11a
18
(K11a
18
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 9 3 11 5 8 7 10
Solving Sequence
7,11 3,8
6 4 10 1 2 9 5
c
7
c
6
c
3
c
10
c
11
c
2
c
9
c
5
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.02368 × 10
22
u
71
+ 1.11016 × 10
23
u
70
+ ··· + 1.88857 × 10
22
b 6.09914 × 10
22
,
4.07828 × 10
22
u
71
1.25681 × 10
23
u
70
+ ··· + 3.77714 × 10
22
a + 1.39984 × 10
23
, u
72
5u
71
+ ··· + 12u 1i
I
u
2
= hb, u
3
u
2
+ a + 1, u
6
u
5
u
4
+ 2u
3
u + 1i
I
u
3
= ha
2
+ 5b + 3a + 5, a
3
+ a
2
+ 4a + 5, u + 1i
* 3 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
= h−2.02 × 10
22
u
71
+ 1.11 × 10
23
u
70
+ · · · + 1.89 × 10
22
b 6.10 ×
10
22
, 4.08 × 10
22
u
71
1.26 × 10
23
u
70
+ · · · + 3.78 × 10
22
a + 1.40 ×
10
23
, u
72
5u
71
+ · · · + 12u 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
1.07973u
71
+ 3.32742u
70
+ ··· + 8.79814u 3.70610
1.07154u
71
5.87833u
70
+ ··· 27.8922u + 3.22950
a
8
=
1
u
2
a
6
=
7.15660u
71
30.9077u
70
+ ··· 110.914u + 13.1587
3.05252u
71
+ 13.6578u
70
+ ··· + 48.6687u 4.93370
a
4
=
8.96090u
71
+ 37.1749u
70
+ ··· + 124.175u 16.1656
6.60610u
71
29.5950u
70
+ ··· 105.720u + 10.6845
a
10
=
u
u
a
1
=
u
3
u
3
+ u
a
2
=
1.44106u
71
+ 6.20595u
70
+ ··· + 24.5011u 5.21118
0.925198u
71
+ 1.52843u
70
+ ··· 9.87376u + 1.65560
a
9
=
u
3
u
5
u
3
+ u
a
5
=
6.74498u
71
26.4676u
70
+ ··· 87.3523u + 10.9648
6.68660u
71
+ 26.6048u
70
+ ··· + 77.8117u 7.58573
a
5
=
6.74498u
71
26.4676u
70
+ ··· 87.3523u + 10.9648
6.68660u
71
+ 26.6048u
70
+ ··· + 77.8117u 7.58573
(ii) Obstruction class = 1
(iii) Cusp Shapes =
76710752927736823653759
9442837768770389262581
u
71
+
509177888669513108789191
18885675537540778525162
u
70
+ ··· +
316804939896701446179690
9442837768770389262581
u
245852902489482612469787
18885675537540778525162
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
72
8u
71
+ ··· 12u + 1
c
2
u
72
+ 32u
71
+ ··· 8u + 1
c
3
, c
6
u
72
2u
71
+ ··· + 128u 64
c
5
, c
8
u
72
+ 2u
71
+ ··· + 20u + 8
c
7
, c
10
u
72
+ 5u
71
+ ··· 12u 1
c
9
u
72
+ 24u
71
+ ··· + 1872u + 64
c
11
u
72
39u
71
+ ··· 52u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
72
32y
71
+ ··· + 8y + 1
c
2
y
72
+ 24y
71
+ ··· + 2568y + 1
c
3
, c
6
y
72
+ 42y
71
+ ··· + 73728y + 4096
c
5
, c
8
y
72
24y
71
+ ··· 1872y + 64
c
7
, c
10
y
72
39y
71
+ ··· 52y + 1
c
9
y
72
+ 44y
71
+ ··· 601344y + 4096
c
11
y
72
7y
71
+ ··· 2176y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.876128 + 0.485866I
a = 1.020580 0.525723I
b = 0.151401 0.941501I
1.78878 + 0.06007I 0
u = 0.876128 0.485866I
a = 1.020580 + 0.525723I
b = 0.151401 + 0.941501I
1.78878 0.06007I 0
u = 0.642602 + 0.759427I
a = 0.004406 0.268942I
