11a
46
(K11a
46
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 9 3 7 6 5 10
Solving Sequence
6,11 2,5
4 10 1 3 9 7 8
c
5
c
4
c
10
c
11
c
2
c
9
c
6
c
8
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
15
− u
14
+ 3u
13
+ 4u
12
− 4u
11
− 7u
10
− u
9
+ 4u
8
+ 4u
7
+ 2u
6
− 4u
5
− 4u
4
− u
3
+ u
2
+ b,
u
15
+ u
14
− 3u
13
− 4u
12
+ 4u
11
+ 7u
10
+ u
9
− 4u
8
− 4u
7
− 2u
6
+ 4u
5
+ 4u
4
+ 2u
3
− u
2
+ a,
u
16
+ u
15
− 4u
14
− 5u
13
+ 7u
12
+ 11u
11
− 3u
10
− 11u
9
− 5u
8
+ 2u
7
+ 8u
6
+ 6u
5
− 2u
4
− 5u
3
− u
2
+ u + 1i
I
u
2
= h−u
26
+ 8u
24
+ ··· + 3u
2
+ b, 2u
27
+ u
26
+ ··· + a − 3, u
28
+ u
27
+ ··· − 2u − 1i
I
u
3
= hb − 1, a + 2, 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
= h−u
15
−u
14
+· · · +u
2
+b, u
15
+u
14
+· · · −u
2
+a, u
16
+u
15
+· · · +u +1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−u
15
− u
14
+ ··· − 2u
3
+ u
2
u
15
+ u
14
+ ··· + u
3
− u
2
a
5
=
1
−u
2
a
4
=
u
14
+ u
13
+ ··· + u
2
− u
−u
14
− u
13
+ ··· + u + 1
a
10
=
u
−u
3
+ u
a
1
=
−u
3
u
5
− u
3
+ u
a
3
=
−u
15
− u
14
+ ··· − 2u
3
+ u
2
u
15
+ u
14
+ ··· + 4u
4
− u
2
a
9
=
u
3
−u
3
+ u
a
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
15
+ 6u
14
− 6u
13
− 24u
12
+ 4u
11
+ 46u
10
+ 14u
9
− 32u
8
−
28u
7
− 4u
6
+ 16u
5
+ 32u
4
+ 4u
3
− 10u
2
− 10u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
16
− u
15
+ ··· − u + 1
c
2
, c
11
u
16
+ 9u
15
+ ··· + 3u + 1
c
3
, c
7
u
16
+ 3u
15
+ ··· + 2u + 2
c
6
, c
8
, c
9
u
16
− 3u
15
+ ··· − 11u
2
+ 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
16
− 9y
15
+ ··· − 3y + 1
c
2
, c
11
y
16
− y
15
+ ··· + 5y + 1
c
3
, c
7
y
16
− 3y
15
+ ··· − 11y
2
+ 4
c
6
, c
8
, c
9
y
16
+ 17y
15
+ ··· − 88y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807171 + 0.504072I
a = −0.65855 − 1.36972I
b = 0.569167 + 0.512553I
1.82651 + 4.13679I 2.56414 − 7.87070I
u = −0.807171 − 0.504072I
a = −0.65855 + 1.36972I
b = 0.569167 − 0.512553I
1.82651 − 4.13679I 2.56414 + 7.87070I
u = 1.048260 + 0.400216I
a = 1.81547 − 2.15452I
b = −2.46363 + 0.89931I
−4.21490 − 4.31562I −7.10271 + 5.64590I
u = 1.048260 − 0.400216I
a = 1.81547 + 2.15452I
b = −2.46363 − 0.89931I
−4.21490 + 4.31562I −7.10271 − 5.64590I
u = −0.034491 + 0.874872I
a = −0.0293241 − 0.1171040I
b = −0.049834 + 0.783610I
−5.17406 − 3.14776I −1.28039 + 2.42611I
u = −0.034491 − 0.874872I
a = −0.0293241 + 0.1171040I
b = −0.049834 − 0.783610I
−5.17406 + 3.14776I −1.28039 − 2.42611I
u = −1.079150 + 0.504952I
a = −1.83629 − 1.53825I
b = 2.26756 − 0.09714I
−2.62432 + 9.39287I −3.86862 − 9.95391I
u = −1.079150 − 0.504952I
a = −1.83629 + 1.53825I
b = 2.26756 + 0.09714I
−2.62432 − 9.39287I −3.86862 + 9.95391I
u = 0.735290 + 0.237976I
a = −0.78828 − 1.71780I
b = 0.51567 + 1.34529I
−1.32039 − 1.29101I −3.35201 + 4.88471I
u = 0.735290 − 0.237976I
a = −0.78828 + 1.71780I
b = 0.51567 − 1.34529I
−1.32039 + 1.29101I −3.35201 − 4.88471I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.255070 + 0.472625I
a = 2.56417 − 1.25500I
b = −3.70009 − 0.87285I
−12.8673 − 6.3576I −8.01117 + 3.79413I
u = 1.255070 − 0.472625I
a = 2.56417 + 1.25500I
b = −3.70009 + 0.87285I
−12.8673 + 6.3576I −8.01117 − 3.79413I
u = −1.258180 + 0.499599I
a = −2.49673 − 1.17352I
b = 3.54634 − 1.07442I
−12.4913 + 13.0634I −7.30770 − 8.20106I
u = −1.258180 − 0.499599I
a = −2.49673 + 1.17352I
b = 3.54634 + 1.07442I
−12.4913 − 13.0634I −7.30770 + 8.20106I
u = −0.359617 + 0.529211I
a = −0.070464 − 0.486206I
b = −0.185176 + 0.429100I
1.49968 − 0.85752I 4.35846 + 1.06718I
u = −0.359617 − 0.529211I
a = −0.070464 + 0.486206I
b = −0.185176 − 0.429100I
1.49968 + 0.85752I 4.35846 − 1.06718I
6
II.
