11n
66
(K11n
66
)
A knot diagram
1
Linearized knot diagam
4 1 9 2 10 9 11 3 6 8 10
Solving Sequence
3,8
9
4,11
7 6 10 1 2 5
c
8
c
3
c
7
c
6
c
10
c
11
c
2
c
4
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4750254357724u
19
+ 14627504028936u
18
+ ··· + 23633551708361b − 81147234294199,
− 74233627976373u
19
− 270771524553115u
18
+ ··· + 378136827333776a + 1442548033804746,
u
20
+ 3u
19
+ ··· − 6u + 8i
I
u
2
= hu
2
a + b + 1, −2u
10
a − 6u
11
+ ··· + a − 2,
u
12
− u
11
− u
10
+ 2u
9
+ 3u
8
− 4u
7
− 2u
6
+ 4u
5
+ 2u
4
− 3u
3
− u
2
+ 1i
I
u
3
= h−u
5
+ 2u
3
+ b − u, −u
4
+ 2u
3
+ 3u
2
+ a − 3u − 2, u
6
− 3u
4
+ 2u
2
+ 1i
I
v
1
= ha, b − 1, 2v + 1i
* 4 irreducible components of dim
C
= 0, with total 51 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
= h4.75×10
12
u
19
+1.46×10
13
u
18
+· · ·+2.36×10
13
b−8.11×10
13
, −7.42×
10
13
u
19
−2.71×10
14
u
18
+· · ·+3.78×10
14
a+1.44×10
15
, u
20
+3u
19
+· · ·−6u+8i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
11
=
0.196314u
19
+ 0.716068u
18
+ ··· − 3.73611u − 3.81488
−0.200996u
19
− 0.618930u
18
+ ··· + 3.09511u + 3.43356
a
7
=
−0.00468201u
19
+ 0.0971380u
18
+ ··· − 0.640997u − 0.381323
0.238201u
19
+ 0.712561u
18
+ ··· − 3.79968u − 2.54409
a
6
=
0.196314u
19
+ 0.716068u
18
+ ··· − 3.73611u − 3.81488
0.107586u
19
+ 0.364861u
18
+ ··· − 2.28735u − 2.41656
a
10
=
−0.00468201u
19
+ 0.0971380u
18
+ ··· − 0.640997u − 0.381323
−0.200996u
19
− 0.618930u
18
+ ··· + 3.09511u + 3.43356
a
1
=
−0.0380706u
19
+ 0.0221177u
18
+ ··· − 0.0686952u − 0.889509
−0.467904u
19
− 1.50365u
18
+ ··· + 8.10809u + 6.85079
a
2
=
0.0279992u
19
+ 0.365360u
18
+ ··· − 2.48168u − 2.62009
−0.344443u
19
− 1.03168u
18
+ ··· + 5.35346u + 6.28047
a
5
=
−0.429833u
19
− 1.52577u
18
+ ··· + 8.17678u + 7.74030
−0.345787u
19
− 1.07742u
18
+ ··· + 6.08703u + 4.96065
a
5
=
−0.429833u
19
− 1.52577u
18
+ ··· + 8.17678u + 7.74030
−0.345787u
19
− 1.07742u
18
+ ··· + 6.08703u + 4.96065
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
29166765795697
27009773380984
u
19
−
107025259759479
27009773380984
u
18
+ ··· +
889027178406181
27009773380984
u +
218402675148733
13504886690492
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 2u
19
+ ··· − 3u − 4
c
2
u
20
+ 10u
19
+ ··· + 65u + 16
c
3
, c
8
u
20
− 3u
19
+ ··· + 6u + 8
c
5
, c
6
, c
7
c
9
, c
10
u
20
+ u
19
+ ··· + u
2
− 1
c
11
u
20
− 5u
19
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
− 10y
19
+ ··· − 65y + 16
c
2
y
20
+ 2y
19
+ ··· + 3935y + 256
