0.144193u
59
− 0.493218u
58
+ ··· − 8.00218u − 0.368881
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.59968u
59
− 12.3313u
58
+ ··· − 95.2581u + 14.2700
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(3u
30
+ 36u
29
+ ··· + 154u − 41)
2
c
2
, c
3
, c
6
c
10
u
60
− u
59
+ ··· − 14u + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
u
60
+ 3u
59
+ ··· + 4u + 1
c
11
9(3u
30
− 3u
29
+ ··· + 15u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(9y
30
− 102y
29
+ ··· − 66274y + 1681)
2
c
2
, c
3
, c
6
c
10
y
60
− 37y
59
+ ··· − 428y + 1
c
4
, c
5
, c
7
c
8
, c
9
, c
12
y
60
− 61y
59
+ ··· − 68y + 1
c
11
81(9y
30
− 147y
29
+ ··· − 69y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.833474 + 0.555513I
a = 0.387187 − 0.319977I
b = 0.185112 + 0.453484I
7.21827 + 1.60938I 0
u = 0.833474 − 0.555513I
a = 0.387187 + 0.319977I
b = 0.185112 − 0.453484I
7.21827 − 1.60938I 0
u = 0.620080 + 0.732888I
a = 0.027446 − 0.613448I
b = −1.204640 − 0.259326I
−5.45352 − 3.30155I 0
u = 0.620080 − 0.732888I
a = 0.027446 + 0.613448I
b = −1.204640 + 0.259326I
−5.45352 + 3.30155I 0
u = −0.629559 + 0.862226I
a = 0.486783 − 1.011150I
b = 1.315580 + 0.457135I
0.61217 − 11.85690I 0
u = −0.629559 − 0.862226I
a = 0.486783 + 1.011150I
b = 1.315580 − 0.457135I
0.61217 + 11.85690I 0
u = −0.363141 + 0.797919I
a = −0.719921 + 0.642225I
b = −1.011050 − 0.278044I
−1.08758 − 3.25958I 2.38011 + 10.20080I
u = −0.363141 − 0.797919I
a = −0.719921 − 0.642225I
b = −1.011050 + 0.278044I
−1.08758 + 3.25958I 2.38011 − 10.20080I
u = −0.647832 + 0.589870I
a = −0.129345 + 0.669989I
b = −0.089131 − 0.919019I
4.91596 − 6.95691I 6.13134 + 6.91488I
u = −0.647832 − 0.589870I
a = −0.129345 − 0.669989I
b = −0.089131 + 0.919019I
4.91596 + 6.95691I 6.13134 − 6.91488I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.560987 + 1.036060I
a = 0.195707 − 0.202609I
b = 1.166400 − 0.314203I
0.26680 + 5.75700I 0
u = −0.560987 − 1.036060I
a = 0.195707 + 0.202609I
b = 1.166400 + 0.314203I
0.26680 − 5.75700I 0
u = −0.228769 + 0.724317I
a = 1.003230 − 0.131008I
b = −0.044280 + 0.505989I
3.67376 + 2.63649I 5.81236 − 1.84652I
u = −0.228769 − 0.724317I
a = 1.003230 + 0.131008I
b = −0.044280 − 0.505989I
3.67376 − 2.63649I 5.81236 + 1.84652I
u = 0.579713 + 1.108340I
a = 0.470071 + 0.518344I
b = 1.000490 − 0.320542I
5.13933 + 4.75641I 0
u = 0.579713 − 1.108340I
a = 0.470071 − 0.518344I
b = 1.000490 + 0.320542I
5.13933 − 4.75641I 0
u = 1.357920 + 0.019295I
a = 1.84637 + 0.92508I
b = 1.066870 − 0.034317I
