11n
43
(K11n
43
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 8 4 10 11 5 6 9
Solving Sequence
1,4
2
5,9
10 11 8 6 3 7
c
1
c
4
c
9
c
11
c
8
c
5
c
3
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.30032 × 10
39
u
50
− 9.01961 × 10
39
u
49
+ ··· + 8.75756 × 10
39
b − 1.79658 × 10
40
,
− 1.18855 × 10
39
u
50
− 7.86992 × 10
39
u
49
+ ··· + 5.47347 × 10
38
a + 1.25534 × 10
39
,
u
51
+ 7u
50
+ ··· − 81u
2
+ 1i
I
u
2
= hb
5
− b
4
− 2b
3
+ b
2
+ b + 1, a − 1, u − 1i
I
u
3
= hb + 1, a − 4u − 6, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 58 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−1.30 × 10
39
u
50
− 9.02 × 10
39
u
49
+ · · · + 8.76 × 10
39
b − 1.80 ×
10
40
, −1.19 × 10
39
u
50
− 7.87 × 10
39
u
49
+ · · · + 5.47 × 10
38
a + 1.26 ×
10
39
, u
51
+ 7u
50
+ · · · − 81u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
2.17147u
50
+ 14.3783u
49
+ ··· − 92.5347u − 2.29349
0.148479u
50
+ 1.02992u
49
+ ··· − 2.01156u + 2.05146
a
10
=
1.09719u
50
+ 7.70594u
49
+ ··· − 90.5056u − 3.24898
1.25327u
50
+ 6.81713u
49
+ ··· − 2.96643u + 2.15932
a
11
=
−1.96518u
50
− 12.8342u
49
+ ··· + 88.9231u + 7.11394
−1.04684u
50
− 6.52621u
49
+ ··· − 0.236967u − 2.82088
a
8
=
2.21621u
50
+ 14.3423u
49
+ ··· − 4.63645u + 11.0109
−0.0694094u
50
+ 0.202698u
49
+ ··· − 9.54759u + 1.43747
a
6
=
−0.109838u
50
+ 0.455800u
49
+ ··· − 35.3698u + 2.83830
2.10336u
50
+ 11.3955u
49
+ ··· − 4.83182u + 1.99352
a
3
=
−u
2
+ 1
u
2
a
7
=
−0.109838u
50
+ 0.455800u
49
+ ··· − 35.3698u + 2.83830
1.41865u
50
+ 6.00756u
49
+ ··· − 4.72198u + 0.768857
a
7
=
−0.109838u
50
+ 0.455800u
49
+ ··· − 35.3698u + 2.83830
1.41865u
50
+ 6.00756u
49
+ ··· − 4.72198u + 0.768857
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.81706u
50
+ 20.2990u
49
+ ··· − 41.2566u + 8.01207
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
51
− 7u
50
+ ··· + 81u
2
− 1
c
2
u
51
+ 23u
50
+ ··· + 162u + 1
c
3
, c
6
u
51
− 2u
50
+ ··· − 96u − 32
c
5
u
51
− 3u
50
+ ··· + 2u − 1
c
7
u
51
+ 8u
50
+ ··· + 64u + 4
c
8
, c
11
u
51
− 4u
50
+ ··· − 87u + 1
c
9
u
51
+ 5u
50
+ ··· − 402u − 137
c
10
u
51
+ u
50
+ ··· − 4u + 31
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
51
− 23y
50
+ ··· + 162y −1
c
2
y
51
+ 17y
50
+ ··· + 12790y −1
c
3
, c
6
y
51
+ 30y
50
+ ··· − 8704y −1024
c
5
y
51
− 15y
50
+ ··· + 20y −1
c
7
y
51
− 12y
50
+ ··· + 1272y −16
c
8
, c
11
y
51
− 30y
50
+ ··· + 6683y −1
c
9
y
51
+ 37y
50
+ ··· + 211472y −18769
c
10
y
51
+ 29y
50
+ ··· + 22708y −961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.923570 + 0.305757I
a = −0.56446 − 2.60605I
b = 1.108610 + 0.499436I
−3.69039 − 2.13393I −15.8264 + 4.5625I
u = 0.923570 − 0.305757I
a = −0.56446 + 2.60605I
b = 1.108610 − 0.499436I
−3.69039 + 2.13393I −15.8264 − 4.5625I
u = −0.359247 + 0.982542I
a = 0.110085 + 0.563683I
b = −0.885970 − 0.593352I
4.54085 − 1.95941I −3.52747 + 2.51429I