c
3
, c
8
y
20
− 9y
19
+ ··· − 372y + 64
c
5
, c
6
, c
7
c
9
, c
10
y
20
+ 5y
19
+ ··· − 2y + 1
c
11
y
20
+ 21y
19
+ ··· − 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673179 + 0.716265I
a = −0.148792 + 0.308519I
b = 1.076780 − 0.752726I
−5.39578 − 0.84915I −7.95749 + 2.97696I
u = −0.673179 − 0.716265I
a = −0.148792 − 0.308519I
b = 1.076780 + 0.752726I
−5.39578 + 0.84915I −7.95749 − 2.97696I
u = 0.457611 + 1.029390I
a = −0.041132 − 0.464695I
b = 0.689086 + 0.818580I
−1.13732 − 2.28200I −3.79248 + 2.52259I
u = 0.457611 − 1.029390I
a = −0.041132 + 0.464695I
b = 0.689086 − 0.818580I
−1.13732 + 2.28200I −3.79248 − 2.52259I
u = −1.057230 + 0.616811I
a = −0.48847 + 1.97668I
b = −0.754597 − 0.948291I
−4.17399 − 4.33843I −5.43818 + 4.87758I
u = −1.057230 − 0.616811I
a = −0.48847 − 1.97668I
b = −0.754597 + 0.948291I
−4.17399 + 4.33843I −5.43818 − 4.87758I
u = −0.114291 + 0.713759I
a = 0.381764 − 0.379380I
b = 0.345961 + 0.369550I
−0.507859 − 1.098400I −5.66835 + 6.51867I
u = −0.114291 − 0.713759I
a = 0.381764 + 0.379380I
b = 0.345961 − 0.369550I
−0.507859 + 1.098400I −5.66835 − 6.51867I
u = −0.686172 + 1.114670I
a = −0.149939 + 0.505520I
b = 0.738092 − 1.033620I
−3.56378 + 7.37420I −5.16607 − 5.93843I
u = −0.686172 − 1.114670I
a = −0.149939 − 0.505520I
b = 0.738092 + 1.033620I
−3.56378 − 7.37420I −5.16607 + 5.93843I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.20041 + 0.74865I
a = −0.52942 − 1.65229I
b = −0.681127 + 1.119630I
1.09912 + 8.73296I −0.91420 − 6.11492I
u = 1.20041 − 0.74865I
a = −0.52942 + 1.65229I
b = −0.681127 − 1.119630I
1.09912 − 8.73296I −0.91420 + 6.11492I
u = −1.15925 + 0.84659I
a = −0.67085 + 1.58475I
b = −0.74872 − 1.20984I
−2.0375 − 14.4341I −3.68264 + 8.80511I
u = −1.15925 − 0.84659I
a = −0.67085 − 1.58475I
b = −0.74872 + 1.20984I
−2.0375 + 14.4341I −3.68264 − 8.80511I
u = −1.44359 + 0.25308I
a = 0.295484 − 1.320210I
b = −0.242677 + 0.771774I
5.28190 − 1.85243I −3.45872 − 2.75624I
u = −1.44359 − 0.25308I
a = 0.295484 + 1.320210I
b = −0.242677 − 0.771774I
5.28190 + 1.85243I −3.45872 + 2.75624I
u = 0.527412
a = 2.13544
b = −0.362131
−2.14785 −2.01910
u = 1.47329 + 0.10154I
a = 0.14365 − 1.48101I
b = −0.346734 + 0.845969I
5.55307 + 4.39884I −1.65086 − 8.29154I
u = 1.47329 − 0.10154I
a = 0.14365 + 1.48101I
b = −0.346734 − 0.845969I
5.55307 − 4.39884I −1.65086 + 8.29154I
u = 0.477398
a = −0.0950270
b = 1.21001
−2.89220 7.72710
6
II. I
u
2
= hu
2
a + b + 1, −2u
10
a − 6u
11
+ · · · + a − 2, u