1.55370 + 0.00608I 0
u = 1.357920 − 0.019295I
a = 1.84637 − 0.92508I
b = 1.066870 + 0.034317I
1.55370 − 0.00608I 0
u = −0.325223 + 0.548272I
a = 0.643224 − 0.820076I
b = 1.39941 + 0.44826I
−5.45352 − 3.30155I −2.99005 + 4.83446I
u = −0.325223 − 0.548272I
a = 0.643224 + 0.820076I
b = 1.39941 − 0.44826I
−5.45352 + 3.30155I −2.99005 − 4.83446I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38075 + 0.35680I
a = −0.068945 + 0.802649I
b = −0.934678 − 0.203671I
1.87339 − 1.59238I 0
u = −1.38075 − 0.35680I
a = −0.068945 − 0.802649I
b = −0.934678 + 0.203671I
1.87339 + 1.59238I 0
u = −1.42198 + 0.11012I
a = −0.49563 − 1.58905I
b = 0.999372 + 0.593646I
3.67376 − 2.63649I 0
u = −1.42198 − 0.11012I
a = −0.49563 + 1.58905I
b = 0.999372 − 0.593646I
3.67376 + 2.63649I 0
u = −1.44134
a = −0.648369
b = −0.0486569
3.34318 0
u = 0.428325 + 0.345067I
a = 0.117620 + 0.589809I
b = 0.243272 − 0.979166I
−1.08758 + 3.25958I 2.38011 − 10.20080I
u = 0.428325 − 0.345067I
a = 0.117620 − 0.589809I
b = 0.243272 + 0.979166I
−1.08758 − 3.25958I 2.38011 + 10.20080I
u = 1.44300 + 0.15336I
a = −0.82586 + 1.54444I
b = 1.51584 − 0.77183I
0.26680 + 5.75700I 0
u = 1.44300 − 0.15336I
a = −0.82586 − 1.54444I
b = 1.51584 + 0.77183I
0.26680 − 5.75700I 0
u = −1.46078
a = 0.376305
b = −1.57915
8.95550 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.47066 + 0.07345I
a = 0.445781 + 1.290480I
b = −0.446296 − 0.915918I
7.21827 + 1.60938I 0
u = 1.47066 − 0.07345I
a = 0.445781 − 1.290480I
b = −0.446296 + 0.915918I
7.21827 − 1.60938I 0
u = −1.47406
a = 0.939294
b = −1.86730
8.91513 0
u = −1.47658 + 0.08795I
a = 0.08740 − 1.86794I
b = 0.11923 + 1.50677I
5.13933 − 4.75641I 0
u = −1.47658 − 0.08795I
a = 0.08740 + 1.86794I
b = 0.11923 − 1.50677I
5.13933 + 4.75641I 0
u = 1.47858 + 0.04341I
a = 1.06994 + 1.32208I
b = −1.47842 − 1.04389I
8.05603 + 2.43541I 0
u = 1.47858 − 0.04341I
a = 1.06994 − 1.32208I
b = −1.47842 + 1.04389I
8.05603 − 2.43541I 0
u = 1.47684 + 0.25365I
a = 0.22074 − 1.43458I
b = −1.134910 + 0.555153I
4.91596 + 6.95691I 0
u = 1.47684 − 0.25365I
a = 0.22074 + 1.43458I
b = −1.134910 − 0.555153I
4.91596 − 6.95691I 0
u = −1.50444 + 0.25222I
a = 0.51791 + 1.58138I
b = −1.40913 − 0.64393I
0.61217 − 11.85690I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50444 − 0.25222I
a = 0.51791 − 1.58138I
b = −1.40913 + 0.64393I
0.61217 + 11.85690I 0
u = −0.397490 + 0.226483I
a = −0.256525 − 0.636041I
b = −1.108750 + 0.697445I
1.87339 − 1.59238I 6.67632 + 9.14419I
u = −0.397490 − 0.226483I
a = −0.256525 + 0.636041I
