11a
105
(K11a
105
)
A knot diagram
1
Linearized knot diagam
5 1 8 7 2 10 3 4 11 6 9
Solving Sequence
4,9
8
1,3
2 7 5 11 10 6
c
8
c
3
c
2
c
7
c
4
c
11
c
9
c
6
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.12515 × 10
31
u
59
+ 2.85842 × 10
31
u
58
+ ··· + 3.51410 × 10
31
b + 1.89741 × 10
31
,
− 3.51793 × 10
30
u
59
− 1.13761 × 10
31
u
58
+ ··· + 3.51410 × 10
31
a − 1.05909 × 10
32
, u
60
+ u
59
+ ··· − 4u − 4i
I
u
2
= h2b + 2a + u, 2a
2
+ 2au + 2a + u + 3, u
2
− 2i
I
v
1
= ha, b − v −1, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 66 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
= h1.13×10
31
u
59
+2.86×10
31
u
58
+· · ·+3.51×10
31
b+1.90×10
31
, −3.52×
10
30
u
59
−1.14×10
31
u
58
+· · ·+3.51×10
31
a−1.06×10
32
, u
60
+u
59
+· · ·−4u−4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
−u
2
a
1
=
0.100109u
59
+ 0.323727u
58
+ ··· + 6.24684u + 3.01381
−0.320182u
59
− 0.813414u
58
+ ··· + 3.67561u − 0.539941
a
3
=
u
−u
3
+ u
a
2
=
0.334020u
59
+ 0.230566u
58
+ ··· + 9.56791u + 3.49275
−0.161128u
59
− 0.574931u
58
+ ··· + 3.42064u − 0.184944
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−0.220073u
59
− 0.489687u
58
+ ··· + 9.92245u + 2.47387
−0.320182u
59
− 0.813414u
58
+ ··· + 3.67561u − 0.539941
a
10
=
1.05972u
59
− 0.120964u
58
+ ··· − 11.8926u − 2.73515
0.550795u
59
+ 1.41033u
58
+ ··· − 3.83041u + 0.910068
a
6
=
−0.301975u
59
− 0.154593u
58
+ ··· − 8.20559u − 4.09227
0.609330u
59
+ 0.192047u
58
+ ··· + 2.33523u − 2.20792
a
6
=
−0.301975u
59
− 0.154593u
58
+ ··· − 8.20559u − 4.09227
0.609330u
59
+ 0.192047u
58
+ ··· + 2.33523u − 2.20792
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.29031u
59
+ 4.98190u
58
+ ··· + 10.5616u + 3.04276
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
60
+ 3u
59
+ ··· − 21u − 7
c
2
u
60
+ 29u
59
+ ··· + 259u + 49
c
3
, c
7
, c
8
u
60
+ u
59
+ ··· − 4u − 4
c
4
u
60
− 3u
59
+ ··· + 1892u + 748
c
6
, c
10
u
60
− 2u
59
+ ··· + 10u + 1
c
9
, c
11
u
60
+ 20u
59
+ ··· − 58u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
60
− 29y
59
+ ··· − 259y + 49
c
2
y
60
+ 11y
59
+ ··· − 38171y + 2401
c
3
, c
7
, c
8
y
60
− 55y
59
+ ··· + 144y + 16
c
4
y
60
+ 5y
59
+ ··· − 713328y + 559504
c
6
, c
10
y
60
+ 20y
59
+ ··· − 58y + 1
c
9
, c
11
y
60
+ 44y
59
+ ··· − 3138y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856412 + 0.448917I
a = 0.069748 − 0.309881I
b = 0.045178 + 1.220370I
2.51877 − 0.25684I −5.58857 − 0.91280I
u = −0.856412 − 0.448917I
a = 0.069748 + 0.309881I
b = 0.045178 − 1.220370I
2.51877 + 0.25684I −5.58857 + 0.91280I
u = −0.977737 + 0.387234I
a = −0.646202 + 0.329883I
b = −0.199913 − 1.371860I
2.99290 − 0.67802I −7.00000 + 0.I
u = −0.977737 − 0.387234I
a = −0.646202 − 0.329883I
b = −0.199913 + 1.371860I
2.99290 + 0.67802I −7.00000 + 0.I
u = 0.791019 + 0.508592I
a = −0.325990 − 0.504077I
