11a
214
(K11a
214
)
A knot diagram
1
Linearized knot diagam
7 1 8 11 10 2 9 3 6 5 4
Solving Sequence
4,8
3
1,9
2 7 6 11 5 10
c
3
c
8
c
2
c
7
c
6
c
11
c
4
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
15
− u
14
+ 2u
13
− u
12
+ 5u
11
− 5u
10
+ 4u
9
− 2u
8
+ 7u
7
− 11u
6
+ 4u
5
− 4u
4
+ 5u
3
− 11u
2
+ 4b − 1,
− u
15
+ u
14
− 2u
13
+ u
12
− 5u
11
+ 5u
10
− 4u
9
+ 2u
8
− 7u
7
+ 11u
6
− 4u
5
− 5u
3
+ 7u
2
+ 4a − 3,
u
16
+ 3u
14
+ u
13
+ 8u
12
+ 2u
11
+ 11u
10
+ 4u
9
+ 15u
8
+ 2u
7
+ 13u
6
+ 2u
5
+ 11u
4
+ 5u
2
+ u + 1i
I
u
2
= h24532u
21
+ 99990u
20
+ ··· + 429733b + 160508,
1188174u
21
− 128444u
20
+ ··· + 2148665a + 5939931, u
22
− u
21
+ ··· − 6u + 5i
I
u
3
= hb + a + 1, a
2
− au + 2a − u + 2, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 42 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
= hu
15
−u
14
+· · ·+4b−1, −u
15
+u
14
+· · ·+4a−3, u
16
+3u
14
+· · ·+u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
1
=
1
4
u
15
−
1
4
u
14
+ ··· −
7
4
u
2
+
3
4
−
1
4
u
15
+
1
4
u
14
+ ··· +
11
4
u
2
+
1
4
a
9
=
u
u
3
+ u
a
2
=
1
4
u
15
−
1
4
u
14
+ ··· −
7
4
u
2
+
3
4
−
1
4
u
15
+
1
4
u
14
+ ··· +
7
4
u
2
+
1
4
a
7
=
u
3
u
5
+ u
3
+ u
a
6
=
1
4
u
15
+
1
4
u
14
+ ··· −
1
2
u +
1
4
−
1
4
u
15
−
1
4
u
14
+ ··· +
1
2
u −
1
4
a
11
=
u
4
+ u
2
+ 1
−
1
4
u
15
+
1
4
u
14
+ ··· +
11
4
u
2
+
1
4
a
5
=
−
1
4
u
15
+
1
4
u
14
+ ··· +
11
4
u
2
+
5
4
u
15
+
5
2
u
13
+ ··· + u −
1
2
a
10
=
1
4
u
15
+
3
4
u
14
+ ··· + u +
5
4
−
1
2
u
14
−
1
2
u
13
+ ··· −
5
2
u − 1
a
10
=
1
4
u
15
+
3
4
u
14
+ ··· + u +
5
4
−
1
2
u
14
−
1
2
u
13
+ ··· −
5
2
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
15
− 2u
14
+ 9u
13
− 2u
12
+ 21u
11
− 9u
10
+ 27u
9
− 8u
8
+ 32u
7
−
26u
6
+ 30u
5
− 17u
4
+ 23u
3
− 23u
2
+ 11u − 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
16
+ 3u
14
+ ··· − u + 1
c
2
, c
7
u
16
+ 6u
15
+ ··· + 9u + 1
c
4
, c
5
, c
9
c
10
, c
11
u
16
− 3u
15
+ ··· − 7u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
16
+ 6y
15
+ ··· + 9y + 1
c
2
, c
7
y
16
+ 14y
15
+ ··· + 13y + 1
c
4
, c
5
, c
9
c
10
, c
11
y
16
+ 21y
15
+ ··· + 23y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.739034 + 0.627334I
a = 0.206056 + 0.079796I
b = 0.110083 + 1.130490I
5.48130 + 1.05317I 4.45688 − 2.38990I
u = 0.739034 − 0.627334I
a = 0.206056 − 0.079796I
b = 0.110083 − 1.130490I
5.48130 − 1.05317I 4.45688 + 2.38990I
u = −0.555046 + 0.909908I
a = −0.752118 + 0.605011I
b = 0.482247 − 0.564899I
−0.19881 − 2.75301I −1.57245 + 2.26508I