b = −1.108750 − 0.697445I
1.87339 + 1.59238I 6.67632 − 9.14419I
u = 0.220469 + 0.386151I
a = 0.88338 + 1.75647I
b = 0.976188 − 0.197719I
−1.65573 + 0.87357I −2.51974 + 1.49849I
u = 0.220469 − 0.386151I
a = 0.88338 − 1.75647I
b = 0.976188 + 0.197719I
−1.65573 − 0.87357I −2.51974 − 1.49849I
u = 0.221492 + 0.372642I
a = −1.74604 + 0.73502I
b = 0.134818 + 0.350741I
−1.65573 − 0.87357I −2.51974 − 1.49849I
u = 0.221492 − 0.372642I
a = −1.74604 − 0.73502I
b = 0.134818 − 0.350741I
−1.65573 + 0.87357I −2.51974 + 1.49849I
u = 1.56045 + 0.18740I
a = −0.25231 − 1.52828I
b = −0.028871 + 1.223480I
12.2304 + 9.8327I 0
u = 1.56045 − 0.18740I
a = −0.25231 + 1.52828I
b = −0.028871 − 1.223480I
12.2304 − 9.8327I 0
u = 0.376786
a = −1.32121
b = −1.51840
2.79630 14.5100
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59069 + 0.33885I
a = −0.156905 − 1.268360I
b = 1.189620 + 0.558071I
12.2304 − 9.8327I 0
u = −1.59069 − 0.33885I
a = −0.156905 + 1.268360I
b = 1.189620 − 0.558071I
12.2304 + 9.8327I 0
u = −1.65135
a = 0.528394
b = −0.824716
2.79630 0
u = 1.68306
a = 0.372386
b = 0.317785
8.95550 0
u = −0.282510 + 0.079111I
a = 10.61020 + 7.07723I
b = −0.816929 − 0.088924I
1.55370 + 0.00608I 23.9533 + 12.6442I
u = −0.282510 − 0.079111I
a = 10.61020 − 7.07723I
b = −0.816929 + 0.088924I
1.55370 − 0.00608I 23.9533 − 12.6442I
u = 1.60577 + 0.59025I
a = 0.094048 + 0.587595I
b = 0.866646 − 0.256018I
8.05603 + 2.43541I 0
u = 1.60577 − 0.59025I
a = 0.094048 − 0.587595I
b = 0.866646 + 0.256018I
8.05603 − 2.43541I 0
u = 1.83729
a = −0.0147378
b = 0.649298
8.91513 0
u = 0.156757
a = −8.14324
b = −1.07240
3.34318 2.41920
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
63(7u
11
− 57u
10
+ ··· − 288u + 64)
· (3u
30
+ 36u
29
+ ··· + 154u − 41)
2
c
2
, c
3
, c
6
c
10
(u
11
+ 2u
10
− 2u
9
− 6u
8
+ 6u
6
+ 6u
5
+ 4u
4
− 3u
3
− 2u
2
+ 2u − 1)
· (u
60
− u
59
+ ··· − 14u + 1)
c
4
, c
5
, c
7
c
8
, c
9
, c
12
(u
11
− 6u
9
+ 12u
7
− 8u
5
− 2u
4
+ 3u
3
+ 4u
2
− 4u + 1)
· (u
60
+ 3u
59
+ ··· + 4u + 1)
c
11
63(7u
11
− 57u
10
+ ··· − 1232u + 160)(3u
30
− 3u
29
+ ··· + 15u + 1)
2
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
3969(49y
11
− 141y
10
+ ··· − 48128y −4096)
· (9y
30
− 102y
29
+ ··· − 66274y + 1681)
2
c
2
, c
3
, c
6
c
10
(y
11
− 8y
10
+ ··· − 8y
2
− 1)(y
60
− 37y
59
+ ··· − 428y + 1)
c
4
, c
5
, c
7
c
8
, c
9
, c
12
(y
11
− 12y
10
+ ··· + 8y −1)(y
60
− 61y
59
+ ··· − 68y + 1)
c
11
3969(49y
11
− 575y
10
+ ··· + 214784y −25600)
· (9y
30
− 147y
29
+ ··· − 69y + 1)
2
17
