12n
0114
(K12n
0114
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 10 3 11 12 1 6 8 9
Solving Sequence
3,6 7,11
8 12 10 5 2 1 4 9
c
6
c
7
c
11
c
10
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.14531 × 10
57
u
35
− 4.14356 × 10
58
u
34
+ ··· + 1.76003 × 10
57
b − 1.59371 × 10
59
,
1.28899 × 10
58
u
35
+ 5.88274 × 10
58
u
34
+ ··· + 1.76003 × 10
57
a + 2.33162 × 10
59
, u
36
+ 5u
35
+ ··· + 100u + 8i
I
v
1
= ha, −2v
2
+ b − 11v −5, v
3
+ 6v
2
+ 5v + 1i
* 2 irreducible components of dim
C
= 0, with total 39 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
= h−9.15 × 10
57
u
35
− 4.14 × 10
58
u
34
+ · · · + 1.76 × 10
57
b − 1.59 ×
10
59
, 1.29 × 10
58
u
35
+ 5.88 × 10
58
u
34
+ · · · + 1.76 × 10
57
a + 2.33 ×
10
59
, u
36
+ 5u
35
+ · · · + 100u + 8i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
11
=
−7.32365u
35
− 33.4240u
34
+ ··· − 1373.93u − 132.476
5.19610u
35
+ 23.5425u
34
+ ··· + 929.199u + 90.5501
a
8
=
−2.85572u
35
− 13.0958u
34
+ ··· − 534.587u − 49.9748
6.43037u
35
+ 29.3531u
34
+ ··· + 1194.14u + 116.627
a
12
=
−8.36579u
35
− 38.2406u
34
+ ··· − 1566.57u − 152.043
−7.62009u
35
− 34.5272u
34
+ ··· − 1350.03u − 129.988
a
10
=
−2.12755u
35
− 9.88152u
34
+ ··· − 444.735u − 41.9259
5.19610u
35
+ 23.5425u
34
+ ··· + 929.199u + 90.5501
a
5
=
−7.87506u
35
− 36.0437u
34
+ ··· − 1496.97u − 147.313
−6.09885u
35
− 27.8847u
34
+ ··· − 1136.15u − 110.850
a
2
=
1.77621u
35
+ 8.15902u
34
+ ··· + 360.821u + 36.4622
−6.09885u
35
− 27.8847u
34
+ ··· − 1136.15u − 110.850
a
1
=
1.77621u
35
+ 8.15902u
34
+ ··· + 360.821u + 36.4622
−6.43037u
35
− 29.3531u
34
+ ··· − 1194.14u − 116.627
a
4
=
u
u
a
9
=
−7.53767u
35
− 34.2907u
34
+ ··· − 1382.29u − 132.035
−7.62009u
35
− 34.5272u
34
+ ··· − 1350.03u − 129.988
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.83261u
35
− 31.8751u
34
+ ··· − 1561.72u − 175.808
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 16u
35
+ ··· + 1288u + 1
c
2
, c
4
u
36
− 4u
35
+ ··· + 40u − 1
c
3
, c
6
u
36
+ 5u
35
+ ··· + 100u + 8
c
5
, c
10
u
36
− 2u
35
+ ··· + u − 1
c
7
, c
8
, c
9
c
11
, c
12
u
36
+ 2u
35
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 12y
35
+ ··· − 1626228y + 1
c
2
, c
4
y
36
− 16y
35
+ ··· − 1288y + 1
c
3
, c
6
y
36
− 21y
35
+ ··· − 2896y + 64
c
5
, c
10
y
36
− 10y
35
+ ··· − 15y + 1
c
7
, c
8
, c
9
c
11
, c
12
y
36
− 46y
35
+ ··· − 15y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951665 + 0.111092I
a = −0.431237 − 0.863781I
b = −1.016850 + 0.561715I
−7.17502 − 0.39945I −11.42530 − 2.21050I
u = −0.951665 − 0.111092I
a = −0.431237 + 0.863781I
b = −1.016850 − 0.561715I