12
− u
11
+ · · · − u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
11
=
a
−u
2
a − 1
a
7
=
2u
10
− 2u
9
− 2u
8
+ 4u
7
+ 6u
6
− 8u
5
− 4u
4
+ u
2
a + 8u
3
+ 3u
2
− a − 6u
−u
4
a + u
4
− u
2
+ 1
a
6
=
2u
10
− 2u
9
− 2u
8
+ 4u
7
+ 6u
6
− 8u
5
− 4u
4
+ 8u
3
+ 4u
2
− a − 6u − 1
1
a
10
=
−u
2
a + a − 1
−u
2
a − 1
a
1
=
u
6
− u
4
+ 2u
2
− 1
u
6
+ u
2
a
2
=
−u
10
+ u
8
− 2u
6
+ u
4
+ u
2
− 1
u
11
− u
10
− 2u
9
+ u
8
+ 4u
7
− 2u
6
− 4u
5
+ u
4
+ 3u
3
+ u
2
− 1
a
5
=
u
4
− u
2
+ 1
u
4
a
5
=
u
4
− u
2
+ 1
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
11
+ 8u
9
− 4u
8
− 16u
7
+ 4u
6
+ 20u
5
− 8u
4
− 12u
3
+ 4u
2
+ 8u − 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
12
− u
11
+ ··· − 2u + 1)
2
c
2
(u
12
+ 7u
11
+ ··· + 2u + 1)
2
c
3
, c
8
(u
12
+ u
11
− u
10
− 2u
9
+ 3u
8
+ 4u
7
− 2u
6
− 4u
5
+ 2u
4
+ 3u
3
− u
2
+ 1)
2
c
5
, c
6
, c
7
c
9
, c
10
u
24
− 3u
23
+ ··· − 52u + 17
c
11
u
24
− 11u
23
+ ··· − 1784u + 289
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
12
− 7y
11
+ ··· − 2y + 1)
2
c
2
(y
12
− 3y
11
+ ··· + 6y + 1)
2
c
3
, c
8
(y
12
− 3y
11
+ ··· − 2y + 1)
2
c
5
, c
6
, c
7
c
9
, c
10
y
24
+ 11y
23
+ ··· + 1784y + 289
c
11
y
24
+ 3y
23
+ ··· + 158184y + 83521
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.915752 + 0.387588I
a = −0.719269 + 0.265989I
b = −0.693689 − 0.693688I
3.36661 − 4.24921I −1.82351 + 6.98310I
u = −0.915752 + 0.387588I
a = 0.31123 − 1.71799I
b = 0.005311 + 1.403560I
3.36661 − 4.24921I −1.82351 + 6.98310I
u = −0.915752 − 0.387588I
a = −0.719269 − 0.265989I
b = −0.693689 + 0.693688I
3.36661 + 4.24921I −1.82351 − 6.98310I
u = −0.915752 − 0.387588I
a = 0.31123 + 1.71799I
b = 0.005311 − 1.403560I
3.36661 + 4.24921I −1.82351 − 6.98310I
u = 0.825437 + 0.157146I
a = −1.25892 − 1.03181I
b = −0.441009 + 1.004140I
4.72717 + 0.35310I 2.66692 − 0.62981I
u = 0.825437 + 0.157146I
a = −0.37562 + 2.07265I
b = −0.215643 − 1.263560I
4.72717 + 0.35310I 2.66692 − 0.62981I
u = 0.825437 − 0.157146I
a = −1.25892 + 1.03181I
b = −0.441009 − 1.004140I
4.72717 − 0.35310I 2.66692 + 0.62981I
u = 0.825437 − 0.157146I
a = −0.37562 − 2.07265I
b = −0.215643 + 1.263560I
4.72717 − 0.35310I 2.66692 + 0.62981I
u = −0.895445 + 0.803537I
a = 0.520071 − 1.227910I
b = 0.685814 + 0.940144I
−0.75031 − 3.01307I −3.36825 + 2.63251I
u = −0.895445 + 0.803537I
a = 0.330877 − 0.145723I
b = −0.841964 + 0.498902I
−0.75031 − 3.01307I −3.36825 + 2.63251I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895445 − 0.803537I
