11n
134
(K11n
134
)
A knot diagram
1
Linearized knot diagam
7 1 10 1 8 2 11 5 4 7 9
Solving Sequence
9,11 1,5
4 8 7 2 3 6 10
c
11
c
4
c
8
c
7
c
1
c
2
c
6
c
10
c
3
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.34789 × 10
32
u
33
− 5.58712 × 10
32
u
32
+ ··· + 1.57006 × 10
31
b − 1.59332 × 10
33
,
3.16774 × 10
33
u
33
− 1.98307 × 10
33
u
32
+ ··· + 1.57006 × 10
31
a − 4.97227 × 10
33
, u
34
− 4u
32
+ ··· − 8u − 1i
I
u
2
= h2u
6
− u
5
− 3u
4
+ 6u
3
+ 2u
2
+ b − 6u + 2, 3u
6
− u
5
− 4u
4
+ 9u
3
+ 4u
2
+ a − 7u + 3,
u
7
− u
6
− u
5
+ 4u
4
− u
3
− 3u
2
+ 3u − 1i
I
u
3
= hu
2
+ b − u − 1, −u
2
+ a + 2u − 1, u
4
− 2u
3
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 45 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
= h9.35 × 10
32
u
33
− 5.59 × 10
32
u
32
+ · · · + 1.57 × 10
31
b − 1.59 × 10
33
, 3.17 ×
10
33
u
33
−1.98×10
33
u
32
+· · ·+1.57×10
31
a−4.97×10
33
, u
34
−4u
32
+· · ·−8u−1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
5
=
−201.759u
33
+ 126.306u
32
+ ··· + 2044.63u + 316.694
−59.5386u
33
+ 35.5855u
32
+ ··· + 631.913u + 101.482
a
4
=
−64.0473u
33
+ 42.6334u
32
+ ··· + 604.027u + 88.9064
−110.441u
33
+ 66.5690u
32
+ ··· + 1163.58u + 185.154
a
8
=
126.520u
33
− 77.8350u
32
+ ··· − 1331.80u − 221.282
144.062u
33
− 89.2523u
32
+ ··· − 1486.79u − 232.342
a
7
=
−17.5420u
33
+ 11.4173u
32
+ ··· + 154.996u + 11.0598
144.062u
33
− 89.2523u
32
+ ··· − 1486.79u − 232.342
a
2
=
191.791u
33
− 115.291u
32
+ ··· − 2025.26u − 313.383
−1.17243u
33
+ 1.47552u
32
+ ··· + 5.92933u + 1.12007
a
3
=
123.827u
33
− 75.2327u
32
+ ··· − 1300.65u − 199.211
22.2954u
33
− 12.2052u
32
+ ··· − 246.576u − 38.9385
a
6
=
−403.100u
33
+ 247.007u
32
+ ··· + 4184.10u + 645.587
−156.172u
33
+ 97.4389u
32
+ ··· + 1597.51u + 249.393
a
10
=
−68.1247u
33
+ 44.5777u
32
+ ··· + 659.086u + 90.0150
28.9676u
33
− 18.5354u
32
+ ··· − 294.427u − 45.6978
a
10
=
−68.1247u
33
+ 44.5777u
32
+ ··· + 659.086u + 90.0150
28.9676u
33
− 18.5354u
32
+ ··· − 294.427u − 45.6978
(ii) Obstruction class = −1
(iii) Cusp Shapes = 263.563u
33
− 150.065u
32
+ ··· − 2900.73u − 454.146
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
34
+ u
33
+ ··· − 223u + 11
c
2
u
34
+ 39u
33
+ ··· − 30545u + 121
c
3
, c
9
u
34
+ 2u
32
+ ··· − 30u + 11
c
4
u
34
+ 6u
33
+ ··· + 88u − 16
c
5
, c
8
u
34
+ 3u
33
+ ··· + 73u + 11
c
7
, c
10
u
34
− u
33
+ ··· − 33u − 1
c
11
u
34
− 4u
32
+ ··· − 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
34
+ 39y
33
+ ··· − 30545y + 121
c
2
y
34
− 89y
33
+ ··· − 1039040457y + 14641
c
3
, c