u = −0.359247 − 0.982542I
a = 0.110085 − 0.563683I
b = −0.885970 + 0.593352I
4.54085 + 1.95941I −3.52747 − 2.51429I
u = −0.872616 + 0.581002I
a = 0.200453 + 0.860825I
b = 1.74486 + 0.17305I
−2.26568 + 2.29719I −12.40272 − 3.03914I
u = −0.872616 − 0.581002I
a = 0.200453 − 0.860825I
b = 1.74486 − 0.17305I
−2.26568 − 2.29719I −12.40272 + 3.03914I
u = −0.788139 + 0.707702I
a = −0.197062 − 1.246490I
b = 0.879652 + 0.299225I
1.43007 + 1.84298I −7.00000 − 8.98031I
u = −0.788139 − 0.707702I
a = −0.197062 + 1.246490I
b = 0.879652 − 0.299225I
1.43007 − 1.84298I −7.00000 + 8.98031I
u = 0.744937 + 0.557874I
a = 0.337383 − 1.321850I
b = −0.203100 + 0.865788I
0.62734 − 3.24727I −5.87868 + 5.45997I
u = 0.744937 − 0.557874I
a = 0.337383 + 1.321850I
b = −0.203100 − 0.865788I
0.62734 + 3.24727I −5.87868 − 5.45997I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073300 + 0.130259I
a = −0.350884 − 1.323440I
b = 1.192740 − 0.253796I
−4.21875 + 0.45905I −12.7704 − 7.0072I
u = 1.073300 − 0.130259I
a = −0.350884 + 1.323440I
b = 1.192740 + 0.253796I
−4.21875 − 0.45905I −12.7704 + 7.0072I
u = −0.665417 + 0.633317I
a = −0.891675 − 0.347330I
b = 0.946736 + 0.983782I
0.08535 − 1.42859I −8.20291 + 2.86015I
u = −0.665417 − 0.633317I
a = −0.891675 + 0.347330I
b = 0.946736 − 0.983782I
0.08535 + 1.42859I −8.20291 − 2.86015I
u = −0.603362 + 0.919845I
a = −0.417893 − 1.298460I
b = −0.357813 + 1.171210I
6.12236 − 2.89222I −7.00000 + 0.I
u = −0.603362 − 0.919845I
a = −0.417893 + 1.298460I
b = −0.357813 − 1.171210I
6.12236 + 2.89222I −7.00000 + 0.I
u = 0.709519 + 0.862840I
a = 0.722213 − 0.172154I
b = −0.978955 + 0.420067I
−1.46329 + 2.48395I 0
u = 0.709519 − 0.862840I
a = 0.722213 + 0.172154I
b = −0.978955 − 0.420067I
−1.46329 − 2.48395I 0
u = −0.923670 + 0.689242I
a = 1.03818 + 2.23313I
b = 1.060170 − 0.222360I
1.01385 + 3.52246I 0
u = −0.923670 − 0.689242I
a = 1.03818 − 2.23313I
b = 1.060170 + 0.222360I
1.01385 − 3.52246I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437529 + 1.071430I
a = 0.555165 + 0.712106I
b = −1.24641 − 0.67694I
3.27749 − 9.36362I 0
u = −0.437529 − 1.071430I
a = 0.555165 − 0.712106I
b = −1.24641 + 0.67694I
3.27749 + 9.36362I 0
u = −0.834183 + 0.022964I
a = −1.240400 − 0.071253I
b = −1.46648 − 0.21508I
−7.16136 − 4.34566I 0.37647 + 1.57270I
u = −0.834183 − 0.022964I
a = −1.240400 + 0.071253I
b = −1.46648 + 0.21508I
−7.16136 + 4.34566I 0.37647 − 1.57270I
u = 1.051020 + 0.519122I
a = −0.876858 + 0.965223I
b = −0.593255 − 0.386139I
−0.294650 − 1.061440I 0
u = 1.051020 − 0.519122I
a = −0.876858 − 0.965223I
b = −0.593255 + 0.386139I
−0.294650 + 1.061440I 0
u = −0.993259 + 0.639230I
a = 0.50831 + 1.57361I
b = 1.30081 − 0.93720I
−0.91339 + 6.46505I 0
u = −0.993259 − 0.639230I
a = 0.50831 − 1.57361I
b = 1.30081 + 0.93720I
−0.91339 − 6.46505I 0
u = 1.222940 + 0.084782I
a = −0.880621 + 0.184837I
