11a
61
(K11a
61
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 4 11 10 3 6 7 9
Solving Sequence
1,5
2 3 4
6,9
8 11 7 10
c
1
c
2
c
4
c
5
c
8
c
11
c
6
c
10
c
3
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8u
56
− 9u
55
+ ··· + 4b − 7, 11u
56
− 40u
55
+ ··· + 4a + 1, u
57
− 4u
56
+ ··· + 7u − 1i
I
u
2
= h−au + b, a
3
+ a
2
u + a
2
+ 1, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 63 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
=
h8u
56
−9u
55
+· · ·+4b−7, 11u
56
−40u
55
+· · ·+4a+1, u
57
−4u
56
+· · ·+7u−1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
4
=
−u
u
3
+ u
a
6
=
−u
3
u
5
+ u
3
+ u
a
9
=
−
11
4
u
56
+ 10u
55
+ ··· +
67
4
u −
1
4
−2u
56
+
9
4
u
55
+ ··· − 11u +
7
4
a
8
=
−
9
4
u
56
+ 16u
55
+ ··· +
189
4
u −
23
4
−7u
56
+
55
4
u
55
+ ··· − 10u +
9
4
a
11
=
−
1
4
u
56
+
3
4
u
55
+ ··· +
13
4
u + 2
1
4
u
56
− u
55
+ ··· −
11
4
u +
1
4
a
7
=
11
4
u
56
−
47
4
u
55
+ ··· −
121
4
u + 4
3
4
u
56
+
1
4
u
55
+ ··· +
59
4
u −
5
2
a
10
=
−
7
4
u
56
+
63
4
u
55
+ ··· +
223
4
u − 7
−7u
56
+
57
4
u
55
+ ··· − 12u +
11
4
a
10
=
−
7
4
u
56
+
63
4
u
55
+ ··· +
223
4
u − 7
−7u
56
+
57
4
u
55
+ ··· − 12u +
11
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
56
+
25
2
u
55
+ ··· − 20u − 7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
57
+ 4u
56
+ ··· + 7u + 1
c
2
, c
5
u
57
+ 18u
56
+ ··· + 23u − 1
c
3
, c
8
u
57
+ u
56
+ ··· + 160u + 64
c
6
, c
7
, c
10
u
57
− 3u
56
+ ··· − 6u + 1
c
9
u
57
+ 3u
56
+ ··· − 624u + 73
c
11
u
57
− 11u
56
+ ··· − 2040u + 209
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
57
+ 18y
56
+ ··· + 23y −1
c
2
, c
5
y
57
+ 46y
56
+ ··· + 1015y −1
c
3
, c
8
y
57
+ 35y
56
+ ··· − 39936y −4096
c
6
, c
7
, c
10
y
57
+ 53y
56
+ ··· + 6y −1
c
9
y
57
+ 9y
56
+ ··· − 41762y −5329
c
11
y
57
+ 29y
56
+ ··· − 624082y −43681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.411000 + 0.945370I
a = 0.758571 + 0.375458I
b = −0.159926 + 0.346294I
−0.43337 − 1.68301I −2.91269 + 0.I
u = −0.411000 − 0.945370I
a = 0.758571 − 0.375458I
b = −0.159926 − 0.346294I
−0.43337 + 1.68301I −2.91269 + 0.I
u = −0.070350 + 0.957209I
a = 0.843157 + 0.528242I
b = 1.012250 + 0.111658I
−0.22072 − 2.23623I −9.39240 + 3.87464I
u = −0.070350 − 0.957209I
a = 0.843157 − 0.528242I
b = 1.012250 − 0.111658I
−0.22072 + 2.23623I −9.39240 − 3.87464I
u = −0.294254 + 0.900156I
a = 0.889838 + 0.254291I
b = 0.192184 + 0.303495I
−0.43103 − 1.63888I −4.79988 + 2.71199I
u = −0.294254 − 0.900156I
a = 0.889838 − 0.254291I
b = 0.192184 − 0.303495I
−0.43103 + 1.63888I −4.79988 − 2.71199I
