12n
0188
(K12n
0188
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 9 4 12 5 6 1 9
Solving Sequence
5,9
10 6 7
3,11
2 1 4 12 8
c
9
c
5
c
6
c
10
c
2
c
1
c
4
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.51544 × 10
40
u
40
+ 2.56027 × 10
40
u
39
+ ··· + 1.06321 × 10
41
b + 4.21643 × 10
41
,
6.97778 × 10
40
u
40
+ 1.95337 × 10
41
u
39
+ ··· + 2.12642 × 10
41
a − 9.27571 × 10
40
, u
41
+ 3u
40
+ ··· − 8u − 8i
I
u
2
= h−2a
2
− au + b − 2a − u − 1, 4a
3
+ 2a
2
u − u, u
2
− 2i
I
v
1
= ha, b + v + 2, v
3
+ 3v
2
+ 2v −1i
* 3 irreducible components of dim
C
= 0, with total 50 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
= h1.52 × 10
40
u
40
+ 2.56 × 10
40
u
39
+ · · · + 1.06 × 10
41
b + 4.22 × 10
41
, 6.98 ×
10
40
u
40
+1.95×10
41
u
39
+· · ·+2.13×10
41
a−9.28×10
40
, u
41
+3u
40
+· · ·−8u−8i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
u
3
− 2u
−u
3
+ u
a
3
=
−0.328147u
40
− 0.918618u
39
+ ··· − 19.5503u + 0.436213
−0.142535u
40
− 0.240806u
39
+ ··· + 7.40030u − 3.96576
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−0.328147u
40
− 0.918618u
39
+ ··· − 19.5503u + 0.436213
0.0824090u
40
+ 0.163606u
39
+ ··· + 9.49889u − 4.49235
a
1
=
0.0838694u
40
+ 0.525518u
39
+ ··· + 23.3356u + 7.39263
−0.124059u
40
− 0.154000u
39
+ ··· + 5.97827u + 0.0223382
a
4
=
−0.340779u
40
− 1.11522u
39
+ ··· − 14.5840u − 9.80822
0.0747081u
40
− 0.0614080u
39
+ ··· − 12.3801u + 1.21809
a
12
=
0.207928u
40
+ 0.679518u
39
+ ··· + 17.3573u + 7.37029
−0.124059u
40
− 0.154000u
39
+ ··· + 5.97827u + 0.0223382
a
8
=
0.401561u
40
+ 1.01803u
39
+ ··· + 27.2274u + 2.78868
−0.142281u
40
− 0.206934u
39
+ ··· − 0.775735u + 2.43501
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.588415u
40
− 0.804243u
39
+ ··· + 87.6228u − 60.0034
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 26u
40
+ ··· + 206u + 1
c
2
, c
4
u
41
− 4u
40
+ ··· − 14u − 1
c
3
, c
7
u
41
+ 2u
40
+ ··· + 8u − 1
c
5
, c
9
, c
10
u
41
+ 3u
40
+ ··· − 8u − 8
c
6
u
41
− 9u
40
+ ··· + 10824u + 12200
c
8
, c
12
u
41
− 4u
40
+ ··· + 5u − 7
c
11
u
41
− 12u
40
+ ··· + 1593u − 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− 18y
40
+ ··· + 44086y −1
c
2
, c
4
y
41
− 26y
40
+ ··· + 206y −1
c
3
, c
7
y
41
+ 6y
40
+ ··· + 54y −1
c
5
, c
9
, c
10
y
41
− 55y
40
+ ··· + 2752y −64
c
6
y
41
− 139y
40
+ ··· + 8334688576y −148840000
c
8
, c
12
y
41
− 12y
40
+ ··· + 1593y −49
c
11
y
41
+ 44y
40
+ ··· + 664281y −2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.852625 + 0.482864I
a = −0.372803 − 0.780038I
b = 0.771778 − 0.848460I
−0.75167 − 5.04176I −5.33106 + 6.16840I
u = 0.852625 − 0.482864I
a = −0.372803 + 0.780038I
b = 0.771778 + 0.848460I
−0.75167 + 5.04176I −5.33106 − 6.16840I
u = −0.003882 + 1.032070I
a = −0.244627 − 1.101450I
b = 0.500255 + 0.850150I
−1.61122 + 4.08215I −8.92321 − 7.89693I
u = −0.003882 − 1.032070I
a = −0.244627 + 1.101450I
b = 0.500255 − 0.850150I
−1.61122 − 4.08215I −8.92321 + 7.89693I
u = −0.992946 + 0.343746I
a = 1.196560 + 0.016956I
b = −0.60773 − 1.75136I
−4.56663 + 3.64468I −10.21223 − 4.25500I
u = −0.992946 − 0.343746I
a = 1.196560 − 0.016956I
b = −0.60773 + 1.75136I
−4.56663 − 3.64468I −10.21223 + 4.25500I
u = 1.044990 + 0.164135I
a = −1.029770 + 0.479582I
b = −0.335570 + 0.883151I
−4.59839 − 1.02943I −11.04507 + 3.64044I
u = 1.044990 − 0.164135I
a = −1.029770 − 0.479582I