b = 0.468956 0.932444I
3.84415 3.26268I 0
u = 0.642602 0.759427I
a = 0.004406 + 0.268942I
b = 0.468956 + 0.932444I
3.84415 + 3.26268I 0
u = 0.809332 + 0.576281I
a = 0.308570 + 0.160474I
b = 0.794967 0.622629I
4.30882 + 3.51764I 0
u = 0.809332 0.576281I
a = 0.308570 0.160474I
b = 0.794967 + 0.622629I
4.30882 3.51764I 0
u = 0.951216 + 0.225981I
a = 0.764228 + 0.449018I
b = 0.173093 0.363920I
1.73034 0.74165I 0
u = 0.951216 0.225981I
a = 0.764228 0.449018I
b = 0.173093 + 0.363920I
1.73034 + 0.74165I 0
u = 1.05211
a = 2.54516
b = 0.432247
0.330921 46.0800
u = 0.914907 + 0.540239I
a = 0.652730 + 1.039110I
b = 0.571615 0.771611I
0.63477 + 4.40212I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.914907 0.540239I
a = 0.652730 1.039110I
b = 0.571615 + 0.771611I
0.63477 4.40212I 0
u = 0.729237 + 0.575747I
a = 1.30537 1.48267I
b = 0.617113 + 0.726794I
4.53906 + 1.05261I 10.58932 3.82745I
u = 0.729237 0.575747I
a = 1.30537 + 1.48267I
b = 0.617113 0.726794I
4.53906 1.05261I 10.58932 + 3.82745I
u = 0.199115 + 0.897753I
a = 0.610450 + 0.607154I
b = 0.64956 1.25765I
1.48181 10.73100I 6.00773 + 7.14911I
u = 0.199115 0.897753I
a = 0.610450 0.607154I
b = 0.64956 + 1.25765I
1.48181 + 10.73100I 6.00773 7.14911I
u = 0.453294 + 0.792285I
a = 0.230638 + 0.142154I
b = 0.207389 + 0.782148I
2.85223 + 0.05705I 5.94816 3.77217I
u = 0.453294 0.792285I
a = 0.230638 0.142154I
b = 0.207389 0.782148I
2.85223 0.05705I 5.94816 + 3.77217I
u = 0.151325 + 0.858429I
a = 0.338744 0.734808I
b = 0.435835 + 1.280920I
3.59461 4.95936I 3.13446 + 3.17768I
u = 0.151325 0.858429I
a = 0.338744 + 0.734808I
b = 0.435835 1.280920I
3.59461 + 4.95936I 3.13446 3.17768I
u = 0.686903 + 0.514666I
a = 1.257030 + 0.541255I
b = 0.337786 + 1.041550I
1.23521 4.19775I 3.49766 + 6.68711I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.686903 0.514666I
a = 1.257030 0.541255I
b = 0.337786 1.041550I
1.23521 + 4.19775I 3.49766 6.68711I
u = 0.921196 + 0.680248I
a = 1.079360 0.688931I
b = 0.563006 + 1.013540I
3.02672 + 8.64627I 0
u = 0.921196 0.680248I
a = 1.079360 + 0.688931I
b = 0.563006 1.013540I
3.02672 8.64627I 0
u = 0.190668 + 0.789710I
a = 0.539342 0.183142I
b = 1.048020 + 0.360828I
1.37174 4.55999I 7.56588 + 4.82929I
u = 0.190668 0.789710I
a = 0.539342 + 0.183142I
b = 1.048020 0.360828I
1.37174 + 4.55999I 7.56588 4.82929I
u = 0.803990 + 0.062025I
a = 0.01110 + 2.46502I
b = 0.188498 1.395620I
4.16423 + 3.00649I 10.90678 5.59644I
u = 0.803990 0.062025I
a = 0.01110 2.46502I
b = 0.188498 + 1.395620I
4.16423 3.00649I 10.90678 + 5.59644I
u = 1.135490 + 0.370936I
a = 1.07671 2.69128I
b = 0.062046 + 0.875399I
1.26979 1.25057I 0
u = 1.135490 0.370936I