9
y
34
+ 4y
33
+ ··· − 1054y + 121
c
4
y
34
+ 18y
33
+ ··· − 5440y + 256
c
5
, c
8
y
34
+ 29y
33
+ ··· + 1513y + 121
c
7
, c
10
y
34
+ 3y
33
+ ··· − 1291y + 1
c
11
y
34
− 8y
33
+ ··· − 28y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924018 + 0.522770I
a = −0.375288 − 1.086530I
b = −0.664139 + 0.876476I
−0.24666 + 2.01770I 4.06600 − 3.01899I
u = 0.924018 − 0.522770I
a = −0.375288 + 1.086530I
b = −0.664139 − 0.876476I
−0.24666 − 2.01770I 4.06600 + 3.01899I
u = −0.692709 + 0.537257I
a = −1.68375 − 0.87571I
b = −0.097108 − 0.209897I
−4.70800 − 5.46166I 4.56324 + 8.11055I
u = −0.692709 − 0.537257I
a = −1.68375 + 0.87571I
b = −0.097108 + 0.209897I
−4.70800 + 5.46166I 4.56324 − 8.11055I
u = −1.174930 + 0.138364I
a = 0.388486 − 0.340737I
b = 0.104920 − 0.756129I
5.26138 − 1.82293I 12.08014 + 4.65351I
u = −1.174930 − 0.138364I
a = 0.388486 + 0.340737I
b = 0.104920 + 0.756129I
5.26138 + 1.82293I 12.08014 − 4.65351I
u = −0.737393 + 0.938306I
a = −0.971739 + 0.588253I
b = −1.48087 − 0.04096I
−4.16665 + 0.08364I 1.19426 − 1.11998I
u = −0.737393 − 0.938306I
a = −0.971739 − 0.588253I
b = −1.48087 + 0.04096I
−4.16665 − 0.08364I 1.19426 + 1.11998I
u = 0.748098 + 1.032910I
a = −0.963309 − 0.180793I
b = −1.65602 + 0.67677I
−1.76083 + 4.62537I 0. − 4.38948I
u = 0.748098 − 1.032910I
a = −0.963309 + 0.180793I
b = −1.65602 − 0.67677I
−1.76083 − 4.62537I 0. + 4.38948I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.753821 + 1.029380I
a = 1.30677 + 0.54848I
b = 1.49027 − 0.72971I
−11.55110 + 3.90804I 0. − 2.96330I
u = 0.753821 − 1.029380I
a = 1.30677 − 0.54848I
b = 1.49027 + 0.72971I
−11.55110 − 3.90804I 0. + 2.96330I
u = 0.680135
a = −1.12718
b = 0.231739
1.42028 5.52280
u = 0.112186 + 0.644139I
a = 0.298589 − 0.208281I
b = −0.77348 − 1.72822I
−5.69136 + 2.93128I −2.16566 + 0.03766I
u = 0.112186 − 0.644139I
a = 0.298589 + 0.208281I
b = −0.77348 + 1.72822I
−5.69136 − 2.93128I −2.16566 − 0.03766I
u = 0.453287 + 0.469740I
a = −0.109156 − 0.662192I
b = 0.134371 + 0.558494I
0.417699 + 1.309310I 4.01409 − 5.53427I
u = 0.453287 − 0.469740I
a = −0.109156 + 0.662192I
b = 0.134371 − 0.558494I
0.417699 − 1.309310I 4.01409 + 5.53427I
u = 0.929612 + 0.997075I
a = 0.739202 + 0.328423I
b = 1.79013 − 0.25646I
−1.19710 + 4.22413I 0
u = 0.929612 − 0.997075I
a = 0.739202 − 0.328423I
b = 1.79013 + 0.25646I
−1.19710 − 4.22413I 0
u = −1.090570 + 0.830918I
a = 0.948911 − 0.688424I
b = 1.45111 + 0.57971I
−3.08759 − 6.63875I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.090570 − 0.830918I
a = 0.948911 + 0.688424I