u = −0.555046 − 0.909908I
a = −0.752118 − 0.605011I
b = 0.482247 + 0.564899I
−0.19881 + 2.75301I −1.57245 − 2.26508I
u = −0.926846 + 0.626361I
a = 0.304991 − 0.497485I
b = 0.03144 − 1.74738I
15.8152 − 0.4292I 4.82755 + 2.00465I
u = −0.926846 − 0.626361I
a = 0.304991 + 0.497485I
b = 0.03144 + 1.74738I
15.8152 + 0.4292I 4.82755 − 2.00465I
u = 0.317155 + 0.789225I
a = 0.47307 − 1.59041I
b = 0.02681 + 1.56809I
6.59915 + 1.30998I 1.95561 − 5.45778I
u = 0.317155 − 0.789225I
a = 0.47307 + 1.59041I
b = 0.02681 − 1.56809I
6.59915 − 1.30998I 1.95561 + 5.45778I
u = 0.596655 + 1.032140I
a = −1.346280 − 0.306488I
b = 0.623112 − 0.209109I
−1.29053 + 6.45307I −4.44807 − 7.45131I
u = 0.596655 − 1.032140I
a = −1.346280 + 0.306488I
b = 0.623112 + 0.209109I
−1.29053 − 6.45307I −4.44807 + 7.45131I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.652805 + 1.114230I
a = −1.64360 − 0.10173I
b = 0.376764 + 1.019230I
2.50481 − 9.84228I −0.10556 + 8.25112I
u = −0.652805 − 1.114230I
a = −1.64360 + 0.10173I
b = 0.376764 − 1.019230I
2.50481 + 9.84228I −0.10556 − 8.25112I
u = 0.691623 + 1.176670I
a = −1.83564 + 0.40291I
b = 0.10149 − 1.72523I
12.2077 + 11.7947I 0.96071 − 6.63599I
u = 0.691623 − 1.176670I
a = −1.83564 − 0.40291I
b = 0.10149 + 1.72523I
12.2077 − 11.7947I 0.96071 + 6.63599I
u = −0.209770 + 0.436269I
a = 1.093530 + 0.297205I
b = −0.251943 − 0.426672I
0.004513 − 0.990902I −0.07468 + 7.34190I
u = −0.209770 − 0.436269I
a = 1.093530 − 0.297205I
b = −0.251943 + 0.426672I
0.004513 + 0.990902I −0.07468 − 7.34190I
6
II. I
u
2
= h24532u
21
+ 99990u
20
+ · · · + 429733b + 160508, 1.19 × 10
6
u
21
−
1.28 × 10
5
u
20
+ · · · + 2.15 × 10
6
a + 5.94 × 10
6
, u
22
− u
21
+ · · · − 6u + 5i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
1
=
−0.552982u
21
+ 0.0597785u
20
+ ··· + 1.60210u − 2.76448
−0.0570866u
21
− 0.232679u
20
+ ··· + 0.277416u − 0.373506
a
9
=
u
u
3
+ u
a
2
=
−0.610069u
21
− 0.172901u
20
+ ··· + 1.87951u − 2.13798
−0.295974u
21
− 0.109836u
20
+ ··· − 0.426602u − 0.137709
a
7
=
u
3
u
5
+ u
3
+ u
a
6
=
−0.857671u
21
+ 1.08755u
20
+ ··· − 5.92382u + 3.22114
−0.358651u
21
+ 0.737100u
20
+ ··· − 1.13075u + 1.90093
a
11
=
−0.610069u
21
− 0.172901u
20
+ ··· + 1.87951u − 3.13798
−0.0570866u
21
− 0.232679u
20
+ ··· + 0.277416u − 0.373506
a
5
=
0.297712u
21
− 0.0832768u
20
+ ··· + 0.722951u − 1.80592
−0.0824745u
21
− 0.0617407u
20
+ ··· + 0.677572u − 1.65554
a
10
=
0.116673u
21
+ 0.386783u
20
+ ··· + 2.80778u + 0.179480