a = 1.07671 + 2.69128I
b = 0.062046 0.875399I
1.26979 + 1.25057I 0
u = 1.148040 + 0.380216I
a = 0.70878 1.85544I
b = 0.49043 + 1.40149I
6.72982 1.38866I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.148040 0.380216I
a = 0.70878 + 1.85544I
b = 0.49043 1.40149I
6.72982 + 1.38866I 0
u = 1.142140 + 0.425738I
a = 0.562710 0.941454I
b = 1.037880 0.268094I
2.61393 3.52046I 0
u = 1.142140 0.425738I
a = 0.562710 + 0.941454I
b = 1.037880 + 0.268094I
2.61393 + 3.52046I 0
u = 0.588819 + 0.498548I
a = 0.1316140 + 0.0334840I
b = 0.661202 + 0.427658I
1.57298 0.11426I 7.05869 + 0.49031I
u = 0.588819 0.498548I
a = 0.1316140 0.0334840I
b = 0.661202 0.427658I
1.57298 + 0.11426I 7.05869 0.49031I
u = 1.074870 + 0.603822I
a = 0.597690 + 0.112026I
b = 0.123079 0.683210I
1.00613 + 5.17017I 0
u = 1.074870 0.603822I
a = 0.597690 0.112026I
b = 0.123079 + 0.683210I
1.00613 5.17017I 0
u = 1.191930 + 0.342239I
a = 0.358281 + 1.074510I
b = 1.013040 0.196707I
2.80142 + 0.88223I 0
u = 1.191930 0.342239I
a = 0.358281 1.074510I
b = 1.013040 + 0.196707I
2.80142 0.88223I 0
u = 1.144240 + 0.478405I
a = 0.536141 + 0.780473I
b = 1.126790 0.035537I
2.23267 + 4.45748I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.144240 0.478405I
a = 0.536141 0.780473I
b = 1.126790 + 0.035537I
2.23267 4.45748I 0
u = 1.176730 + 0.425158I
a = 0.78375 + 2.01694I
b = 0.21774 1.44325I
8.03882 + 4.81398I 0
u = 1.176730 0.425158I
a = 0.78375 2.01694I
b = 0.21774 + 1.44325I
8.03882 4.81398I 0
u = 0.209029 + 0.716378I
a = 0.26407 + 1.66791I
b = 0.225033 0.897395I
2.48615 2.12650I 6.43169 + 3.64338I
u = 0.209029 0.716378I
a = 0.26407 1.66791I
b = 0.225033 + 0.897395I
2.48615 + 2.12650I 6.43169 3.64338I
u = 1.153340 + 0.507415I
a = 1.60055 2.01202I
b = 0.60825 + 1.28103I
5.82177 9.49602I 0
u = 1.153340 0.507415I
a = 1.60055 + 2.01202I
b = 0.60825 1.28103I
5.82177 + 9.49602I 0
u = 1.152310 + 0.513166I
a = 0.96387 2.44235I
b = 0.189978 + 1.047730I
0.24731 + 6.78521I 0
u = 1.152310 0.513166I
a = 0.96387 + 2.44235I
b = 0.189978 1.047730I
0.24731 6.78521I 0
u = 1.261390 + 0.058100I
a = 0.01557 + 1.46315I
b = 0.223456 1.041190I
3.01523 2.24466I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.261390 0.058100I
a = 0.01557 1.46315I
b = 0.223456 + 1.041190I
3.01523 + 2.24466I 0
u = 0.064161 + 0.732453I
a = 0.767662 0.651334I
b = 0.235839 + 1.293170I
4.51528 0.75882I 2.00847 + 2.21103I
u = 0.064161 0.732453I
a = 0.767662 + 0.651334I
b = 0.235839 1.293170I
4.51528 + 0.75882I 2.00847 2.21103I
u = 1.179000 + 0.470286I
a = 1.43630 + 2.06463I
b = 0.372085 1.312220I
7.71847 3.66806I 0
u = 1.179000 0.470286I
a = 1.43630 2.06463I
b = 0.372085 + 1.312220I
7.71847 + 3.66806I 0