a = 0.520071 + 1.227910I
b = 0.685814 − 0.940144I
−0.75031 + 3.01307I −3.36825 − 2.63251I
u = −0.895445 − 0.803537I
a = 0.330877 + 0.145723I
b = −0.841964 − 0.498902I
−0.75031 + 3.01307I −3.36825 − 2.63251I
u = 0.849698 + 0.874392I
a = 0.495565 + 1.219030I
b = 0.832505 − 0.684481I
−4.62532 − 1.48234I −7.15258 + 0.67542I
u = 0.849698 + 0.874392I
a = 0.542966 + 0.125815I
b = −0.789930 − 0.801459I
−4.62532 − 1.48234I −7.15258 + 0.67542I
u = 0.849698 − 0.874392I
a = 0.495565 − 1.219030I
b = 0.832505 + 0.684481I
−4.62532 + 1.48234I −7.15258 − 0.67542I
u = 0.849698 − 0.874392I
a = 0.542966 − 0.125815I
b = −0.789930 + 0.801459I
−4.62532 + 1.48234I −7.15258 − 0.67542I
u = 0.962887 + 0.828850I
a = 0.498094 + 1.238190I
b = 0.856755 − 1.092410I
−4.26829 + 7.80134I −6.36611 − 5.63981I
u = 0.962887 + 0.828850I
a = 0.317556 − 0.012937I
b = −1.096910 − 0.503770I
−4.26829 + 7.80134I −6.36611 − 5.63981I
u = 0.962887 − 0.828850I
a = 0.498094 − 1.238190I
b = 0.856755 + 1.092410I
−4.26829 − 7.80134I −6.36611 + 5.63981I
u = 0.962887 − 0.828850I
a = 0.317556 + 0.012937I
b = −1.096910 + 0.503770I
−4.26829 − 7.80134I −6.36611 + 5.63981I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.326826 + 0.552791I
a = −0.32038 − 3.37299I
b = 0.155092 − 0.786191I
1.55013 + 0.71593I −7.95647 − 0.64874I
u = −0.326826 + 0.552791I
a = 3.65784 − 0.87628I
b = 0.043670 + 1.147520I
1.55013 + 0.71593I −7.95647 − 0.64874I
u = −0.326826 − 0.552791I
a = −0.32038 + 3.37299I
b = 0.155092 + 0.786191I
1.55013 − 0.71593I −7.95647 + 0.64874I
u = −0.326826 − 0.552791I
a = 3.65784 + 0.87628I
b = 0.043670 − 1.147520I
1.55013 − 0.71593I −7.95647 + 0.64874I
12
III.
I
u
3
= h−u
5
+ 2u
3
+ b − u, −u
4
+ 2u
3
+ 3u
2
+ a − 3u − 2, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
11
=
u
4
− 2u
3
− 3u
2
+ 3u + 2
u
5
− 2u
3
+ u
a
7
=
−u
5
+ u
4
+ 4u
3
− 3u
2
− 4u + 2
1
a
6
=
u
4
+ 2u
3
− 3u
2
− 3u + 2
−u
5
+ u
3
+ u + 1
a
10
=
u
5
+ u
4
− 4u
3
− 3u
2
+ 4u + 2
u
5
− 2u
3
+ u
a
1
=
−u
5
+ 2u
3
− u
0
a
2
=
−u
u
a
5
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
a
5
=
u
5
− 2u
3
+ u
−u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 8u
2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)
2
c
2
(u
3
+ u
2
+ 2u + 1)
2
c
3
, c
8
u
6
− 3u
4
+ 2u
2
+ 1
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
7
c
9
, c
10
(u
2
+ 1)
3
c
11
(u − 1)
6
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
2
(y
3
+ 3y
2
+ 2y − 1)
2
c
3
, c
8
(y
3
− 3y
2
+ 2y + 1)
2
c
5