b = 1.45111 − 0.57971I
−3.08759 + 6.63875I 0
u = −0.622046 + 0.005377I
a = −1.15689 − 1.34706I
b = −1.42222 − 0.22309I
−4.73573 + 2.86800I 6.77612 − 0.77716I
u = −0.622046 − 0.005377I
a = −1.15689 + 1.34706I
b = −1.42222 + 0.22309I
−4.73573 − 2.86800I 6.77612 + 0.77716I
u = −0.585191
a = 2.47240
b = 0.385356
2.39902 −9.40470
u = 1.17107 + 0.83565I
a = −0.599060 − 0.768632I
b = −1.62594 − 0.21586I
−10.20860 + 2.99636I 0
u = 1.17107 − 0.83565I
a = −0.599060 + 0.768632I
b = −1.62594 + 0.21586I
−10.20860 − 2.99636I 0
u = −0.89276 + 1.21384I
a = 0.677208 − 0.690623I
b = 1.67380 + 0.04106I
−11.26850 + 5.15956I 0
u = −0.89276 − 1.21384I
a = 0.677208 + 0.690623I
b = 1.67380 − 0.04106I
−11.26850 − 5.15956I 0
u = −1.15354 + 0.99005I
a = −0.987284 + 0.511276I
b = −1.81085 − 0.79676I
−10.3471 − 13.0489I 0
u = −1.15354 − 0.99005I
a = −0.987284 − 0.511276I
b = −1.81085 + 0.79676I
−10.3471 + 13.0489I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49990 + 0.45110I
a = 0.044192 + 0.529855I
b = 0.493623 − 0.408556I
1.03541 + 1.94405I 0
u = 1.49990 − 0.45110I
a = 0.044192 − 0.529855I
b = 0.493623 + 0.408556I
1.03541 − 1.94405I 0
u = −0.275516 + 0.088727I
a = 3.27050 − 3.61161I
b = 0.583860 + 0.707675I
1.94989 − 1.48394I 11.56368 − 0.88523I
u = −0.275516 − 0.088727I
a = 3.27050 + 3.61161I
b = 0.583860 − 0.707675I
1.94989 + 1.48394I 11.56368 + 0.88523I
8
II. I
u
2
= h2u
6
− u
5
− 3u
4
+ 6u
3
+ 2u
2
+ b − 6u + 2, 3u
6
− u
5
− 4u
4
+ 9u
3
+
4u
2
+ a − 7u + 3, u
7
− u
6
− u
5
+ 4u
4
− u
3
− 3u
2
+ 3u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
5
=
−3u
6
+ u
5
+ 4u
4
− 9u
3
− 4u
2
+ 7u − 3
−2u
6
+ u
5
+ 3u
4
− 6u
3
− 2u
2
+ 6u − 2
a
4
=
−u
5
+ u
3
− 2u
2
− 2u + 1
−2u
6
+ 2u
5
+ 2u
4
− 7u
3
+ 6u − 3
a
8
=
−u
6
+ u
4
− 3u
3
− 2u
2
+ u − 2
u
6
− u
5
− u
4
+ 4u
3
− u
2
− 3u + 2
a
7
=
−2u
6
+ u
5
+ 2u
4
− 7u
3
− u
2
+ 4u − 4
u
6
− u
5
− u
4
+ 4u
3
− u
2
− 3u + 2
a
2
=
−2u
6
+ 2u
4
− 5u
3
− 4u
2
+ 2u − 1
−u
6
+ 2u
4
− 3u
3
− 3u
2
+ 3u
a
3
=
u
6
− u
5
− 2u
4
+ 4u
3
− 5u + 1
−2u
6
+ u
5
+ 3u
4
− 7u
3
− 2u
2
+ 6u − 2
a
6
=
−7u
6
+ 3u
5
+ 9u
4
− 23u
3
− 7u
2
+ 18u − 10
−u
6
+ u
5
+ 2u
4
− 4u
3
+ 5u − 2
a
10
=
−2u
6
+ u
5
+ 3u
4
− 7u
3
− 2u
2
+ 7u − 3
u
6
− 2u
4
+ 3u
3
+ 3u
2
− 4u + 1
a
10
=
−2u
6
+ u
5
+ 3u
4
− 7u
3
− 2u
2
+ 7u − 3
u
6
− 2u
4
+ 3u
3
+ 3u
2
− 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 21u
6
− 10u
5
− 27u
4
+ 69u
3
+ 15u
2
− 57u + 38
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
+ 3u
5
+ u
4
+ u
3
+ 3u
2
− u + 1
c
2
u
7
+ 6u
6
+ 11u
5
+ 3u
4
− 11u
3
− 13u
2
− 5u − 1