−7.17502 + 0.39945I −11.42530 + 2.21050I
u = −1.135690 + 0.254702I
a = 0.146387 − 0.970130I
b = 1.133020 + 0.740784I
0.62483 − 2.04170I −10.35918 + 1.70065I
u = −1.135690 − 0.254702I
a = 0.146387 + 0.970130I
b = 1.133020 − 0.740784I
0.62483 + 2.04170I −10.35918 − 1.70065I
u = 1.170730 + 0.165186I
a = −0.146630 − 1.072540I
b = 0.723486 + 1.096980I
0.80642 + 2.95434I −10.23945 − 4.42135I
u = 1.170730 − 0.165186I
a = −0.146630 + 1.072540I
b = 0.723486 − 1.096980I
0.80642 − 2.95434I −10.23945 + 4.42135I
u = 1.093820 + 0.450940I
a = 0.198422 + 1.111360I
b = −0.80338 − 1.18468I
−8.47527 + 5.02113I −12.68797 − 4.01507I
u = 1.093820 − 0.450940I
a = 0.198422 − 1.111360I
b = −0.80338 + 1.18468I
−8.47527 − 5.02113I −12.68797 + 4.01507I
u = −0.124199 + 0.801257I
a = 0.665075 − 0.293846I
b = 0.553901 − 0.383757I
−0.98172 + 1.29447I −8.27671 − 4.94353I
u = −0.124199 − 0.801257I
a = 0.665075 + 0.293846I
b = 0.553901 + 0.383757I
−0.98172 − 1.29447I −8.27671 + 4.94353I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362629 + 0.610597I
a = 2.69945 + 2.81797I
b = 0.262208 − 0.537409I
−10.67130 − 0.80920I −11.8725 − 7.9012I
u = 0.362629 − 0.610597I
a = 2.69945 − 2.81797I
b = 0.262208 + 0.537409I
−10.67130 + 0.80920I −11.8725 + 7.9012I
u = 1.299370 + 0.175302I
a = 0.109102 − 0.984674I
b = −0.711387 + 0.963106I
3.93613 + 0.48813I −8.00000 + 0.I
u = 1.299370 − 0.175302I
a = 0.109102 + 0.984674I
b = −0.711387 − 0.963106I
3.93613 − 0.48813I −8.00000 + 0.I
u = −1.33664
a = −0.884238
b = 0.733489
−5.20604 −20.5790
u = −1.274050 + 0.484036I
a = −0.061622 + 1.057230I
b = −1.131720 − 0.834492I
2.62931 − 6.16336I 0
u = −1.274050 − 0.484036I
a = −0.061622 − 1.057230I
b = −1.131720 + 0.834492I
2.62931 + 6.16336I 0
u = −0.620095
a = −0.352428
b = −1.23303
−7.22329 −9.44110
u = −0.368042 + 1.337050I
a = 0.0916710 + 0.0573874I
b = −0.721465 + 0.368329I
−3.57709 + 3.06628I 0
u = −0.368042 − 1.337050I
a = 0.0916710 − 0.0573874I
b = −0.721465 − 0.368329I
−3.57709 − 3.06628I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38770 + 0.55268I
a = −0.100698 + 0.877700I
b = 0.738741 − 0.854400I
1.86604 + 3.97837I 0
u = 1.38770 − 0.55268I
a = −0.100698 − 0.877700I
b = 0.738741 + 0.854400I
1.86604 − 3.97837I 0
u = −1.32289 + 0.71008I
a = −0.001088 − 1.100240I
b = 1.13619 + 0.89382I
−0.47169 − 10.13360I 0
u = −1.32289 − 0.71008I
a = −0.001088 + 1.100240I
b = 1.13619 − 0.89382I
−0.47169 + 10.13360I 0
u = 0.109684 + 0.468653I
a = −4.34383 − 0.78050I
b = −0.305755 + 0.402075I
−2.47816 − 0.36322I −22.4241 − 7.2894I
u = 0.109684 − 0.468653I
a = −4.34383 + 0.78050I