b = −0.39274 + 1.43077I
1.89650 + 6.03755I −6.88192 − 4.20349I
u = 0.791019 − 0.508592I
a = −0.325990 + 0.504077I
b = −0.39274 − 1.43077I
1.89650 − 6.03755I −6.88192 + 4.20349I
u = 1.068800 + 0.379471I
a = 0.494885 + 0.197200I
b = −0.116006 − 1.361990I
3.09128 − 5.18590I 0
u = 1.068800 − 0.379471I
a = 0.494885 − 0.197200I
b = −0.116006 + 1.361990I
3.09128 + 5.18590I 0
u = 0.301071 + 0.803639I
a = 1.174960 − 0.782603I
b = −0.48181 − 1.50728I
3.49971 − 10.62980I −5.43356 + 8.51745I
u = 0.301071 − 0.803639I
a = 1.174960 + 0.782603I
b = −0.48181 + 1.50728I
3.49971 + 10.62980I −5.43356 − 8.51745I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.256488 + 0.801752I
a = −1.204450 − 0.589990I
b = 0.206818 − 1.186610I
4.44819 + 4.71708I −3.57538 − 3.65619I
u = −0.256488 − 0.801752I
a = −1.204450 + 0.589990I
b = 0.206818 + 1.186610I
4.44819 − 4.71708I −3.57538 + 3.65619I
u = −0.189775 + 0.793215I
a = 0.692391 + 1.041360I
b = −0.34795 + 1.45648I
5.43709 + 4.96254I −2.32735 − 3.96471I
u = −0.189775 − 0.793215I
a = 0.692391 − 1.041360I
b = −0.34795 − 1.45648I
5.43709 − 4.96254I −2.32735 + 3.96471I
u = 0.129554 + 0.796054I
a = −0.844160 + 0.874550I
b = 0.043508 + 1.278600I
5.97615 + 0.93056I −1.28101 − 1.70769I
u = 0.129554 − 0.796054I
a = −0.844160 − 0.874550I
b = 0.043508 − 1.278600I
5.97615 − 0.93056I −1.28101 + 1.70769I
u = −1.206730 + 0.176348I
a = −1.133230 − 0.267587I
b = 0.418519 + 0.150611I
−1.73220 + 0.82680I 0
u = −1.206730 − 0.176348I
a = −1.133230 + 0.267587I
b = 0.418519 − 0.150611I
−1.73220 − 0.82680I 0
u = 1.243970 + 0.018853I
a = 1.26750 − 0.88605I
b = −0.868501 + 0.830940I
−4.34425 + 2.84333I 0
u = 1.243970 − 0.018853I
a = 1.26750 + 0.88605I
b = −0.868501 − 0.830940I
−4.34425 − 2.84333I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.268078 + 0.645087I
a = 0.627642 − 0.518062I
b = −1.102390 − 0.396751I
−2.44529 − 4.90792I −9.88732 + 7.39777I
u = 0.268078 − 0.645087I
a = 0.627642 + 0.518062I
b = −1.102390 + 0.396751I
−2.44529 + 4.90792I −9.88732 − 7.39777I
u = 1.289880 + 0.180120I
a = −1.66882 + 0.29795I
b = −0.038165 + 1.051040I
−4.50001 − 0.00587I 0
u = 1.289880 − 0.180120I
a = −1.66882 − 0.29795I
b = −0.038165 − 1.051040I
−4.50001 + 0.00587I 0
u = −0.112152 + 0.661191I
a = −0.714620 − 0.045202I
b = 0.426053 + 0.174796I
1.43580 + 2.21650I −1.82720 − 4.33305I
u = −0.112152 − 0.661191I
a = −0.714620 + 0.045202I
b = 0.426053 − 0.174796I
1.43580 − 2.21650I −1.82720 + 4.33305I
u = −1.334650 + 0.196412I
a = 1.04014 + 1.40007I
b = −0.877556 − 1.103860I
−5.48660 + 1.01058I 0
u = −1.334650 − 0.196412I
a = 1.04014 − 1.40007I
b = −0.877556 + 1.103860I
−5.48660 − 1.01058I 0
u = −1.333660 + 0.221254I
a = 1.82839 + 0.49243I
b = −0.448347 + 1.321910I
−5.17207 + 5.38877I 0
u = −1.333660 − 0.221254I
a = 1.82839 − 0.49243I
b = −0.448347 − 1.321910I