u = 0.716145 + 0.819187I
a = −0.945498 + 0.434435I
b = 1.40998 + 0.63877I
4.56397 − 1.17086I 0
u = 0.716145 − 0.819187I
a = −0.945498 − 0.434435I
b = 1.40998 − 0.63877I
4.56397 + 1.17086I 0
u = −0.722279 + 0.830660I
a = 1.00866 − 1.56975I
b = −0.112045 + 0.922007I
1.73223 − 1.00864I −7.00000 + 0.I
u = −0.722279 − 0.830660I
a = 1.00866 + 1.56975I
b = −0.112045 − 0.922007I
1.73223 + 1.00864I −7.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.221111 + 1.079490I
a = −0.821842 − 0.181447I
b = −0.613293 − 1.011210I
−1.42166 − 4.84212I −7.00000 + 7.62059I
u = −0.221111 − 1.079490I
a = −0.821842 + 0.181447I
b = −0.613293 + 1.011210I
−1.42166 + 4.84212I −7.00000 − 7.62059I
u = 0.864422 + 0.721606I
a = 0.74235 + 1.40599I
b = −0.62330 − 1.47673I
5.87637 − 4.55093I 0
u = 0.864422 − 0.721606I
a = 0.74235 − 1.40599I
b = −0.62330 + 1.47673I
5.87637 + 4.55093I 0
u = 0.710335 + 0.874003I
a = 0.541401 − 0.977846I
b = −1.50306 − 0.11683I
0.69484 + 2.72065I 0
u = 0.710335 − 0.874003I
a = 0.541401 + 0.977846I
b = −1.50306 + 0.11683I
0.69484 − 2.72065I 0
u = −0.782668 + 0.823558I
a = −1.38003 + 1.86072I
b = 0.318434 − 1.211320I
7.55130 + 1.74072I 0
u = −0.782668 − 0.823558I
a = −1.38003 − 1.86072I
b = 0.318434 + 1.211320I
7.55130 − 1.74072I 0
u = 0.846418 + 0.761999I
a = −0.471724 − 1.032250I
b = 0.571036 + 1.197990I
6.72836 − 0.26468I 0
u = 0.846418 − 0.761999I
a = −0.471724 + 1.032250I
b = 0.571036 − 1.197990I
6.72836 + 0.26468I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.892838 + 0.709779I
a = −0.72817 − 1.72293I
b = 0.54713 + 1.65321I
11.7431 − 8.1696I 0
u = 0.892838 − 0.709779I
a = −0.72817 + 1.72293I
b = 0.54713 − 1.65321I
11.7431 + 8.1696I 0
u = −0.579065 + 0.988208I
a = −0.527800 − 1.214050I
b = 0.733184 + 0.166462I
2.70688 − 3.25300I 0
u = −0.579065 − 0.988208I
a = −0.527800 + 1.214050I
b = 0.733184 − 0.166462I
2.70688 + 3.25300I 0
u = 0.046272 + 0.846532I
a = −1.18927 − 0.76890I
b = −0.905005 + 0.577259I
−2.85410 + 0.74308I −13.57323 − 1.00600I
u = 0.046272 − 0.846532I
a = −1.18927 + 0.76890I
b = −0.905005 − 0.577259I
−2.85410 − 0.74308I −13.57323 + 1.00600I
u = −0.234257 + 1.130480I
a = 0.840745 + 0.057014I
b = 0.59116 + 1.34495I
4.07584 − 8.10637I 0
u = −0.234257 − 1.130480I
a = 0.840745 − 0.057014I
b = 0.59116 − 1.34495I
4.07584 + 8.10637I 0
u = −0.386185 + 1.092590I
a = −1.129960 − 0.354062I
b = 0.360548 − 1.019790I
5.00981 + 0.63384I 0
u = −0.386185 − 1.092590I
a = −1.129960 + 0.354062I
b = 0.360548 + 1.019790I
5.00981 − 0.63384I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718160 + 0.909667I