I
u
2
= h−u
26
+8u
24
+· · ·+3u
2
+b, 2u
27
+u
26
+· · ·+a−3, u
28
+u
27
+· · ·−2u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−2u
27
− u
26
+ ··· + 4u + 3
u
26
− 8u
24
+ ··· − 4u
3
− 3u
2
a
5
=
1
−u
2
a
4
=
2u
27
− 17u
25
+ ··· − 5u − 3
u
25
− 7u
23
+ ··· + 4u
2
+ u
a
10
=
u
−u
3
+ u
a
1
=
−u
3
u
5
− u
3
+ u
a
3
=
−2u
27
+ 16u
25
+ ··· + 5u + 3
u
22
− 6u
20
+ ··· − 3u
2
− u
a
9
=
u
3
−u
3
+ u
a
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
24
− 28u
22
− 4u
21
+ 88u
20
+ 24u
19
− 140u
18
− 64u
17
+ 80u
16
+ 80u
15
+ 96u
14
−
20u
13
−188u
12
−72u
11
+ 80u
10
+ 76u
9
+ 60u
8
−8u
7
−56u
6
−28u
5
+ 4u
4
+ 8u
3
+ 8u
2
−2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
28
− u
27
+ ··· + 2u − 1
c
2
, c
11
u
28
+ 17u
27
+ ··· − 4u + 1
c
3
, c
7
(u
14
− u
13
+ ··· − u − 1)
2
c
6
, c
8
, c
9
(u
14
− 3u
13
+ ··· − 5u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
28
− 17y
27
+ ··· + 4y + 1
c
2
, c
11
y
28
− 13y
27
+ ··· − 28y + 1
c
3
, c
7
(y
14
− 3y
13
+ ··· − 5y + 1)
2
c
6
, c
8
, c
9
(y
14
+ 17y
13
+ ··· − y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.997731 + 0.254321I
a = −0.812406 − 0.190507I
b = 0.788217 + 0.159208I
−1.87700 − 0.85224I −4.40198 + 0.38712I
u = 0.997731 − 0.254321I
a = −0.812406 + 0.190507I
b = 0.788217 − 0.159208I
−1.87700 + 0.85224I −4.40198 − 0.38712I
u = −0.053235 + 0.909759I
a = −1.181850 + 0.612019I
b = −2.28006 − 0.09309I
−8.82756 − 8.01486I −4.36796 + 5.37427I
u = −0.053235 − 0.909759I
a = −1.181850 − 0.612019I
b = −2.28006 + 0.09309I
−8.82756 + 8.01486I −4.36796 − 5.37427I
u = −1.051200 + 0.342720I
a = 2.04075 + 0.52134I
b = −1.21015 + 1.19657I
−4.64212 + 1.98638I −7.34408 − 5.08636I
u = −1.051200 − 0.342720I
a = 2.04075 − 0.52134I
b = −1.21015 − 1.19657I
−4.64212 − 1.98638I −7.34408 + 5.08636I
u = −1.013550 + 0.462956I
a = 0.550084 − 0.313876I
b = −0.418870 + 0.084661I
−0.31026 + 4.88256I −0.31401 − 6.44337I
u = −1.013550 − 0.462956I
a = 0.550084 + 0.313876I
b = −0.418870 − 0.084661I
−0.31026 − 4.88256I −0.31401 + 6.44337I
u = 0.009396 + 0.884908I
a = 1.24317 + 0.68253I
b = 2.23988 + 0.06633I
−9.09089 + 1.51934I −4.87778 − 0.64840I
u = 0.009396 − 0.884908I
a = 1.24317 − 0.68253I
b = 2.23988 − 0.06633I
−9.09089 − 1.51934I −4.87778 + 0.64840I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13074
a = −1.65240
b = 1.34469
−2.55923 2.09270
u = −0.644858 + 0.497518I
a = 0.327243 + 0.252473I
b = −0.861939 − 0.330036I
2.27008 4.70520 + 0.I
u = −0.644858 − 0.497518I
a = 0.327243 − 0.252473I
b = −0.861939 + 0.330036I
2.27008 4.70520 + 0.I
u = 1.180860 + 0.240994I
a = −1.86418 + 0.50864I
b = 1.72950 + 0.72402I
−4.64212 + 1.98638I −7.34408 − 5.08636I
u = 1.180860 − 0.240994I
a = −1.86418 − 0.50864I
b = 1.72950 − 0.72402I
