11a
33
(K11a
33
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 9 11 3 5 6 7 10
Solving Sequence
6,11 3,7
8 10 1 2 9 5 4
c
6
c
7
c
10
c
11
c
2
c
9
c
5
c
4
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
50
− u
49
+ ··· + b − u, u
50
− u
49
+ ··· + a − 1, u
52
− 2u
51
+ ··· + u − 1i
I
u
2
= h−u
4
− u
3
− u
2
+ b, −u
2
+ a − u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 57 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−u
50
− u
49
+ · · · + b − u, u
50
− u
49
+ · · · + a − 1, u
52
− 2u
51
+ · · · + u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−u
50
+ u
49
+ ··· − 2u + 1
u
50
+ u
49
+ ··· + 2u
2
+ u
a
7
=
1
u
2
a
8
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
10
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
2
=
u
47
− u
46
+ ··· − u
2
− 2u
u
49
− u
48
+ ··· + 6u
4
+ 2u
2
a
9
=
−u
3
u
3
+ u
a
5
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
u
50
− u
49
+ ··· − 2u
2
− 2u
−u
50
+ u
49
+ ··· − u
3
+ 2u
2
a
4
=
u
50
− u
49
+ ··· − 2u
2
− 2u
−u
50
+ u
49
+ ··· − u
3
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
51
+ 5u
50
+ ··· + 2u − 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
52
− 6u
51
+ ··· + 5u − 1
c
2
u
52
+ 22u
51
+ ··· − 11u + 1
c
3
, c
7
u
52
+ u
51
+ ··· − 232u
2
+ 32
c
5
, c
8
, c
9
u
52
− 2u
51
+ ··· − 25u − 17
c
6
, c
10
u
52
+ 2u
51
+ ··· − u − 1
c
11
u
52
− 30u
51
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
52
− 22y
51
+ ··· + 11y + 1
c
2
y
52
+ 22y
51
+ ··· − 349y + 1
c
3
, c
7
y
52
− 33y
51
+ ··· − 14848y + 1024
c
5
, c
8
, c
9
y
52
− 58y
51
+ ··· − 2291y + 289
c
6
, c
10
y
52
+ 30y
51
+ ··· + 5y + 1
c
11
y
52
− 14y
51
+ ··· + 21y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280725 + 0.984494I
a = 0.654643 + 0.042402I
b = −0.595405 − 0.490264I
0.986067 − 0.922209I 5.57805 + 0.78370I
u = 0.280725 − 0.984494I
a = 0.654643 − 0.042402I
b = −0.595405 + 0.490264I
0.986067 + 0.922209I 5.57805 − 0.78370I
u = −0.377650 + 0.954360I
a = 2.41555 − 1.60256I
b = −2.28692 − 0.23404I
−0.88919 + 2.40502I 4.23135 − 7.49678I
u = −0.377650 − 0.954360I
a = 2.41555 + 1.60256I
b = −2.28692 + 0.23404I
−0.88919 − 2.40502I 4.23135 + 7.49678I
u = 0.508227 + 0.805847I
a = −0.742914 + 0.724717I
b = 0.658582 − 0.670829I
−0.0437779 − 0.0269953I 1.92084 + 0.19212I
u = 0.508227 − 0.805847I
a = −0.742914 − 0.724717I
b = 0.658582 + 0.670829I
−0.0437779 + 0.0269953I 1.92084 − 0.19212I
u = 0.422777 + 0.995937I
a = −0.819376 − 0.080332I
b = 1.105830 + 0.262915I
−0.04250 − 4.54357I 1.88793 + 7.26372I
u = 0.422777 − 0.995937I
a = −0.819376 + 0.080332I
b = 1.105830 − 0.262915I
−0.04250 + 4.54357I 1.88793 − 7.26372I
u = 0.889760 + 0.039446I
a = −0.980477 + 0.475985I
b = −2.22766 − 0.07116I
9.80914 + 2.73925I 5.98913 − 0.86649I
u = 0.889760 − 0.039446I
a = −0.980477 − 0.475985I
b = −2.22766 + 0.07116I
9.80914 − 2.73925I 5.98913 + 0.86649I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885810 + 0.066307I
a = 0.908664 − 0.767749I
b = 2.15596 + 0.13200I
7.94022 + 8.91057I 3.69132 − 5.27448I
u = 0.885810 − 0.066307I
a = 0.908664 + 0.767749I
b = 2.15596 − 0.13200I
7.94022 − 8.91057I 3.69132 + 5.27448I
u = −0.165811 + 1.121200I
a = 1.83757 − 0.40541I
b = −1.130520 − 0.544612I
5.10574 − 3.32861I 8.68775 + 2.82645I
u = −0.165811 − 1.121200I
a = 1.83757 + 0.40541I
b = −1.130520 + 0.544612I