a = −0.49430 + 1.92093I
b = −0.337710 − 1.036600I
1.48928 − 4.49756I 0
u = −0.718160 − 0.909667I
a = −0.49430 − 1.92093I
b = −0.337710 + 1.036600I
1.48928 + 4.49756I 0
u = 0.711635 + 0.923729I
a = −0.071999 + 1.393300I
b = 1.46379 − 0.43402I
4.23779 + 6.64103I 0
u = 0.711635 − 0.923729I
a = −0.071999 − 1.393300I
b = 1.46379 + 0.43402I
4.23779 − 6.64103I 0
u = 0.145913 + 0.817129I
a = 1.44787 + 1.01076I
b = 0.884513 − 1.043560I
1.92041 + 4.01720I −8.21820 − 1.67425I
u = 0.145913 − 0.817129I
a = 1.44787 − 1.01076I
b = 0.884513 + 1.043560I
1.92041 − 4.01720I −8.21820 + 1.67425I
u = −0.610136 + 0.543922I
a = −1.393620 + 0.207735I
b = 0.544710 + 0.046272I
3.98401 − 1.43384I −1.02074 + 3.18853I
u = −0.610136 − 0.543922I
a = −1.393620 − 0.207735I
b = 0.544710 − 0.046272I
3.98401 + 1.43384I −1.02074 − 3.18853I
u = 0.880016 + 0.800315I
a = −0.098223 + 1.121400I
b = −0.203921 − 1.080730I
13.50000 + 2.10845I 0
u = 0.880016 − 0.800315I
a = −0.098223 − 1.121400I
b = −0.203921 + 1.080730I
13.50000 − 2.10845I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.800227 + 0.097770I
a = −0.55703 − 1.38837I
b = 0.340559 + 1.293110I
8.22007 − 4.72575I 1.80987 + 3.60964I
u = −0.800227 − 0.097770I
a = −0.55703 + 1.38837I
b = 0.340559 − 1.293110I
8.22007 + 4.72575I 1.80987 − 3.60964I
u = −0.755939 + 0.930694I
a = 0.52607 − 2.29910I
b = 0.425194 + 1.323000I
7.22101 − 7.54444I 0
u = −0.755939 − 0.930694I
a = 0.52607 + 2.29910I
b = 0.425194 − 1.323000I
7.22101 + 7.54444I 0
u = 0.766562 + 0.991374I
a = 0.96808 + 1.47841I
b = 0.729701 − 1.117910I
6.01697 + 6.28313I 0
u = 0.766562 − 0.991374I
a = 0.96808 − 1.47841I
b = 0.729701 + 1.117910I
6.01697 − 6.28313I 0
u = 0.759691 + 1.020250I
a = −1.13322 − 1.78580I
b = −0.76006 + 1.47046I
4.95411 + 10.59560I 0
u = 0.759691 − 1.020250I
a = −1.13322 + 1.78580I
b = −0.76006 − 1.47046I
4.95411 − 10.59560I 0
u = 0.806919 + 0.984385I
a = −1.27465 − 1.07750I
b = −0.272115 + 0.948431I
12.92480 + 4.14012I 0
u = 0.806919 − 0.984385I
a = −1.27465 + 1.07750I
b = −0.272115 − 0.948431I
12.92480 − 4.14012I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708895 + 0.073284I
a = 0.351150 + 0.941533I
b = −0.192151 − 1.042080I
2.36739 − 1.80456I −1.57677 + 4.11913I
u = −0.708895 − 0.073284I
a = 0.351150 − 0.941533I
b = −0.192151 + 1.042080I
2.36739 + 1.80456I −1.57677 − 4.11913I
u = 0.767113 + 1.038140I
a = 1.33064 + 1.89314I
b = 0.64323 − 1.67431I
10.7235 + 14.3183I 0
u = 0.767113 − 1.038140I
a = 1.33064 − 1.89314I
b = 0.64323 + 1.67431I
10.7235 − 14.3183I 0
u = 0.293144 + 0.279322I