0.531833u
21
− 0.160528u
20
+ ··· + 2.45702u − 1.02872
a
10
=
0.116673u
21
+ 0.386783u
20
+ ··· + 2.80778u + 0.179480
0.531833u
21
− 0.160528u
20
+ ··· + 2.45702u − 1.02872
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
412776
429733
u
21
−
136152
429733
u
20
+ ··· +
1938508
429733
u −
1667194
429733
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
22
+ u
21
+ ··· + 6u + 5
c
2
, c
7
u
22
+ 11u
21
+ ··· + 124u + 25
c
4
, c
5
, c
9
c
10
, c
11
(u
11
+ u
10
+ 8u
9
+ 7u
8
+ 22u
7
+ 16u
6
+ 24u
5
+ 13u
4
+ 9u
3
+ 3u
2
− 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
22
+ 11y
21
+ ··· + 124y + 25
c
2
, c
7
y
22
− y
21
+ ··· + 4824y + 625
c
4
, c
5
, c
9
c
10
, c
11
(y
11
+ 15y
10
+ ··· + 6y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.579803 + 0.857238I
a = −1.85524 − 1.12681I
b = 0.03037 − 1.69780I
7.95553 + 2.30219I 0.32022 − 2.86330I
u = 0.579803 − 0.857238I
a = −1.85524 + 1.12681I
b = 0.03037 + 1.69780I
7.95553 − 2.30219I 0.32022 + 2.86330I
u = −0.399913 + 0.875160I
a = −1.65574 + 0.96794I
b = 0.147502 + 0.884325I
−1.26759 − 1.65848I −0.54419 + 4.72916I
u = −0.399913 − 0.875160I
a = −1.65574 − 0.96794I
b = 0.147502 − 0.884325I
−1.26759 + 1.65848I −0.54419 − 4.72916I
u = −0.529162 + 0.802687I
a = 1.204780 − 0.193673I
b = −0.499488 − 0.319159I
0.18031 − 1.62554I −1.42199 + 3.91435I
u = −0.529162 − 0.802687I
a = 1.204780 + 0.193673I
b = −0.499488 + 0.319159I
0.18031 + 1.62554I −1.42199 − 3.91435I
u = −0.848321 + 0.450725I
a = 0.353490 + 0.072972I
b = −0.275765 + 1.061690I
4.47712 + 4.26374I 2.95029 − 4.02329I
u = −0.848321 − 0.450725I
a = 0.353490 − 0.072972I
b = −0.275765 − 1.061690I
4.47712 − 4.26374I 2.95029 + 4.02329I
u = 0.197868 + 1.057100I
a = −1.010600 − 0.780021I
b = 0.337740
−3.92670 −11.69818 + 0.I
u = 0.197868 − 1.057100I
a = −1.010600 + 0.780021I
b = 0.337740
−3.92670 −11.69818 + 0.I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.986171 + 0.439556I
a = 0.194359 − 0.406737I
b = −0.07149 − 1.73688I
14.4695 − 5.6984I 3.54476 + 2.83577I
u = 0.986171 − 0.439556I
a = 0.194359 + 0.406737I
b = −0.07149 + 1.73688I
14.4695 + 5.6984I 3.54476 − 2.83577I
u = 0.662778 + 0.976432I
a = 1.42879 + 0.04455I
b = −0.275765 + 1.061690I
4.47712 + 4.26374I 2.95029 − 4.02329I
u = 0.662778 − 0.976432I
a = 1.42879 − 0.04455I
b = −0.275765 − 1.061690I
4.47712 − 4.26374I 2.95029 + 4.02329I
u = 0.610796 + 0.518790I
a = 0.780853 + 0.341379I
b = −0.499488 − 0.319159I
0.18031 − 1.62554I −1.42199 + 3.91435I