, c
6
, c
7
c
9
, c
10
(y + 1)
6
c
11
(y − 1)
6
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = −0.72238 − 1.35722I
b = 1.000000I
6.31400 + 2.82812I 3.50976 − 2.97945I
u = 1.307140 − 0.215080I
a = −0.72238 + 1.35722I
b = − 1.000000I
6.31400 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 + 0.215080I
a = −0.35722 − 1.72238I
b = 1.000000I
6.31400 − 2.82812I 3.50976 + 2.97945I
u = −1.307140 − 0.215080I
a = −0.35722 + 1.72238I
b = − 1.000000I
6.31400 + 2.82812I 3.50976 − 2.97945I
u = 0.569840I
a = 3.07960 + 2.07960I
b = 1.000000I
2.17641 −3.01950
u = − 0.569840I
a = 3.07960 − 2.07960I
b = − 1.000000I
2.17641 −3.01950
16
IV. I
v
1
= ha, b − 1, 2v + 1i
(i) Arc colorings
a
3
=
−0.5
0
a
8
=
1
0
a
9
=
1
0
a
4
=
−0.5
0
a
11
=
0
1
a
7
=
1
−1
a
6
=
0
−1
a
10
=
1
1
a
1
=
1
2
a
2
=
0.5
2
a
5
=
−1
−2
a
5
=
−1
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14.25
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
u − 1
c
2
, c
4
, c
9
c
10
, c
11
u + 1
c
3
, c
8
u
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y − 1
c
3
, c
8
y
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000
a = 0
b = 1.00000
−3.28987 −14.2500
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
3
+ u
2
− 1)
2
(u
12
− u
11
+ ··· − 2u + 1)
2
· (u
20
− 2u
19
+ ··· − 3u − 4)
c
2
(u + 1)(u
3
+ u
2
+ 2u + 1)
2
(u
12
+ 7u
11
+ ··· + 2u + 1)
2
· (u
20
+ 10u
19
+ ··· + 65u + 16)
c
3
, c
8
u(u
6
− 3u
4
+ 2u
2
+ 1)
· (u
12
+ u
11
− u
10
− 2u
9
+ 3u
8
+ 4u
7
− 2u
6
− 4u
5
+ 2u
4
+ 3u
3
− u
2
+ 1)
2
· (u
20
− 3u
19
+ ··· + 6u + 8)
c
4
(u + 1)(u
3
− u
2
+ 1)
2
(u
12
− u
11
+ ··· − 2u + 1)
2
· (u
20
− 2u
19
+ ··· − 3u − 4)
c
5
, c
6
, c
7
(u − 1)(u
2
+ 1)
3
(u
20
+ u
19
+ ··· + u
2
− 1)(u
24
− 3u
23
+ ··· − 52u + 17)
c
9
, c
10
(u + 1)(u
2
+ 1)
3
(u
20
+ u
19
+ ··· + u
2
− 1)(u
24
− 3u
23
+ ··· − 52u + 17)
c
11
((u − 1)
6
)(u + 1)(u
20
− 5u
19
+ ··· + 2u + 1)
· (u
24
− 11u
23
+ ··· − 1784u + 289)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y − 1)(y
3
− y
2
+ 2y − 1)
2
(y
12
− 7y
11
+ ··· − 2y + 1)
2
· (y
20
− 10y
19
+ ··· − 65y + 16)
c
2
(y − 1)(y
3
+ 3y
2
+ 2y − 1)
2
(y
12
− 3y
11
+ ··· + 6y + 1)
2
· (y
20
+ 2y
19
+ ··· + 3935y + 256)
c
3
, c
8
y(y
3
− 3y
2
+ 2y + 1)
2
(y
12
− 3y
11
+ ··· − 2y + 1)
2
· (y
20
− 9y
19
+ ··· − 372y + 64)
c
5
, c
6
, c
7
c
9
, c
10
(y − 1)(y + 1)
6
(y
20
+ 5y
19
+ ··· − 2y + 1)
· (y
24
+ 11y
23
+ ··· + 1784y + 289)
c
11
((y − 1)
7
)(y
20
+ 21y
19
+ ··· − 26y + 1)
· (y
24
+ 3y
23
+ ··· + 158184y + 83521)
22