5.10574 + 3.32861I 8.68775 − 2.82645I
u = −0.860610 + 0.023085I
a = −0.066448 − 0.251952I
b = 0.153988 + 0.972076I
4.28726 − 2.50747I 2.75724 + 2.68671I
u = −0.860610 − 0.023085I
a = −0.066448 + 0.251952I
b = 0.153988 − 0.972076I
4.28726 + 2.50747I 2.75724 − 2.68671I
u = 0.529646 + 0.675176I
a = 0.520778 − 1.165510I
b = −0.287257 + 0.910625I
−0.40755 − 4.20725I 0.31053 + 6.85372I
u = 0.529646 − 0.675176I
a = 0.520778 + 1.165510I
b = −0.287257 − 0.910625I
−0.40755 + 4.20725I 0.31053 − 6.85372I
u = −0.511753 + 1.024350I
a = 1.26087 − 1.89055I
b = −1.78707 + 0.70393I
2.58119 + 9.82991I 3.68059 − 9.74649I
u = −0.511753 − 1.024350I
a = 1.26087 + 1.89055I
b = −1.78707 − 0.70393I
2.58119 − 9.82991I 3.68059 + 9.74649I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848851
a = 1.68388
b = 2.26297
2.68190 3.52270
u = −0.245968 + 1.124790I
a = −1.86661 + 0.47174I
b = 1.248780 + 0.497288I
5.88940 + 2.23703I 9.81871 − 3.17171I
u = −0.245968 − 1.124790I
a = −1.86661 − 0.47174I
b = 1.248780 − 0.497288I
5.88940 − 2.23703I 9.81871 + 3.17171I
u = −0.460826 + 1.063150I
a = −1.28681 + 1.46544I
b = 1.53108 − 0.39330I
4.31532 + 4.63289I 7.37710 − 5.03996I
u = −0.460826 − 1.063150I
a = −1.28681 − 1.46544I
b = 1.53108 + 0.39330I
4.31532 − 4.63289I 7.37710 + 5.03996I
u = 0.249339 + 0.786720I
a = 0.457886 + 0.514045I
b = −0.154878 − 0.504949I
0.450033 − 1.234720I 4.74084 + 5.50358I
u = 0.249339 − 0.786720I
a = 0.457886 − 0.514045I
b = −0.154878 + 0.504949I
0.450033 + 1.234720I 4.74084 − 5.50358I
u = −0.457667 + 1.181360I
a = −0.427283 + 0.598681I
b = 0.526120 − 0.236335I
5.00504 + 4.26604I 0
u = −0.457667 − 1.181360I
a = −0.427283 − 0.598681I
b = 0.526120 + 0.236335I
5.00504 − 4.26604I 0
u = −0.626363 + 0.365158I
a = 0.331365 − 0.906721I
b = −1.48252 + 0.06887I
0.72885 − 5.40223I 0.76570 + 5.29849I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626363 − 0.365158I
a = 0.331365 + 0.906721I
b = −1.48252 − 0.06887I
0.72885 + 5.40223I 0.76570 − 5.29849I
u = −0.707531
a = −0.0272312
b = 0.597785
1.69898 7.12320
u = 0.463049 + 1.238040I
a = −2.55511 − 0.88903I
b = 3.29992 − 1.71101I
6.39075 − 4.67632I 0
u = 0.463049 − 1.238040I
a = −2.55511 + 0.88903I
b = 3.29992 + 1.71101I
6.39075 + 4.67632I 0
u = −0.451975 + 1.246010I
a = −0.987426 − 0.642867I
b = 0.437332 + 0.795179I
8.11586 + 2.13977I 0
u = −0.451975 − 1.246010I
a = −0.987426 + 0.642867I
b = 0.437332 − 0.795179I
8.11586 − 2.13977I 0
u = −0.475337 + 1.240760I
a = 0.772991 + 0.898748I
b = −0.203290 − 0.904404I
7.94604 + 7.28946I 0
u = −0.475337 − 1.240760I
a = 0.772991 − 0.898748I
b = −0.203290 + 0.904404I
7.94604 − 7.28946I 0
u = −0.625397 + 0.228924I
a = −0.107645 + 0.510658I
b = 1.145420 + 0.098339I
1.98030 − 0.48005I 3.97181 + 0.10468I
u = −0.625397 − 0.228924I
a = −0.107645 − 0.510658I
b = 1.145420 − 0.098339I
1.98030 + 0.48005I 3.97181 − 0.10468I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427798 + 1.265370I
a = −1.75085 − 0.81280I
b = 1.97471 − 1.35185I
12.02740 + 4.30908I 0
u = 0.427798 − 1.265370I
a = −1.75085 + 0.81280I
b = 1.97471 + 1.35185I
12.02740 − 4.30908I 0
u = 0.500173 + 1.244000I
a = −2.42580 − 1.28995I
b = 3.39254 − 0.69209I
11.4963 − 13.8946I 0
u = 0.500173 − 1.244000I
a = −2.42580 + 1.28995I
b = 3.39254 + 0.69209I
11.4963 + 13.8946I 0
u = 0.445030 + 1.264870I