b = −0.335570 − 0.883151I
−4.59839 + 1.02943I −11.04507 − 3.64044I
u = −0.848129 + 0.093318I
a = 0.256235 − 0.617893I
b = 0.429896 − 0.866899I
−1.53932 + 0.15416I −7.41256 − 0.66382I
u = −0.848129 − 0.093318I
a = 0.256235 + 0.617893I
b = 0.429896 + 0.866899I
−1.53932 − 0.15416I −7.41256 + 0.66382I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960191 + 0.725231I
a = 1.064690 − 0.333931I
b = −0.87449 + 1.44326I
−4.46221 − 9.77258I −8.72581 + 8.02773I
u = 0.960191 − 0.725231I
a = 1.064690 + 0.333931I
b = −0.87449 − 1.44326I
−4.46221 + 9.77258I −8.72581 − 8.02773I
u = 0.754982 + 0.217030I
a = 0.849726 − 0.921367I
b = −0.523840 + 0.308432I
3.10105 + 2.13666I −4.09917 − 2.47051I
u = 0.754982 − 0.217030I
a = 0.849726 + 0.921367I
b = −0.523840 − 0.308432I
3.10105 − 2.13666I −4.09917 + 2.47051I
u = 1.39900
a = −0.702767
b = −12.5949
−4.90374 −140.900
u = 0.133621 + 0.570297I
a = 0.730715 + 0.096398I
b = −0.904782 − 0.312265I
1.42682 + 1.35308I 0.34829 − 2.41862I
u = 0.133621 − 0.570297I
a = 0.730715 − 0.096398I
b = −0.904782 + 0.312265I
1.42682 − 1.35308I 0.34829 + 2.41862I
u = −1.25091 + 0.70431I
a = −0.754563 − 0.312340I
b = 0.351245 + 0.928373I
−5.21609 + 2.28754I 0
u = −1.25091 − 0.70431I
a = −0.754563 + 0.312340I
b = 0.351245 − 0.928373I
−5.21609 − 2.28754I 0
u = −1.45442
a = 0.0474720
b = 1.21109
−3.37736 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45857 + 0.03382I
a = −0.622583 − 0.555978I
b = 0.018701 − 1.107830I
−1.93777 − 2.95731I 0
u = −1.45857 − 0.03382I
a = −0.622583 + 0.555978I
b = 0.018701 + 1.107830I
−1.93777 + 2.95731I 0
u = 0.056546 + 0.456890I
a = −0.64877 + 2.24584I
b = 0.904670 − 0.938053I
−1.28446 − 0.76291I −5.31890 − 1.67979I
u = 0.056546 − 0.456890I
a = −0.64877 − 2.24584I
b = 0.904670 + 0.938053I
−1.28446 + 0.76291I −5.31890 + 1.67979I
u = 0.383174 + 0.054663I
a = 2.52375 + 1.73333I
b = 0.214376 + 0.665960I
4.29502 − 2.99232I −13.6444 + 6.7796I
u = 0.383174 − 0.054663I
a = 2.52375 − 1.73333I
b = 0.214376 − 0.665960I
4.29502 + 2.99232I −13.6444 − 6.7796I
u = −0.330545
a = 1.68251
b = 0.579990
−0.892017 −11.9900
u = −1.68875 + 0.14392I
a = −0.003537 − 0.668461I
b = −0.518040 − 1.262490I
−9.61160 + 7.52378I 0
u = −1.68875 − 0.14392I
a = −0.003537 + 0.668461I
b = −0.518040 + 1.262490I
−9.61160 − 7.52378I 0
u = 1.70883 + 0.02668I
a = −0.117584 − 0.623199I
b = −0.23211 − 1.39628I
−10.81520 − 0.66337I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70883 − 0.02668I
a = −0.117584 + 0.623199I
b = −0.23211 + 1.39628I
−10.81520 + 0.66337I 0
u = −1.71449 + 0.22965I
a = −0.820677 + 0.232700I
b = 0.88143 + 1.93236I
−13.5365 + 13.6208I 0
u = −1.71449 − 0.22965I
a = −0.820677 − 0.232700I
b = 0.88143 − 1.93236I
−13.5365 − 13.6208I 0
u = 1.73059 + 0.09206I
a = −0.776808 − 0.320765I
b = 0.52492 − 1.87002I
−14.2793 − 5.4313I 0
u = 1.73059 − 0.09206I
a = −0.776808 + 0.320765I
b = 0.52492 + 1.87002I
−14.2793 + 5.4313I 0
u = −1.73927 + 0.03941I
a = 0.823370 + 0.279136I
b = −0.408494 + 0.947607I
−14.6346 + 1.8508I 0
u = −1.73927 − 0.03941I
a = 0.823370 − 0.279136I
b = −0.408494 − 0.947607I
−14.6346 − 1.8508I 0
u = −0.220223
a = 3.89905
b = −3.25550
0.393691 −52.4600
u = 1.79882 + 0.15440I
a = 0.795536 + 0.161122I
b = −0.531853 + 1.253250I
−15.9531 − 5.8349I 0
u = 1.79882 − 0.15440I
a = 0.795536 − 0.161122I
b = −0.531853 − 1.253250I
