11n
26
(K11n
26
)
A knot diagram
1
Linearized knot diagam
4 1 6 2 10 4 5 11 6 8 9
Solving Sequence
5,10 2,6
4 7 8 1 3 9 11
c
5
c
4
c
6
c
7
c
1
c
3
c
9
c
11
c
2
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.49349 × 10
26
u
27
+ 1.90286 × 10
27
u
26
+ ··· + 6.31630 × 10
27
b − 6.60130 × 10
27
,
− 1.10262 × 10
28
u
27
− 1.96649 × 10
28
u
26
+ ··· + 1.26326 × 10
28
a − 2.28561 × 10
29
,
u
28
+ 2u
27
+ ··· + 20u + 8i
I
u
2
= hb + 1, u
4
+ u
2
+ a − u + 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v −1i
* 3 irreducible components of dim
C
= 0, with total 36 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
= h6.49 × 10
26
u
27
+ 1.90 × 10
27
u
26
+ · · · + 6.32 × 10
27
b − 6.60 ×
10
27
, −1.10 × 10
28
u
27
− 1.97 × 10
28
u
26
+ · · · + 1.26 × 10
28
a − 2.29 ×
10
29
, u
28
+ 2u
27
+ · · · + 20u + 8i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
0.872833u
27
+ 1.55668u
26
+ ··· − 6.74875u + 18.0929
−0.102805u
27
− 0.301262u
26
+ ··· + 5.99581u + 1.04512
a
6
=
1
u
2
a
4
=
0.748842u
27
+ 1.32169u
26
+ ··· − 4.76990u + 17.3225
0.236809u
27
+ 0.571914u
26
+ ··· − 10.8084u − 2.70142
a
7
=
0.212982u
27
+ 0.380557u
26
+ ··· − 3.15104u + 3.02347
−0.0259598u
27
− 0.0939752u
26
+ ··· + 1.35732u + 1.55242
a
8
=
0.187022u
27
+ 0.286582u
26
+ ··· − 1.79372u + 4.57588
−0.0259598u
27
− 0.0939752u
26
+ ··· + 1.35732u + 1.55242
a
1
=
0.212982u
27
+ 0.380557u
26
+ ··· − 3.15104u + 3.02347
0.0387264u
27
+ 0.130165u
26
+ ··· − 2.15306u − 1.18917
a
3
=
0.902672u
27
+ 1.78001u
26
+ ··· − 13.1074u + 13.2132
0.300350u
27
+ 0.747310u
26
+ ··· − 15.0523u − 3.90671
a
9
=
u
u
3
+ u
a
11
=
0.216279u
27
+ 0.376927u
26
+ ··· − 2.89799u + 3.72316
0.0537576u
27
+ 0.145064u
26
+ ··· − 1.72187u − 0.407669
a
11
=
0.216279u
27
+ 0.376927u
26
+ ··· − 2.89799u + 3.72316
0.0537576u
27
+ 0.145064u
26
+ ··· − 1.72187u − 0.407669
(ii) Obstruction class = −1
(iii) Cusp Shapes =
10054887119174523839900746713
6316300717618506105858780668
u
27
+
3421814896803148511487522420
1579075179404626526464695167
u
26
+
··· +
38462222224803397140841081069
3158150358809253052929390334
u +
73867545823191868965381639557
1579075179404626526464695167
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
− 7u
27
+ ··· − 5u + 1
c
2
u
28
+ 5u
27
+ ··· − 3u + 1
c
3
, c
6
u
28
− 2u
27
+ ··· − 24u
2
− 32
c
5
, c
9
u
28
+ 2u
27
+ ··· + 20u + 8
c
7
u
28
+ 3u
27
+ ··· − u − 1
c
8
, c
10
, c
11
u
28
+ 5u
27
+ ··· − 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
− 5y
27
+ ··· + 3y + 1
c
2
y
28
+ 43y
27
+ ··· + 3y + 1
c
3
, c
6
y
28
+ 36y
27
+ ··· + 1536y + 1024
c
5
, c
9
y
28
+ 24y
27
+ ··· − 848y + 64
c
7
y
28
− 37y
27
+ ··· − 35y + 1
c
8
, c
10
, c
11
y
28
− 31y
27
+ ··· − 128y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502386 + 0.824854I
a = 0.823470 + 0.487809I
b = 0.414733 − 0.266521I
−0.04395 + 1.99045I −0.01306 − 4.61620I
u = −0.502386 − 0.824854I
a = 0.823470 − 0.487809I
b = 0.414733 + 0.266521I
−0.04395 − 1.99045I −0.01306 + 4.61620I
u = −0.011679 + 0.922740I
a = 0.91458 − 1.21166I
b = −0.220238 + 0.502777I
1.30841 + 1.56433I 2.39227 − 4.63205I
u = −0.011679 − 0.922740I
a = 0.91458 + 1.21166I