−4.64212 − 1.98638I −7.34408 + 5.08636I
u = −0.768027
a = 2.43278
b = −0.304273
−2.55923 2.09270
u = −0.266232 + 0.686741I
a = −0.522796 + 0.802943I
b = −1.51666 − 0.33236I
−0.31026 − 4.88256I −0.31401 + 6.44337I
u = −0.266232 − 0.686741I
a = −0.522796 − 0.802943I
b = −1.51666 + 0.33236I
−0.31026 + 4.88256I −0.31401 − 6.44337I
u = 1.255170 + 0.447404I
a = −0.697496 − 0.632935I
b = 0.257772 + 0.768928I
−9.09089 − 1.51934I −4.87778 + 0.64840I
u = 1.255170 − 0.447404I
a = −0.697496 + 0.632935I
b = 0.257772 − 0.768928I
−9.09089 + 1.51934I −4.87778 − 0.64840I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.245950 + 0.483423I
a = 0.644350 − 0.639100I
b = −0.133052 + 0.709234I
−8.82756 + 8.01486I −4.36796 − 5.37427I
u = −1.245950 − 0.483423I
a = 0.644350 + 0.639100I
b = −0.133052 − 0.709234I
−8.82756 − 8.01486I −4.36796 + 5.37427I
u = −1.257930 + 0.462599I
a = 1.97998 + 0.69687I
b = −2.24068 + 1.79013I
−12.94110 + 3.26499I −8.09314 − 2.49004I
u = −1.257930 − 0.462599I
a = 1.97998 − 0.69687I
b = −2.24068 − 1.79013I
−12.94110 − 3.26499I −8.09314 + 2.49004I
u = 1.279730 + 0.439354I
a = −1.95695 + 0.70259I
b = 2.35927 + 1.64819I
−12.94110 + 3.26499I −8.09314 − 2.49004I
u = 1.279730 − 0.439354I
a = −1.95695 − 0.70259I
b = 2.35927 − 1.64819I
−12.94110 − 3.26499I −8.09314 + 2.49004I
u = 0.128720 + 0.430400I
a = 0.35991 + 1.87835I
b = 1.266560 + 0.022630I
−1.87700 + 0.85224I −4.40198 − 0.38712I
u = 0.128720 − 0.430400I
a = 0.35991 − 1.87835I
b = 1.266560 − 0.022630I
−1.87700 − 0.85224I −4.40198 + 0.38712I
12
III. I
u
3
= hb − 1, a + 2, u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
1
a
2
=
−2
1
a
5
=
1
−1
a
4
=
−1
0
a
10
=
1
0
a
1
=
−1
1
a
3
=
−1
0
a
9
=
1
0
a
7
=
1
0
a
8
=
1
0
a
8
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u − 1
c
2
, c
4
, c
10
c
11
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
, c
11
y −1
c
3
, c
6
, c
7
c
8
, c
9
y
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.00000
b = 1.00000
−3.28987 −12.0000
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)(u
16
− u
15
+ ··· − u + 1)(u
28
− u
27
+ ··· + 2u − 1)
c
2
, c
11
(u + 1)(u
16
+ 9u
15
+ ··· + 3u + 1)(u
28
+ 17u
27
+ ··· − 4u + 1)
c
3
, c
7
u(u
14
− u
13
+ ··· − u − 1)
2
(u
16
+ 3u
15
+ ··· + 2u + 2)
c
4
, c
10
(u + 1)(u
16
− u
15
+ ··· − u + 1)(u
28
− u
27
+ ··· + 2u − 1)
c
6
, c
8
, c
9
u(u
14
− 3u
13
+ ··· − 5u + 1)
2
(u
16
− 3u
15
+ ··· − 11u
2
+ 4)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
(y −1)(y
16
− 9y
15
+ ··· − 3y + 1)(y
28
− 17y
27
+ ··· + 4y + 1)
c
2
, c
11
(y −1)(y
16
− y
15
+ ··· + 5y + 1)(y
28
− 13y
27
+ ··· − 28y + 1)
c
3
, c
7
y(y
14
− 3y
13
+ ··· − 5y + 1)
2
(y
16
− 3y
15
+ ··· − 11y
2
+ 4)
c
6
, c
8
, c
9
y(y
14
+ 17y
13
+ ··· − y + 1)
2
(y
16
+ 17y
15
+ ··· − 88y + 16)
18