−5.17207 − 5.38877I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.331350 + 0.263582I
a = −1.077490 + 0.564419I
b = 0.496619 − 0.385771I
−3.10541 − 5.57944I 0
u = 1.331350 − 0.263582I
a = −1.077490 − 0.564419I
b = 0.496619 + 0.385771I
−3.10541 + 5.57944I 0
u = 1.352790 + 0.191832I
a = 1.57075 − 0.21221I
b = −1.044160 − 0.411993I
−5.42970 − 3.53470I 0
u = 1.352790 − 0.191832I
a = 1.57075 + 0.21221I
b = −1.044160 + 0.411993I
−5.42970 + 3.53470I 0
u = −1.334670 + 0.330501I
a = −1.55791 + 0.32540I
b = 0.175954 − 1.190020I
1.38298 + 3.12184I 0
u = −1.334670 − 0.330501I
a = −1.55791 − 0.32540I
b = 0.175954 + 1.190020I
1.38298 − 3.12184I 0
u = 0.461911 + 0.406202I
a = 0.28123 − 1.64366I
b = −0.821473 + 0.229272I
−3.41083 + 1.56394I −13.77106 − 0.02572I
u = 0.461911 − 0.406202I
a = 0.28123 + 1.64366I
b = −0.821473 − 0.229272I
−3.41083 − 1.56394I −13.77106 + 0.02572I
u = 1.38882
a = −0.894922
b = 0.0181684
−6.53287 0
u = 1.373810 + 0.327896I
a = 1.74591 + 0.30759I
b = −0.46361 − 1.49242I
0.49565 − 9.00597I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.373810 − 0.327896I
a = 1.74591 − 0.30759I
b = −0.46361 + 1.49242I
0.49565 + 9.00597I 0
u = −1.40111 + 0.26118I
a = 1.94947 + 0.43052I
b = −1.259340 + 0.325492I
−7.75888 + 8.23897I 0
u = −1.40111 − 0.26118I
a = 1.94947 − 0.43052I
b = −1.259340 − 0.325492I
−7.75888 − 8.23897I 0
u = 0.071840 + 0.552974I
a = 0.01528 − 3.02987I
b = −0.330288 − 1.143560I
−0.69378 − 2.54574I −3.93469 + 4.38996I
u = 0.071840 − 0.552974I
a = 0.01528 + 3.02987I
b = −0.330288 + 1.143560I
−0.69378 + 2.54574I −3.93469 − 4.38996I
u = −1.43987 + 0.14560I
a = 1.24613 + 0.98490I
b = −0.917886 + 0.053868I
−9.46417 + 0.48874I 0
u = −1.43987 − 0.14560I
a = 1.24613 − 0.98490I
b = −0.917886 − 0.053868I
−9.46417 − 0.48874I 0
u = 1.41119 + 0.32817I
a = −1.73533 − 0.42501I
b = 0.304129 + 1.125510I
−0.85298 − 8.80531I 0
u = 1.41119 − 0.32817I
a = −1.73533 + 0.42501I
b = 0.304129 − 1.125510I
−0.85298 + 8.80531I 0
u = −1.43461 + 0.32355I
a = 2.01968 − 0.51742I
b = −0.55973 + 1.52348I
−2.0394 + 14.7170I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43461 − 0.32355I
a = 2.01968 + 0.51742I
b = −0.55973 − 1.52348I
−2.0394 − 14.7170I 0
u = −0.263721 + 0.414290I
a = −0.089083 + 0.498277I
b = −0.547343 + 0.345848I
−0.480323 + 1.226230I −5.70379 − 5.33805I
u = −0.263721 − 0.414290I
a = −0.089083 − 0.498277I
b = −0.547343 − 0.345848I
−0.480323 − 1.226230I −5.70379 + 5.33805I
u = 1.51224 + 0.04246I
a = −0.021792 + 1.121390I
b = −0.159960 − 1.012480I
−5.24444 − 0.82507I 0
u = 1.51224 − 0.04246I
a = −0.021792 − 1.121390I
b = −0.159960 + 1.012480I
−5.24444 + 0.82507I 0
u = 0.085208 + 0.469629I
a = 0.229268 − 0.034778I
b = −0.760151 + 0.894401I
−0.97414 + 1.49816I −3.90867 + 1.16289I
u = 0.085208 − 0.469629I
a = 0.229268 + 0.034778I
b = −0.760151 − 0.894401I
−0.97414 − 1.49816I −3.90867 − 1.16289I