b = −0.220238 − 0.502777I
1.30841 − 1.56433I 2.39227 + 4.63205I
u = 0.841010 + 0.306823I
a = 0.495652 − 0.321293I
b = 0.136281 − 0.404052I
2.62794 + 0.46347I 2.20728 + 0.53901I
u = 0.841010 − 0.306823I
a = 0.495652 + 0.321293I
b = 0.136281 + 0.404052I
2.62794 − 0.46347I 2.20728 − 0.53901I
u = 0.456033 + 1.080380I
a = 0.760375 − 0.367537I
b = 0.744635 + 0.318856I
4.82268 − 5.10002I 4.96882 + 7.61668I
u = 0.456033 − 1.080380I
a = 0.760375 + 0.367537I
b = 0.744635 − 0.318856I
4.82268 + 5.10002I 4.96882 − 7.61668I
u = 0.639311 + 0.009558I
a = 0.530838 + 0.374755I
b = 0.894453 − 0.824309I
3.90340 + 3.06304I −6.04954 − 3.66902I
u = 0.639311 − 0.009558I
a = 0.530838 − 0.374755I
b = 0.894453 + 0.824309I
3.90340 − 3.06304I −6.04954 + 3.66902I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.100025 + 0.630262I
a = 0.34419 + 2.12537I
b = −1.051400 − 0.149533I
−1.169040 − 0.736496I −2.56323 − 2.93619I
u = 0.100025 − 0.630262I
a = 0.34419 − 2.12537I
b = −1.051400 + 0.149533I
−1.169040 + 0.736496I −2.56323 + 2.93619I
u = −0.09653 + 1.44384I
a = −0.313167 − 0.868043I
b = −1.322620 + 0.396919I
5.47968 + 1.56446I 1.30115 − 0.62804I
u = −0.09653 − 1.44384I
a = −0.313167 + 0.868043I
b = −1.322620 − 0.396919I
5.47968 − 1.56446I 1.30115 + 0.62804I
u = 0.11027 + 1.45639I
a = −0.590568 + 1.231490I
b = 0.95494 − 1.07229I
9.13873 + 0.66915I 1.241168 + 0.226691I
u = 0.11027 − 1.45639I
a = −0.590568 − 1.231490I
b = 0.95494 + 1.07229I
9.13873 − 0.66915I 1.241168 − 0.226691I
u = 0.33116 + 1.43263I
a = −0.03375 − 1.59565I
b = 1.08042 + 0.99381I
8.71794 − 6.87707I 0.35894 + 4.81213I
u = 0.33116 − 1.43263I
a = −0.03375 + 1.59565I
b = 1.08042 − 0.99381I
8.71794 + 6.87707I 0.35894 − 4.81213I
u = −1.51203 + 0.11931I
a = 0.447872 − 0.348583I
b = 1.03272 + 1.05137I
11.20710 − 3.83748I 1.59779 + 2.22620I
u = −1.51203 − 0.11931I
a = 0.447872 + 0.348583I
b = 1.03272 − 1.05137I
11.20710 + 3.83748I 1.59779 − 2.22620I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29853 + 1.54812I
a = 0.139401 + 1.066540I
b = −0.423937 − 0.981765I
8.83250 − 3.91759I 2.90293 + 3.10234I
u = 0.29853 − 1.54812I
a = 0.139401 − 1.066540I
b = −0.423937 + 0.981765I
8.83250 + 3.91759I 2.90293 − 3.10234I
u = −0.349253
a = −12.0202
b = −0.917213
0.303143 −47.2620
u = −0.304533
a = 1.10498
b = −0.668462
−1.01341 −10.2410
u = −0.72992 + 1.54911I
a = 0.43631 + 1.34583I
b = 1.21166 − 0.95824I
15.7181 + 11.7289I 1.85525 − 5.52053I
u = −0.72992 − 1.54911I
a = 0.43631 − 1.34583I
b = 1.21166 + 0.95824I
15.7181 − 11.7289I 1.85525 + 5.52053I
u = −0.59689 + 1.68228I
a = −0.497600 − 0.677471I
b = 0.84120 + 1.23310I
16.9931 + 3.8383I 0
u = −0.59689 − 1.68228I
a = −0.497600 + 0.677471I
b = 0.84120 − 1.23310I
16.9931 − 3.8383I 0
7
II. I
u
2
= hb + 1, u
4
+ u
2
+ a − u + 1, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
−u
4
− u
2
+ u − 1
−1
a
6
=
1
u
2
a
4
=
−u
4
− u
2
+ u
−1
a
7
=
1
u
2
a
8
=
u
2
+ 1
u
2
a
1
=
−1
0
a
3
=
−u
4
− u
2
+ u
−1
a
9
=
u
u
3
+ u
a
11
=
−u
4
− u
2
− 1
−u
4
− u
3
− u
2
− 1
a
11
=
−u
4
− u
2
− 1
−u
4
− u
3
− u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
+ 5u
3
+ 7u
2
+ 5u
8
(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