−15.9531 + 5.8349I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.84865
a = −0.623981
b = 0.738641
−6.53181 0
9
II. I
u
2
= h−2a
2
− au + b − 2a − u − 1, 4a
3
+ 2a
2
u − u, u
2
− 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
2
a
6
=
−u
−u
a
7
=
0
−u
a
3
=
a
2a
2
+ au + 2a + u + 1
a
11
=
−1
0
a
2
=
a
2a
2
+ au + u + 1
a
1
=
a
2
u + a −
1
2
u
1
a
4
=
a
2
u
au + 2a + u + 1
a
12
=
a
2
u + a −
1
2
u − 1
1
a
8
=
a
2
u + a −
1
2
u
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4au − 8
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
9
c
10
(u
2
− 2)
3
c
8
(u − 1)
6
c
11
, c
12
(u + 1)
6
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
9
c
10
(y −2)
6
c
8
, c
11
, c
12
(y −1)
6
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.620443 + 0.526697I
b = 0.510969 + 0.491114I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = 1.41421
a = −0.620443 − 0.526697I
b = 0.510969 − 0.491114I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = 1.41421
a = 0.533779
b = 4.80649
−4.40332 −11.0200
u = −1.41421
a = 0.620443 + 0.526697I
b = 0.16431 + 1.61567I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = −1.41421
a = 0.620443 − 0.526697I
b = 0.16431 − 1.61567I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = −1.41421
a = −0.533779
b = −0.157054
−4.40332 −11.0200
13
III. I
v
1
= ha, b + v + 2, v
3
+ 3v
2
+ 2v − 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
10
=
1
0
a
6
=
v
0
a
7
=
v
0
a
3
=
0
−v − 2
a
11
=
1
0
a
2
=
v
2
+ 2v − 1
−v − 2
a
1
=
v
2
+ 2v − 1
−1
a
4
=
−2v
2
− 2v + 1
−v
2
− 2v − 1
a
12
=
v
2
+ 2v
−1
a
8
=
−v
2
− 2v + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
+ 6v + 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
9
c
10
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
11
(u + 1)
3
c
12
(u − 1)
3
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
6
, c
9
c
10
y
3
c
8
, c
11
, c
12
(y − 1)
3
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.324718
a = 0
b = −2.32472
0.531480 12.1590
v = −1.66236 + 0.56228I
a = 0
b = −0.337641 − 0.562280I
4.66906 − 2.82812I 4.92040 − 0.36516I
v = −1.66236 − 0.56228I
a = 0
b = −0.337641 + 0.562280I
4.66906 + 2.82812I 4.92040 + 0.36516I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
3
)(u
41
+ 26u
40
+ ··· + 206u + 1)
c
2
((u
3
+ u
2
− 1)
3
)(u
41
− 4u
40
+ ··· − 14u − 1)
c
3
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
41
+ 2u
40
+ ··· + 8u − 1)
c
4
((u
3
− u
2
+ 1)
3
)(u
41
− 4u
40
+ ··· − 14u − 1)
c
5
, c
9
, c
10
u
3
(u
2
− 2)
3
(u
41
+ 3u
40
+ ··· − 8u − 8)
c
6
u
3
(u
2
− 2)
3
(u
41
− 9u
40
+ ··· + 10824u + 12200)
c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
41
+ 2u
40
+ ··· + 8u − 1)
c
8
((u − 1)
6
)(u + 1)
3
(u
41
− 4u
40
+ ··· + 5u − 7)
c
11
((u + 1)
9
)(u
41
− 12u
40
+ ··· + 1593u − 49)
c
12
((u − 1)
3
)(u + 1)
6
(u
41
− 4u
40
+ ··· + 5u − 7)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
41
− 18y
40
+ ··· + 44086y − 1)
c
2
, c
4
((y
3
− y
2
+ 2y − 1)
3
)(y
41
− 26y
40
+ ··· + 206y − 1)
c
3
, c
7
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
41
+ 6y
40
+ ··· + 54y − 1)
c
5
, c
9
, c
10
y
3
(y − 2)
6
(y
41
− 55y
40
+ ··· + 2752y − 64)
c
6
y
3
(y − 2)
6
(y
41
− 139y
40
+ ··· + 8.33469 × 10
9
y − 1.48840 × 10
8
)
c
8
, c
12
((y − 1)
9
)(y
41
− 12y
40
+ ··· + 1593y − 49)
c
11
((y − 1)
9
)(y
41
+ 44y
40
+ ··· + 664281y − 2401)
19