u = −1.52569 + 0.08141I
a = 0.37288 + 1.45493I
b = −0.438151 − 1.250040I
−5.76976 − 4.33338I 0
u = −1.52569 − 0.08141I
a = 0.37288 − 1.45493I
b = −0.438151 + 1.250040I
−5.76976 + 4.33338I 0
u = −0.439722
a = −1.31943
b = 0.0992099
−0.965483 −10.6880
10
II. I
u
2
= h2b + 2a + u, 2a
2
+ 2au + 2a + u + 3, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
−2
a
1
=
a
−a −
1
2
u
a
3
=
u
−u
a
2
=
a + u
−a −
3
2
u
a
7
=
−1
0
a
5
=
−u
u
a
11
=
−
1
2
u
−a −
1
2
u
a
10
=
1
2
au +
3
2
−a −
1
2
u − 1
a
6
=
a
−a −
1
2
u
a
6
=
a
−a −
1
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 2u − 16
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
− 2)
2
c
5
(u − 1)
4
c
6
, c
9
(u
2
− u + 1)
2
c
10
, c
11
(u
2
+ u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y −2)
4
c
6
, c
9
, c
10
c
11
(y
2
+ y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −1.20711 + 0.86603I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = 1.41421
a = −1.20711 − 0.86603I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −14.0000 + 3.4641I
u = −1.41421
a = 0.207107 + 0.866025I
b = 0.500000 − 0.866025I
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = 0.207107 − 0.866025I
b = 0.500000 + 0.866025I
−6.57974 − 2.02988I −14.0000 + 3.4641I
14
III. I
v
1
= ha, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
8
=
1
0
a
1
=
0
v + 1
a
3
=
v
0
a
2
=
v
v + 1
a
7
=
1
0
a
5
=
v
0
a
11
=
v + 1
v + 1
a
10
=
v + 1
v
a
6
=
0
−v − 1
a
6
=
0
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 10
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
6
, c
11
u
2
+ u + 1
c
9
, c
10
u
2
− u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
y
2
+ y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
−1.64493 − 2.02988I −12.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
−1.64493 + 2.02988I −12.00000 − 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u + 1)
4
(u
60
+ 3u
59
+ ··· − 21u − 7)
c
2
((u + 1)
6
)(u
60
+ 29u
59
+ ··· + 259u + 49)
c
3
, c
7
, c
8
u
2
(u
2
− 2)
2
(u
60
+ u
59
+ ··· − 4u − 4)
c
4
u
2
(u
2
− 2)
2
(u
60
− 3u
59
+ ··· + 1892u + 748)
c
5
((u − 1)
4
)(u + 1)
2
(u
60
+ 3u
59
+ ··· − 21u − 7)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
60
− 2u
59
+ ··· + 10u + 1)
c
9
((u
2
− u + 1)
3
)(u
60
+ 20u
59
+ ··· − 58u + 1)
c
10
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
60
− 2u
59
+ ··· + 10u + 1)
c
11
((u
2
+ u + 1)
3
)(u
60
+ 20u
59
+ ··· − 58u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y − 1)
6
)(y
60
− 29y
59
+ ··· − 259y + 49)
c
2
((y − 1)
6
)(y
60
+ 11y
59
+ ··· − 38171y + 2401)
c
3
, c
7
, c
8
y
2
(y − 2)
4
(y
60
− 55y
59
+ ··· + 144y + 16)
c
4
y
2
(y − 2)
4
(y
60
+ 5y
59
+ ··· − 713328y + 559504)
c
6
, c
10
((y
2
+ y + 1)
3
)(y
60
+ 20y
59
+ ··· − 58y + 1)
c
9
, c
11
((y
2
+ y + 1)
3
)(y
60
+ 44y
59
+ ··· − 3138y + 1)
20
