11a
361
(K11a
361
)
A knot diagram
1
Linearized knot diagam
8 7 9 1 11 10 2 4 3 5 6
Solving Sequence
5,10
11 6 7
1,3
2 4 9 8
c
10
c
5
c
6
c
11
c
2
c
4
c
9
c
8
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
17
+ 2u
16
+ ··· + b − 1, −5u
17
+ 9u
16
+ ··· + 2a − 7, u
18
− 3u
17
+ ··· − 7u − 2i
I
u
2
= hu
10
a − u
10
+ ··· + 2a − 1, 2u
10
a − u
10
+ ··· + a − 3,
u
11
+ u
10
− 4u
9
− 3u
8
+ 6u
7
+ 2u
6
− 2u
5
+ 3u
4
− 3u
3
− 3u
2
+ 2u − 1i
I
u
3
= hu
5
− 2u
3
+ b + u, −u
5
+ 3u
3
− u
2
+ a − 2u + 1, u
6
− 3u
4
+ 2u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 46 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
17
+2u
16
+· · ·+b −1, −5u
17
+9u
16
+· · ·+2a −7, u
18
−3u
17
+· · ·−7u −2i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
5
2
u
17
−
9
2
u
16
+ ··· + 16u +
7
2
u
17
− 2u
16
+ ··· + 6u + 1
a
2
=
3
2
u
17
−
5
2
u
16
+ ··· + 9u +
3
2
u
17
− 2u
16
+ ··· + 5u + 1
a
4
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
1
2
u
17
−
1
2
u
16
+ ··· + 3u +
3
2
−u
17
+ u
16
+ ··· − 4u − 1
a
8
=
1
2
u
17
−
1
2
u
16
+ ··· + 4u +
3
2
−2u
17
+ 3u
16
+ ··· − 12u − 3
a
8
=
1
2
u
17
−
1
2
u
16
+ ··· + 4u +
3
2
−2u
17
+ 3u
16
+ ··· − 12u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
+ 4u
16
+ 26u
15
− 16u
14
− 76u
13
+ 10u
12
+ 112u
11
+
58u
10
− 50u
9
− 126u
8
− 88u
7
+ 58u
6
+ 122u
5
+ 70u
4
− 12u
3
− 50u
2
− 46u − 30
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
18
+ 12u
16
+ ··· − 3u − 1
c
4
, c
6
u
18
+ 9u
17
+ ··· + 223u + 26
c
5
, c
10
, c
11
u
18
− 3u
17
+ ··· − 7u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
18
+ 24y
17
+ ··· − 5y + 1
c
4
, c
6
y
18
+ 13y
17
+ ··· − 7609y + 676
c
5
, c
10
, c
11
y
18
− 15y
17
+ ··· − 41y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.123856 + 0.896133I
a = −0.64726 − 2.44716I
b = −0.30161 + 1.61404I
16.3220 + 7.5688I −2.56060 − 3.84684I
u = −0.123856 − 0.896133I
a = −0.64726 + 2.44716I
b = −0.30161 − 1.61404I
16.3220 − 7.5688I −2.56060 + 3.84684I
u = −0.538460 + 0.620351I
a = 1.03715 + 1.21621I
b = 0.05142 − 1.55107I
10.10640 + 2.19718I −4.14124 − 3.09555I
u = −0.538460 − 0.620351I
a = 1.03715 − 1.21621I
b = 0.05142 + 1.55107I
10.10640 − 2.19718I −4.14124 + 3.09555I
u = −1.151600 + 0.470809I
a = −0.509790 − 1.091590I
b = 0.24523 + 1.63308I
13.17120 − 2.70335I −5.20794 + 0.16548I
u = −1.151600 − 0.470809I
a = −0.509790 + 1.091590I
b = 0.24523 − 1.63308I
13.17120 + 2.70335I −5.20794 − 0.16548I
u = −1.261310 + 0.252068I
a = 0.211990 + 0.318908I
b = −0.236066 − 0.509153I
−1.47242 + 2.06370I −11.90510 + 0.97448I
u = −1.261310 − 0.252068I
a = 0.211990 − 0.318908I
b = −0.236066 + 0.509153I
−1.47242 − 2.06370I −11.90510 − 0.97448I
u = −0.031986 + 0.701532I
a = −0.175359 + 1.101380I
b = 0.386143 − 0.454390I