u = 0.184930 + 0.702974I
a = 1.142920 + 0.364325I
b = 0.511874 1.258740I
3.04313 + 4.90017I 4.09415 2.80236I
u = 0.184930 0.702974I
a = 1.142920 0.364325I
b = 0.511874 + 1.258740I
3.04313 4.90017I 4.09415 + 2.80236I
u = 1.175940 + 0.526545I
a = 0.711909 0.601787I
b = 1.150070 0.355611I
1.52562 + 9.43889I 0
u = 1.175940 0.526545I
a = 0.711909 + 0.601787I
b = 1.150070 + 0.355611I
1.52562 9.43889I 0
u = 0.696737 + 0.142085I
a = 2.57175 + 0.05432I
b = 0.517031 0.372132I
0.802882 0.774259I 7.90864 1.29464I
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.696737 0.142085I
a = 2.57175 0.05432I
b = 0.517031 + 0.372132I
0.802882 + 0.774259I 7.90864 + 1.29464I
u = 1.255590 + 0.362909I
a = 0.86019 + 1.86322I
b = 0.319526 1.319120I
7.96250 + 0.80203I 0
u = 1.255590 0.362909I
a = 0.86019 1.86322I
b = 0.319526 + 1.319120I
7.96250 0.80203I 0
u = 1.209240 + 0.530646I
a = 1.09985 + 2.14991I
b = 0.48229 1.35413I
6.75363 + 10.01730I 0
u = 1.209240 0.530646I
a = 1.09985 2.14991I
b = 0.48229 + 1.35413I
6.75363 10.01730I 0
u = 1.284540 + 0.323794I
a = 0.70474 1.66611I
b = 0.570649 + 1.286370I
6.23840 + 6.61734I 0
u = 1.284540 0.323794I
a = 0.70474 + 1.66611I
b = 0.570649 1.286370I
6.23840 6.61734I 0
u = 1.213020 + 0.559420I
a = 1.18093 2.10008I
b = 0.68584 + 1.29855I
4.5389 + 16.0300I 0
u = 1.213020 0.559420I
a = 1.18093 + 2.10008I
b = 0.68584 1.29855I
4.5389 16.0300I 0
u = 0.108198 + 0.607054I
a = 0.456063 + 0.553200I
b = 0.933701 + 0.059450I
0.602714 0.211764I 6.49349 0.29601I
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.108198 0.607054I
a = 0.456063 0.553200I
b = 0.933701 0.059450I
0.602714 + 0.211764I 6.49349 + 0.29601I
u = 0.146855
a = 2.66318
b = 0.617774
0.987420 10.0940
12
II. I
u
2
= hb, u
3
u
2
+ a + 1, u
6
u
5
u
4
+ 2u
3
u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
u
3
+ u
2
1
0
a
8
=
1
u
2
a
6
=
1
0
a
4
=
u
3
+ u
2
1
0
a
10
=
u
u
a
1
=
u
3
u
3
+ u
a
2
=
u
2
1
u
3
+ u
a
9
=
u
3
u
5
u
3
+ u
a
5
=
u
3
u
3
u
a
5
=
u
3
u
3
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
2u
3
+ 3u
2
2u 11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
6
u
6
c
5
, c
10
u
6
+ u
5
u
4
2u
3
+ u + 1
c
7
, c
8
u
6
u
5
u
4
+ 2u
3
u + 1
c
9
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
11
u
6
3u
5
+ 5u
4
4u
3
+ 2u
2
u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y 1)
6
c
3
, c
6
y
6
c
5
, c
7
, c
8
c
10
y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1
c
9
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.66103 1.45708I
b = 0
0.245672 0.924305I 6.22669 0.83820I
u = 1.002190 0.295542I
a = 0.66103 + 1.45708I
b = 0
0.245672 + 0.924305I 6.22669 + 0.83820I
u = 0.428243 + 0.664531I