c
3
u
7
+ 2u
5
+ u
3
+ u
2
+ u + 1
c
4
u
7
− u
6
+ 2u
5
− 4u
4
+ 13u
3
− 28u
2
+ 37u − 21
c
5
u
7
+ u
6
+ u
5
+ u
4
+ 2u
2
+ 1
c
6
u
7
+ 3u
5
− u
4
+ u
3
− 3u
2
− u − 1
c
7
u
7
− 4u
6
+ 6u
5
− 6u
4
+ 5u
3
− u
2
− u + 1
c
8
u
7
− u
6
+ u
5
− u
4
− 2u
2
− 1
c
9
u
7
+ 2u
5
+ u
3
− u
2
+ u − 1
c
10
u
7
+ 4u
6
+ 6u
5
+ 6u
4
+ 5u
3
+ u
2
− u − 1
c
11
u
7
− u
6
− u
5
+ 4u
4
− u
3
− 3u
2
+ 3u − 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
7
+ 6y
6
+ 11y
5
+ 3y
4
− 11y
3
− 13y
2
− 5y −1
c
2
y
7
− 14y
6
+ 63y
5
− 105y
4
+ 101y
3
− 53y
2
− y −1
c
3
, c
9
y
7
+ 4y
6
+ 6y
5
+ 6y
4
+ 5y
3
+ y
2
− y −1
c
4
y
7
+ 3y
6
+ 22y
5
+ 54y
4
+ 51y
3
+ 10y
2
+ 193y −441
c
5
, c
8
y
7
+ y
6
− y
5
− 5y
4
− 6y
3
− 6y
2
− 4y −1
c
7
, c
10
y
7
− 4y
6
− 2y
5
+ 14y
4
+ 9y
3
+ y
2
+ 3y −1
c
11
y
7
− 3y
6
+ 7y
5
− 14y
4
+ 17y
3
− 7y
2
+ 3y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253390 + 0.299435I
a = −0.106502 + 0.574481I
b = −0.670425 + 0.632428I
4.48789 − 1.14089I 4.48970 − 0.40326I
u = −1.253390 − 0.299435I
a = −0.106502 − 0.574481I
b = −0.670425 − 0.632428I
4.48789 + 1.14089I 4.48970 + 0.40326I
u = 0.459759 + 0.484378I
a = 1.43538 − 0.05783I
b = 1.46152 + 0.86219I
−5.24144 + 3.67154I 2.26281 − 7.80389I
u = 0.459759 − 0.484378I
a = 1.43538 + 0.05783I
b = 1.46152 − 0.86219I
−5.24144 − 3.67154I 2.26281 + 7.80389I
u = 0.667034
a = −2.12191
b = −0.118597
2.66082 22.3150
u = 0.96011 + 1.04993I
a = −0.767929 − 0.281521I
b = −1.73179 + 0.66955I
−0.57687 + 5.05320I 8.58977 − 8.09248I
u = 0.96011 − 1.04993I
a = −0.767929 + 0.281521I
b = −1.73179 − 0.66955I
−0.57687 − 5.05320I 8.58977 + 8.09248I
12
III. I
u
3
= hu
2
+ b − u − 1, −u
2
+ a + 2u − 1, u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
1
=
1
−u
2
a
5
=
u
2
− 2u + 1
−u
2
+ u + 1
a
4
=
u
2
− 2u + 1
−u
2
+ u + 1
a
8
=
−2u
3
+ 5u
2
− 2u − 2
1
a
7
=
−2u
3
+ 5u
2
− 2u − 3
1
a
2
=
−u
3
+ u
2
+ 2u − 2
−u
a
3
=
−u
3
+ 2u
2
+ u − 3
−u
3
+ u
2
+ 1
a
6
=
−u
3
+ 2u
2
+ u − 3
−u
3
+ u
2
+ 1
a
10
=
−2u
3
+ 5u
2
− 2u − 2
1
a
10
=
−2u
3
+ 5u
2
− 2u − 2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
3
− 8u
2
+ 11u + 11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
+ u + 1)
2
c
3
, c
5
u
4
+ u
3
+ 3u
2
+ u + 1
c
4
u
4
c
6
(u
2
− u + 1)
2
c
7
(u + 1)
4
c
8
, c
9
u
4
− u
3
+ 3u
2
− u + 1
c
10
(u − 1)
4
c
11
u
4
− 2u
3
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
2
c
3
, c
5
, c
8
c
9
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
4
y
4
c
7
, c
10
(y −1)
4
c
11
y
4
− 4y
3
+ 6y
2
− y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.473561 + 0.444772I