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
8
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
10
, c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
9
(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
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
8
, c
10
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −0.103562 + 0.890762I
b = −1.00000
−1.31583 − 1.53058I −5.47076 + 5.40154I
u = 0.339110 − 0.822375I
a = −0.103562 − 0.890762I
b = −1.00000
−1.31583 + 1.53058I −5.47076 − 5.40154I
u = −0.766826
a = −2.70062
b = −1.00000
0.756147 −1.28100
u = −0.455697 + 1.200150I
a = −0.546130 − 0.402731I
b = −1.00000
4.22763 + 4.40083I −0.88874 − 1.16747I
u = −0.455697 − 1.200150I
a = −0.546130 + 0.402731I
b = −1.00000
4.22763 − 4.40083I −0.88874 + 1.16747I
11
III. I
v
1
= ha, −v
2
+ b + 3v + 1, v
3
− 2v
2
− 3v − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
2
=
0
v
2
− 3v − 1
a
6
=
1
0
a
4
=
1
−2v
2
+ 5v + 3
a
7
=
−2v
2
+ 5v + 4
v
2
− 2v − 3
a
8
=
−v
2
+ 3v + 1
v
2
− 2v − 3
a
1
=
v
2
− 3v − 1
−v
2
+ 2v + 3
a
3
=
−2v
2
+ 5v + 4
−2v
2
+ 5v + 3
a
9
=
v
0
a
11
=
v
2
− 2v − 1
−v
2
+ 2v + 3
a
11
=
v
2
− 2v − 1
−v
2
+ 2v + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
− 5v + 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
6
u
3
+ u
2
+ 2u + 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
, c
9
u
3
c
7
u
3
− 3u
2
+ 2u + 1
c
8
(u + 1)
3
c
10
, c
11
(u − 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− y
2
+ 2y − 1
c
2
, c
3
, c
6
y
3
+ 3y
2
+ 2y − 1
c
5
, c
9
y
3
c
7
y
3
− 5y
2
+ 10y − 1
c
8
, c
10
, c
11
(y − 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.539798 + 0.182582I
a = 0
b = 0.877439 − 0.744862I
4.66906 + 2.82812I 4.21508 − 1.30714I
v = −0.539798 − 0.182582I
a = 0
b = 0.877439 + 0.744862I
4.66906 − 2.82812I 4.21508 + 1.30714I
v = 3.07960
a = 0
b = −0.754878
0.531480 4.56980
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
3
+ u
2
− 1)(u
28
− 7u
27
+ ··· − 5u + 1)
c
2
((u + 1)
5
)(u
3
+ u
2
+ 2u + 1)(u
28
+ 5u
27
+ ··· − 3u + 1)
c
3
u
5
(u
3
− u
2
+ 2u − 1)(u
28
− 2u
27
+ ··· − 24u
2
− 32)
c
4
((u + 1)
5
)(u
3
− u
2
+ 1)(u
28
− 7u
27
+ ··· − 5u + 1)
c
5
u
3
(u
5
+ u
4
+ ··· + u + 1)(u
28
+ 2u
27
+ ··· + 20u + 8)
c
6
u
5
(u
3
+ u
2
+ 2u + 1)(u
28
− 2u
27
+ ··· − 24u
2
− 32)
c
7
(u
3
− 3u
2
+ 2u + 1)(u
5
− 3u
4
+ ··· − u + 1)(u
28
+ 3u
27
+ ··· − u − 1)
c
8
((u + 1)
3
)(u
5
− u
4
+ ··· + u + 1)(u
28
+ 5u
27
+ ··· − 8u − 1)
c
9
u
3
(u
5
− u
4
+ ··· + u − 1)(u
28
+ 2u
27
+ ··· + 20u + 8)
c
10
, c
11
((u − 1)
3
)(u
5
+ u
4
+ ··· + u − 1)(u
28
+ 5u
27
+ ··· − 8u − 1)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y − 1)
5
)(y
3
− y
2
+ 2y − 1)(y
28
− 5y
27
+ ··· + 3y + 1)
c
2
((y − 1)
5
)(y
3
+ 3y
2
+ 2y − 1)(y
28
+ 43y
27
+ ··· + 3y + 1)
c
3
, c
6
y
5
(y
3
+ 3y
2
+ 2y − 1)(y
28
+ 36y
27
+ ··· + 1536y + 1024)
c
5
, c
9
y
3
(y
5
+ 3y
4
+ ··· − y − 1)(y
28
+ 24y
27
+ ··· − 848y + 64)
c
7
(y
3
− 5y
2
+ 10y − 1)(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
· (y
28
− 37y
27
+ ··· − 35y + 1)
c
8
, c
10
, c
11
((y − 1)
3
)(y
5
− 5y
4
+ ··· − y − 1)(y
28
− 31y
27
+ ··· − 128y + 1)
17