a = 0.769407 + 0.497010I
b = 0
3.53554 0.92430I 10.88169 + 1.11590I
u = 0.428243 0.664531I
a = 0.769407 0.497010I
b = 0
3.53554 + 0.92430I 10.88169 1.11590I
u = 1.073950 + 0.558752I
a = 0.391622 0.558752I
b = 0
1.64493 + 5.69302I 8.89162 7.09196I
u = 1.073950 0.558752I
a = 0.391622 + 0.558752I
b = 0
1.64493 5.69302I 8.89162 + 7.09196I
16
III. I
u
3
= ha
2
+ 5b + 3a + 5, a
3
+ a
2
+ 4a + 5, u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
1
a
3
=
a
1
5
a
2
3
5
a 1
a
8
=
1
1
a
6
=
2
5
a
2
+
1
5
a
2
5
a
2
1
5
a
a
4
=
1
1
5
a
2
+
2
5
a
a
10
=
1
1
a
1
=
1
0
a
2
=
1
5
a
2
+
2
5
a 1
1
5
a
2
3
5
a 1
a
9
=
1
1
a
5
=
2
5
a
2
+
1
5
a
2
5
a
2
1
5
a
a
5
=
2
5
a
2
+
1
5
a
2
5
a
2
1
5
a
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
5
a
2
+
3
5
a + 5
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
1
c
2
, c
6
u
3
+ u
2
+ 2u + 1
c
3
u
3
u
2
+ 2u 1
c
4
u
3
u
2
+ 1
c
5
, c
8
, c
9
u
3
c
7
(u + 1)
3
c
10
, c
11
(u 1)
3
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
y
2
+ 2y 1
c
2
, c
3
, c
6
y
3
+ 3y
2
+ 2y 1
c
5
, c
8
, c
9
y
3
c
7
, c
10
, c
11
(y 1)
3
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.18504
b = 0.569840
0.531480 4.56980
u = 1.00000
a = 0.09252 + 2.05200I
b = 0.215080 1.307140I
4.66906 2.82812I 4.21508 + 1.30714I
u = 1.00000
a = 0.09252 2.05200I
b = 0.215080 + 1.307140I
4.66906 + 2.82812I 4.21508 1.30714I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u 1)
6
)(u
3
+ u
2
1)(u
72
8u
71
+ ··· 12u + 1)
c
2
((u + 1)
6
)(u
3
+ u
2
+ 2u + 1)(u
72
+ 32u
71
+ ··· 8u + 1)
c
3
u
6
(u
3
u
2
+ 2u 1)(u
72
2u
71
+ ··· + 128u 64)
c
4
((u + 1)
6
)(u
3
u
2
+ 1)(u
72
8u
71
+ ··· 12u + 1)
c
5
u
3
(u
6
+ u
5
+ ··· + u + 1)(u
72
+ 2u
71
+ ··· + 20u + 8)
c
6
u
6
(u
3
+ u
2
+ 2u + 1)(u
72
2u
71
+ ··· + 128u 64)
c
7
((u + 1)
3
)(u
6
u
5
+ ··· u + 1)(u
72
+ 5u
71
+ ··· 12u 1)
c
8
u
3
(u
6
u
5
+ ··· u + 1)(u
72
+ 2u
71
+ ··· + 20u + 8)
c
9
u
3
(u
6
+ 3u
5
+ ··· + u + 1)(u
72
+ 24u
71
+ ··· + 1872u + 64)
c
10
((u 1)
3
)(u
6
+ u
5
+ ··· + u + 1)(u
72
+ 5u
71
+ ··· 12u 1)
c
11
(u 1)
3
(u
6
3u
5
+ 5u
4
4u
3
+ 2u
2
u + 1)
· (u
72
39u
71
+ ··· 52u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y 1)
6
)(y
3
y
2
+ 2y 1)(y
72
32y
71
+ ··· + 8y + 1)
c
2
((y 1)
6
)(y
3
+ 3y
2
+ 2y 1)(y
72
+ 24y
71
+ ··· + 2568y + 1)
c
3
, c
6
y
6
(y
3
+ 3y
2
+ 2y 1)(y
72
+ 42y
71
+ ··· + 73728y + 4096)
c
5
, c
8
y
3
(y
6
3y
5
+ ··· y + 1)(y
72
24y
71
+ ··· 1872y + 64)
c
7
, c
10
(y 1)
3
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
· (y
72
39y
71
+ ··· 52y + 1)
c
9
y
3
(y
6
+ y
5
+ ··· + 3y + 1)(y
72
+ 44y
71
+ ··· 601344y + 4096)
c
11
((y 1)
3
)(y
6
+ y
5
+ ··· + 3y + 1)(y
72
7y
71
+ ··· 2176y + 1)
22