a = −2.67050 − 0.08527I
b = 0.668951 + 0.608073I
3.36777 − 2.26311I −4.02051 + 3.80459I
u = 0.293144 − 0.279322I
a = −2.67050 + 0.08527I
b = 0.668951 − 0.608073I
3.36777 + 2.26311I −4.02051 − 3.80459I
u = 0.174207
a = 3.27862
b = −0.507940
−0.822844 −12.1160
10
II. I
u
2
= h−au + b, a
3
+ a
2
u + a
2
+ 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
4
=
−u
u + 1
a
6
=
−1
0
a
9
=
a
au
a
8
=
a
au
a
11
=
−a
2
u + 1
a
2
u + a
2
a
7
=
−2a
2
u − a
2
+ a − u − 2
a
2
u + a
2
+ au + 1
a
10
=
−au + a
au
a
10
=
−au + a
au
(ii) Obstruction class = 1
(iii) Cusp Shapes = a
2
u + 5au + a + 5u − 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
8
u
6
c
4
(u
2
− u + 1)
3
c
6
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
9
, c
11
(u
3
− u
2
+ 1)
2
c
10
(u
3
+ u
2
+ 2u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
8
y
6
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
11
(y
3
− y
2
+ 2y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.083790 − 0.387453I
b = 0.877439 − 0.744862I
3.02413 + 0.79824I −6.43615 + 0.68567I
u = −0.500000 + 0.866025I
a = 0.206350 − 1.132320I
b = 0.877439 + 0.744862I
3.02413 − 4.85801I −2.88198 + 6.08229I
u = −0.500000 + 0.866025I
a = 0.377439 + 0.653743I
b = −0.754878
−1.11345 − 2.02988I −12.18187 + 4.49037I
u = −0.500000 − 0.866025I
a = −1.083790 + 0.387453I
b = 0.877439 + 0.744862I
3.02413 − 0.79824I −6.43615 − 0.68567I
u = −0.500000 − 0.866025I
a = 0.206350 + 1.132320I
b = 0.877439 − 0.744862I
3.02413 + 4.85801I −2.88198 − 6.08229I
u = −0.500000 − 0.866025I
a = 0.377439 − 0.653743I
b = −0.754878
−1.11345 + 2.02988I −12.18187 − 4.49037I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
57
+ 4u
56
+ ··· + 7u + 1)
c
2
, c
5
((u
2
+ u + 1)
3
)(u
57
+ 18u
56
+ ··· + 23u − 1)
c
3
, c
8
u
6
(u
57
+ u
56
+ ··· + 160u + 64)
c
4
((u
2
− u + 1)
3
)(u
57
+ 4u
56
+ ··· + 7u + 1)
c
6
, c
7
((u
3
− u
2
+ 2u − 1)
2
)(u
57
− 3u
56
+ ··· − 6u + 1)
c
9
((u
3
− u
2
+ 1)
2
)(u
57
+ 3u
56
+ ··· − 624u + 73)
c
10
((u
3
+ u
2
+ 2u + 1)
2
)(u
57
− 3u
56
+ ··· − 6u + 1)
c
11
((u
3
− u
2
+ 1)
2
)(u
57
− 11u
56
+ ··· − 2040u + 209)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
57
+ 18y
56
+ ··· + 23y −1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
57
+ 46y
56
+ ··· + 1015y −1)
c
3
, c
8
y
6
(y
57
+ 35y
56
+ ··· − 39936y −4096)
c
6
, c
7
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
57
+ 53y
56
+ ··· + 6y −1)
c
9
((y
3
− y
2
+ 2y −1)
2
)(y
57
+ 9y
56
+ ··· − 41762y −5329)
c
11
((y
3
− y
2
+ 2y −1)
2
)(y
57
+ 29y
56
+ ··· − 624082y −43681)
16