b = −0.175938 + 0.530024I
−1.13007 − 1.28368I 0
u = 1.222940 − 0.084782I
a = −0.880621 − 0.184837I
b = −0.175938 − 0.530024I
−1.13007 + 1.28368I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.719478 + 1.003150I
a = −0.078844 − 0.785446I
b = −0.623365 + 0.588618I
5.28316 + 2.70789I 0
u = −0.719478 − 1.003150I
a = −0.078844 + 0.785446I
b = −0.623365 − 0.588618I
5.28316 − 2.70789I 0
u = 0.990585 + 0.737126I
a = 0.01937 + 1.54321I
b = −1.190760 − 0.548951I
−2.32039 − 8.39966I 0
u = 0.990585 − 0.737126I
a = 0.01937 − 1.54321I
b = −1.190760 + 0.548951I
−2.32039 + 8.39966I 0
u = 0.742417 + 0.124155I
a = −3.86813 − 7.11674I
b = 0.960382 − 0.003997I
−2.64938 − 0.11132I −58.9394 + 3.8883I
u = 0.742417 − 0.124155I
a = −3.86813 + 7.11674I
b = 0.960382 + 0.003997I
−2.64938 + 0.11132I −58.9394 − 3.8883I
u = −1.086370 + 0.734156I
a = 0.744054 + 0.739625I
b = −0.176246 − 1.311490I
4.63878 + 8.97661I 0
u = −1.086370 − 0.734156I
a = 0.744054 − 0.739625I
b = −0.176246 + 1.311490I
4.63878 − 8.97661I 0
u = −1.035770 + 0.809017I
a = 0.136581 + 0.365352I
b = −0.281742 − 0.574694I
4.27954 + 3.84215I 0
u = −1.035770 − 0.809017I
a = 0.136581 − 0.365352I
b = −0.281742 + 0.574694I
4.27954 − 3.84215I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650449
a = −0.858462
b = −0.0122379
−1.00288 −10.0670
u = −1.227370 + 0.667999I
a = −0.673896 − 1.098580I
b = −1.113660 + 0.462367I
1.87901 + 7.98783I 0
u = −1.227370 − 0.667999I
a = −0.673896 + 1.098580I
b = −1.113660 − 0.462367I
1.87901 − 7.98783I 0
u = −1.213470 + 0.718395I
a = −0.57099 − 1.54335I
b = −1.36456 + 0.66315I
0.8642 + 15.7945I 0
u = −1.213470 − 0.718395I
a = −0.57099 + 1.54335I
b = −1.36456 − 0.66315I
0.8642 − 15.7945I 0
u = 1.46886 + 0.10563I
a = −0.596843 + 0.030342I
b = −1.121090 + 0.463770I
−3.74009 + 5.32281I 0
u = 1.46886 − 0.10563I
a = −0.596843 − 0.030342I
b = −1.121090 − 0.463770I
−3.74009 − 5.32281I 0
u = −1.64237
a = −0.478176
b = −0.962556
−10.4502 0
u = −0.218706 + 0.056088I
a = −0.19747 + 1.88909I
b = 0.500772 + 0.518382I
−0.61038 − 1.48999I −4.46560 + 4.54978I
u = −0.218706 − 0.056088I
a = −0.19747 − 1.88909I
b = 0.500772 − 0.518382I
−0.61038 + 1.48999I −4.46560 − 4.54978I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0948151
a = −15.5949
b = 1.14404
−2.29513 −1.15090
10
II. I
u
2
= hb
5
− b
4
− 2b
3
+ b
2
+ b + 1, a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
1
b
a
10
=
−b + 1
b
a
11
=
−b + 1
−b
2
a
8
=
−b
2
+ b + 1
−b
3
+ b
a
6
=
0
−b
4
− b
3
+ b
2
+ 2b + 1
a
3
=
0
1
a
7
=
0
−b
4
− b
3
+ b
2
+ 2b + 1
a
7
=
0
−b
4
− b
3
+ b
2
+ 2b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3b
4
+ b
3
− 2b
2
− 10b − 17
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
6
u
5
c
5
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
7
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
8
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