a = 1.97356 − 1.31080I
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 5.75416 + 8.47377I
u = −0.473561 − 0.444772I
a = 1.97356 + 1.31080I
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 5.75416 − 8.47377I
u = 1.47356 + 0.44477I
a = 0.026439 + 0.421254I
b = 0.500000 − 0.866025I
1.64493 + 2.02988I 13.74584 − 2.78456I
u = 1.47356 − 0.44477I
a = 0.026439 − 0.421254I
b = 0.500000 + 0.866025I
1.64493 − 2.02988I 13.74584 + 2.78456I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)
2
(u
7
+ 3u
5
+ u
4
+ u
3
+ 3u
2
− u + 1)
· (u
34
+ u
33
+ ··· − 223u + 11)
c
2
(u
2
+ u + 1)
2
(u
7
+ 6u
6
+ 11u
5
+ 3u
4
− 11u
3
− 13u
2
− 5u − 1)
· (u
34
+ 39u
33
+ ··· − 30545u + 121)
c
3
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
7
+ 2u
5
+ u
3
+ u
2
+ u + 1)
· (u
34
+ 2u
32
+ ··· − 30u + 11)
c
4
u
4
(u
7
− u
6
+ 2u
5
− 4u
4
+ 13u
3
− 28u
2
+ 37u − 21)
· (u
34
+ 6u
33
+ ··· + 88u − 16)
c
5
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
7
+ u
6
+ u
5
+ u
4
+ 2u
2
+ 1)
· (u
34
+ 3u
33
+ ··· + 73u + 11)
c
6
(u
2
− u + 1)
2
(u
7
+ 3u
5
− u
4
+ u
3
− 3u
2
− u − 1)
· (u
34
+ u
33
+ ··· − 223u + 11)
c
7
(u + 1)
4
(u
7
− 4u
6
+ 6u
5
− 6u
4
+ 5u
3
− u
2
− u + 1)
· (u
34
− u
33
+ ··· − 33u − 1)
c
8
(u
4
− u
3
+ 3u
2
− u + 1)(u
7
− u
6
+ u
5
− u
4
− 2u
2
− 1)
· (u
34
+ 3u
33
+ ··· + 73u + 11)
c
9
(u
4
− u
3
+ 3u
2
− u + 1)(u
7
+ 2u
5
+ u
3
− u
2
+ u − 1)
· (u
34
+ 2u
32
+ ··· − 30u + 11)
c
10
(u − 1)
4
(u
7
+ 4u
6
+ 6u
5
+ 6u
4
+ 5u
3
+ u
2
− u − 1)
· (u
34
− u
33
+ ··· − 33u − 1)
c
11
(u
4
− 2u
3
+ u + 1)(u
7
− u
6
− u
5
+ 4u
4
− u
3
− 3u
2
+ 3u − 1)
· (u
34
− 4u
32
+ ··· − 8u − 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
2
+ y + 1)
2
(y
7
+ 6y
6
+ 11y
5
+ 3y
4
− 11y
3
− 13y
2
− 5y −1)
· (y
34
+ 39y
33
+ ··· − 30545y + 121)
c
2
(y
2
+ y + 1)
2
(y
7
− 14y
6
+ 63y
5
− 105y
4
+ 101y
3
− 53y
2
− y −1)
· (y
34
− 89y
33
+ ··· − 1039040457y + 14641)
c
3
, c
9
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
7
+ 4y
6
+ 6y
5
+ 6y
4
+ 5y
3
+ y
2
− y −1)
· (y
34
+ 4y
33
+ ··· − 1054y + 121)
c
4
y
4
(y
7
+ 3y
6
+ 22y
5
+ 54y
4
+ 51y
3
+ 10y
2
+ 193y −441)
· (y
34
+ 18y
33
+ ··· − 5440y + 256)
c
5
, c
8
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
7
+ y
6
− y
5
− 5y
4
− 6y
3
− 6y
2
− 4y −1)
· (y
34
+ 29y
33
+ ··· + 1513y + 121)
c
7
, c
10
(y −1)
4
(y
7
− 4y
6
− 2y
5
+ 14y
4
+ 9y
3
+ y
2
+ 3y −1)
· (y
34
+ 3y
33
+ ··· − 1291y + 1)
c
11
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
7
− 3y
6
+ ··· + 3y −1)
· (y
34
− 8y
33
+ ··· − 28y + 1)
18