b = −0.305755 − 0.402075I
−2.47816 + 0.36322I −22.4241 + 7.2894I
u = −0.457715
a = −0.349404
b = 1.88779
−18.9939 0.748010
u = −0.419542
a = 3.94537
b = −0.449274
−2.16435 6.04220
u = −1.35964 + 0.90324I
a = 0.041014 + 1.132360I
b = −1.13264 − 0.93383I
−9.5740 − 12.5541I 0
u = −1.35964 − 0.90324I
a = 0.041014 − 1.132360I
b = −1.13264 + 0.93383I
−9.5740 + 12.5541I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55670 + 0.88459I
a = 0.149365 − 0.795837I
b = −0.795627 + 0.795592I
−6.45728 + 5.83835I 0
u = 1.55670 − 0.88459I
a = 0.149365 + 0.795837I
b = −0.795627 − 0.795592I
−6.45728 − 5.83835I 0
u = −1.82632
a = 0.746253
b = −0.820048
−14.0797 0
u = −0.53066 + 1.74778I
a = −0.267774 + 0.061830I
b = 0.804398 − 0.366712I
−12.28810 + 3.87987I 0
u = −0.53066 − 1.74778I
a = −0.267774 − 0.061830I
b = 0.804398 + 0.366712I
−12.28810 − 3.87987I 0
u = −0.167275
a = 2.39925
b = 0.414843
−0.738035 −13.3280
8
II. I
v
1
= ha, −2v
2
+ b − 11v − 5, v
3
+ 6v
2
+ 5v + 1i
(i) Arc colorings
a
3
=
v
0
a
6
=
1
0
a
7
=
1
0
a
11
=
0
2v
2
+ 11v + 5
a
8
=
1
v
2
+ 6v + 5
a
12
=
−2v
2
− 11v − 5
−3v
2
− 17v − 9
a
10
=
2v
2
+ 11v + 5
2v
2
+ 11v + 5
a
5
=
−v
2
− 6v − 4
−v
2
− 6v − 5
a
2
=
v
2
+ 7v + 4
v
2
+ 6v + 5
a
1
=
v
2
+ 6v + 4
v
2
+ 6v + 5
a
4
=
v
0
a
9
=
−v
2
− 6v − 4
−3v
2
− 17v − 9
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6v
2
− 29v − 37
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
, c
7
, c
8
c
9
u
3
− u
2
− 2u + 1
c
10
, c
11
, c
12
u
3
+ u
2
− 2u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
6
y
3
c
5
, c
7
, c
8
c
9
, c
10
, c
11
c
12
y
3
− 5y
2
+ 6y − 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.643104
a = 0
b = −1.24698
−7.98968 −20.8310
v = −0.307979
a = 0
b = 1.80194
−19.2692 −28.6380
v = −5.04892
a = 0
b = 0.445042
−2.34991 −43.5310
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
36
+ 16u
35
+ ··· + 1288u + 1)
c
2
((u − 1)
3
)(u
36
− 4u
35
+ ··· + 40u − 1)
c
3
, c
6
u
3
(u
36
+ 5u
35
+ ··· + 100u + 8)
c
4
((u + 1)
3
)(u
36
− 4u
35
+ ··· + 40u − 1)
c
5
(u
3
− u
2
− 2u + 1)(u
36
− 2u
35
+ ··· + u − 1)
c
7
, c
8
, c
9
(u
3
− u
2
− 2u + 1)(u
36
+ 2u
35
+ ··· + 7u + 1)
c
10
(u
3
+ u
2
− 2u − 1)(u
36
− 2u
35
+ ··· + u − 1)
c
11
, c
12
(u
3
+ u
2
− 2u − 1)(u
36
+ 2u
35
+ ··· + 7u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
3
)(y
36
+ 12y
35
+ ··· − 1626228y + 1)
c
2
, c
4
((y − 1)
3
)(y
36
− 16y
35
+ ··· − 1288y + 1)
c
3
, c
6
y
3
(y
36
− 21y
35
+ ··· − 2896y + 64)
c
5
, c
10
(y
3
− 5y
2
+ 6y − 1)(y
36
− 10y
35
+ ··· − 15y + 1)
c
7
, c
8
, c
9
c
11
, c
12
(y
3
− 5y
2
+ 6y − 1)(y
36
− 46y
35
+ ··· − 15y + 1)
14