9
, c
11
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
10
u
5
+ u
4
+ 2u
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
6
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
7
, c
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
8
, c
9
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.21774
−4.04602 −2.99730
u = 1.00000
a = 1.00000
b = −0.309916 + 0.549911I
−1.97403 + 1.53058I −13.4575 − 4.4032I
u = 1.00000
a = 1.00000
b = −0.309916 − 0.549911I
−1.97403 − 1.53058I −13.4575 + 4.4032I
u = 1.00000
a = 1.00000
b = 1.41878 + 0.21917I
−7.51750 − 4.40083I −22.0438 + 5.2094I
u = 1.00000
a = 1.00000
b = 1.41878 − 0.21917I
−7.51750 + 4.40083I −22.0438 − 5.2094I
14
III. I
u
3
= hb + 1, a − 4u − 6, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
9
=
4u + 6
−1
a
10
=
3u + 5
0
a
11
=
4u + 7
−1
a
8
=
−1
0
a
6
=
−1
−u + 1
a
3
=
u
−u + 1
a
7
=
−1
0
a
7
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −61
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
+ u − 1
c
2
u
2
+ 3u + 1
c
4
, c
6
u
2
− u − 1
c
5
, c
9
, c
10
u
2
− 3u + 1
c
7
u
2
c
8
(u − 1)
2
c
11
(u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
2
− 3y + 1
c
2
, c
5
, c
9
c
10
y
2
− 7y + 1
c
7
y
2
c
8
, c
11
(y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 8.47214
b = −1.00000
−2.63189 −61.0000
u = −1.61803
a = −0.472136
b = −1.00000
−10.5276 −61.0000
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
2
+ u − 1)(u
51
− 7u
50
+ ··· + 81u
2
− 1)
c
2
((u + 1)
5
)(u
2
+ 3u + 1)(u
51
+ 23u
50
+ ··· + 162u + 1)
c
3
u
5
(u
2
+ u − 1)(u
51
− 2u
50
+ ··· − 96u − 32)
c
4
((u + 1)
5
)(u
2
− u − 1)(u
51
− 7u
50
+ ··· + 81u
2
− 1)
c
5
(u
2
− 3u + 1)(u
5
− 3u
4
+ ··· − u + 1)(u
51
− 3u
50
+ ··· + 2u − 1)
c
6
u
5
(u
2
− u − 1)(u
51
− 2u
50
+ ··· − 96u − 32)
c
7
u
2
(u
5
− u
4
+ ··· + u − 1)(u
51
+ 8u
50
+ ··· + 64u + 4)
c
8
((u − 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
51
− 4u
50
+ ··· − 87u + 1)
c
9
(u
2
− 3u + 1)(u
5
− u
4
+ ··· + u + 1)(u
51
+ 5u
50
+ ··· − 402u − 137)
c
10
(u
2
− 3u + 1)(u
5
+ u
4
+ ··· + u + 1)(u
51
+ u
50
+ ··· − 4u + 31)
c
11
((u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
51
− 4u
50
+ ··· − 87u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
2
− 3y + 1)(y
51
− 23y
50
+ ··· + 162y −1)
c
2
((y −1)
5
)(y
2
− 7y + 1)(y
51
+ 17y
50
+ ··· + 12790y −1)
c
3
, c
6
y
5
(y
2
− 3y + 1)(y
51
+ 30y
50
+ ··· − 8704y −1024)
c
5
(y
2
− 7y + 1)(y
5
− y
4
+ ··· + 3y −1)(y
51
− 15y
50
+ ··· + 20y −1)
c
7
y
2
(y
5
+ 3y
4
+ ··· − y −1)(y
51
− 12y
50
+ ··· + 1272y −16)
c
8
, c
11
((y −1)
2
)(y
5
− 5y
4
+ ··· − y −1)(y
51
− 30y
50
+ ··· + 6683y −1)
c
9
(y
2
− 7y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
51
+ 37y
50
+ ··· + 211472y −18769)
c
10
(y
2
− 7y + 1)(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
· (y
51
+ 29y
50
+ ··· + 22708y −961)
20