u = 0.610796 − 0.518790I
a = 0.780853 − 0.341379I
b = −0.499488 + 0.319159I
0.18031 + 1.62554I −1.42199 − 3.91435I
u = −0.125296 + 1.244620I
a = −0.270054 + 1.088140I
b = 0.147502 − 0.884325I
−1.26759 + 1.65848I −0.54419 − 4.72916I
u = −0.125296 − 1.244620I
a = −0.270054 − 1.088140I
b = 0.147502 + 0.884325I
−1.26759 − 1.65848I −0.54419 + 4.72916I
u = −0.746289 + 1.064200I
a = 1.62058 + 0.05160I
b = −0.07149 − 1.73688I
14.4695 − 5.6984I 3.54476 + 2.83577I
u = −0.746289 − 1.064200I
a = 1.62058 − 0.05160I
b = −0.07149 + 1.73688I
14.4695 + 5.6984I 3.54476 − 2.83577I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111564 + 1.357150I
a = 0.00879 − 1.46999I
b = 0.03037 + 1.69780I
7.95553 − 2.30219I 0.32022 + 2.86330I
u = 0.111564 − 1.357150I
a = 0.00879 + 1.46999I
b = 0.03037 − 1.69780I
7.95553 + 2.30219I 0.32022 − 2.86330I
12
III. I
u
3
= hb + a + 1, a
2
− au + 2a − u + 2, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
−1
a
1
=
a
−a − 1
a
9
=
u
0
a
2
=
a + 1
−a − 2
a
7
=
−u
u
a
6
=
au
−au − u
a
11
=
−1
−a − 1
a
5
=
a + 2
au + u − 1
a
10
=
−au − a − u − 1
a + u + 1
a
10
=
−au − a − u − 1
a + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
(u
2
+ 1)
2
c
2
(u + 1)
4
c
4
, c
5
, c
9
c
10
, c
11
u
4
+ 3u
2
+ 1
c
7
(u − 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
(y + 1)
4
c
2
, c
7
(y −1)
4
c
4
, c
5
, c
9
c
10
, c
11
(y
2
+ 3y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.000000 − 0.618034I
b = 0.618034I
−2.30291 −4.00000
u = 1.000000I
a = −1.00000 + 1.61803I
b = − 1.61803I
5.59278 −4.00000
u = − 1.000000I
a = −1.000000 + 0.618034I
b = − 0.618034I
−2.30291 −4.00000
u = − 1.000000I
a = −1.00000 − 1.61803I
b = 1.61803I
5.59278 −4.00000
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
((u
2
+ 1)
2
)(u
16
+ 3u
14
+ ··· − u + 1)(u
22
+ u
21
+ ··· + 6u + 5)
c
2
((u + 1)
4
)(u
16
+ 6u
15
+ ··· + 9u + 1)(u
22
+ 11u
21
+ ··· + 124u + 25)
c
4
, c
5
, c
9
c
10
, c
11
(u
4
+ 3u
2
+ 1)
· (u
11
+ u
10
+ 8u
9
+ 7u
8
+ 22u
7
+ 16u
6
+ 24u
5
+ 13u
4
+ 9u
3
+ 3u
2
− 1)
2
· (u
16
− 3u
15
+ ··· − 7u + 2)
c
7
((u − 1)
4
)(u
16
+ 6u
15
+ ··· + 9u + 1)(u
22
+ 11u
21
+ ··· + 124u + 25)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
((y + 1)
4
)(y
16
+ 6y
15
+ ··· + 9y + 1)(y
22
+ 11y
21
+ ··· + 124y + 25)
c
2
, c
7
((y −1)
4
)(y
16
+ 14y
15
+ ··· + 13y + 1)(y
22
− y
21
+ ··· + 4824y + 625)
c
4
, c
5
, c
9
c
10
, c
11
((y
2
+ 3y + 1)
2
)(y
11
+ 15y
10
+ ··· + 6y −1)
2
· (y
16
+ 21y
15
+ ··· + 23y + 4)
18