a = 1.99511 + 0.91581I
b = −2.37247 + 1.31494I
13.79830 − 1.96896I 0
u = 0.445030 − 1.264870I
a = 1.99511 − 0.91581I
b = −2.37247 − 1.31494I
13.79830 + 1.96896I 0
u = 0.488189 + 1.251510I
a = 2.39866 + 1.22603I
b = −3.25277 + 0.88645I
13.4799 − 7.6731I 0
u = 0.488189 − 1.251510I
a = 2.39866 − 1.22603I
b = −3.25277 − 0.88645I
13.4799 + 7.6731I 0
u = −0.287199 + 0.547902I
a = −0.76127 − 1.80488I
b = −0.88257 + 1.12082I
−2.08809 + 0.78607I −3.98062 + 1.52380I
u = −0.287199 − 0.547902I
a = −0.76127 + 1.80488I
b = −0.88257 − 1.12082I
−2.08809 − 0.78607I −3.98062 − 1.52380I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.385374 + 0.321628I
a = −0.10441 − 1.83686I
b = 0.102691 + 0.571781I
−1.79468 + 0.95889I −4.14280 − 1.57937I
u = 0.385374 − 0.321628I
a = −0.10441 + 1.83686I
b = 0.102691 − 0.571781I
−1.79468 − 0.95889I −4.14280 + 1.57937I
10
II. I
u
2
= h−u
4
− u
3
− u
2
+ b, −u
2
+ a − u − 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
u
2
+ u + 1
u
4
+ u
3
+ u
2
a
7
=
1
u
2
a
8
=
1
u
2
a
10
=
u
u
3
+ u
a
1
=
u
3
−u
4
− u
3
− u
2
− 1
a
2
=
u
3
+ u
2
+ u + 1
−1
a
9
=
−u
3
u
3
+ u
a
5
=
−u
3
u
4
+ u
3
+ u
2
+ 1
a
4
=
u
2
+ u + 1
u
4
+ u
3
+ u
2
a
4
=
u
2
+ u + 1
u
4
+ u
3
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
4
+ u
3
+ 2u
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
7
u
5
c
5
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
8
, c
9
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
10
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
11
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
8
, c
9
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
6
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
11
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 0.77780 + 1.38013I
b = −1.206350 − 0.340852I
−1.31583 − 1.53058I 0.02124 + 2.62456I
u = 0.339110 − 0.822375I
a = 0.77780 − 1.38013I
b = −1.206350 + 0.340852I
−1.31583 + 1.53058I 0.02124 − 2.62456I
u = −0.766826
a = 0.821196
b = 0.482881
0.756147 −2.67610
u = −0.455697 + 1.200150I
a = −0.688402 + 0.106340I
b = 0.964913 + 0.621896I
4.22763 + 4.40083I 0.31681 − 3.97407I
u = −0.455697 − 1.200150I
a = −0.688402 − 0.106340I
b = 0.964913 − 0.621896I
4.22763 − 4.40083I 0.31681 + 3.97407I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
52
− 6u
51
+ ··· + 5u − 1)
c
2
((u + 1)
5
)(u
52
+ 22u
51
+ ··· − 11u + 1)
c
3
, c
7
u
5
(u
52
+ u
51
+ ··· − 232u
2
+ 32)
c
4
((u + 1)
5
)(u
52
− 6u
51
+ ··· + 5u − 1)
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
52
− 2u
51
+ ··· − 25u − 17)
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
52
+ 2u
51
+ ··· − u − 1)
c
8
, c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
52
− 2u
51
+ ··· − 25u − 17)
c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
52
+ 2u
51
+ ··· − u − 1)
c
11
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
52
− 30u
51
+ ··· − 5u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
52
− 22y
51
+ ··· + 11y + 1)
c
2
((y −1)
5
)(y
52
+ 22y
51
+ ··· − 349y + 1)
c
3
, c
7
y
5
(y
52
− 33y
51
+ ··· − 14848y + 1024)
c
5
, c
8
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
52
− 58y
51
+ ··· − 2291y + 289)
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
52
+ 30y
51
+ ··· + 5y + 1)
c
11
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
52
− 14y
51
+ ··· + 21y + 1)
16