2.29851 + 1.35610I −7.33537 − 5.27531I
u = −0.031986 − 0.701532I
a = −0.175359 − 1.101380I
b = 0.386143 + 0.454390I
2.29851 − 1.35610I −7.33537 + 5.27531I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.30632
a = 0.919432
b = 0.613328
−5.28445 −18.9030
u = 1.286650 + 0.297323I
a = −0.675519 + 0.845692I
b = −0.521429 − 0.448538I
−1.81273 − 4.98441I −12.9081 + 7.6610I
u = 1.286650 − 0.297323I
a = −0.675519 − 0.845692I
b = −0.521429 + 0.448538I
−1.81273 + 4.98441I −12.9081 − 7.6610I
u = 1.36136 + 0.40071I
a = 1.71836 − 1.08684I
b = 0.33798 + 1.58437I
11.6528 − 12.2200I −6.45692 + 6.09309I
u = 1.36136 − 0.40071I
a = 1.71836 + 1.08684I
b = 0.33798 − 1.58437I
11.6528 + 12.2200I −6.45692 − 6.09309I
u = 1.45252 + 0.15463I
a = −0.916883 − 0.366782I
b = −0.11443 − 1.46229I
3.61426 − 4.76803I −7.92624 + 3.38619I
u = 1.45252 − 0.15463I
a = −0.916883 + 0.366782I
b = −0.11443 + 1.46229I
3.61426 + 4.76803I −7.92624 − 3.38619I
u = −0.292956
a = −0.504799
b = −0.307793
−0.489564 −20.2140
6
II.
I
u
2
= hu
10
a−u
10
+· · ·+2a−1, 2u
10
a−u
10
+· · ·+a−3, u
11
+u
10
+· · ·+2u−1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
a
−
1
3
u
10
a +
1
3
u
10
+ ··· −
2
3
a +
1
3
a
2
=
−
1
3
u
10
a −
2
3
u
10
+ ··· +
1
3
a −
2
3
−
1
3
u
10
a + u
10
+ ··· −
1
3
a +
1
3
a
4
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
−
2
3
u
10
a −
2
3
u
9
a + ··· +
1
3
a +
5
3
−
1
3
u
10
a −
1
3
u
10
+ ··· +
1
3
u +
1
3
a
8
=
−
1
3
u
10
a +
1
3
u
10
+ ··· +
1
3
a +
4
3
1
3
u
10
a +
1
3
u
9
a + ··· +
1
3
a +
2
3
a
8
=
−
1
3
u
10
a +
1
3
u
10
+ ··· +
1
3
a +
4
3
1
3
u
10
a +
1
3
u
9
a + ··· +
1
3
a +
2
3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
9
+ 16u
7
− 4u
6
− 20u
5
+ 12u
4
− 4u
3
− 8u
2
+ 20u − 14
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
22
− u
21
+ ··· + 6u + 5
c
4
, c
6
(u
11
− 3u
10
+ ··· − 2u + 1)
2
c
5
, c
10
, c
11
(u
11
+ u
10
− 4u
9
− 3u
8
+ 6u
7
+ 2u
6
− 2u
5
+ 3u
4
− 3u
3
− 3u
2
+ 2u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
22
+ 19y
21
+ ··· + 24y + 25
c
4
, c
6
(y
11
+ 11y
10
+ ··· + 6y −1)
2
c
5
, c
10
, c
11
(y
11
− 9y
10
+ ··· − 2y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14725
a = −1.48144 + 0.67002I
b = −0.301144 − 1.127860I
1.09450 −7.62370
u = 1.14725
a = −1.48144 − 0.67002I
b = −0.301144 + 1.127860I
1.09450 −7.62370
u = 0.044199 + 0.849205I
a = 0.388928 + 0.983366I
b = −0.915282 − 0.626510I
8.93247 − 3.04152I −3.93879 + 2.82242I
u = 0.044199 + 0.849205I
a = 0.36363 − 2.98960I
b = 0.10178 + 1.52179I
8.93247 − 3.04152I −3.93879 + 2.82242I
u = 0.044199 − 0.849205I
a = 0.388928 − 0.983366I
b = −0.915282 + 0.626510I
8.93247 + 3.04152I −3.93879 − 2.82242I
u = 0.044199 − 0.849205I
a = 0.36363 + 2.98960I
b = 0.10178 − 1.52179I
8.93247 + 3.04152I −3.93879 − 2.82242I
u = 1.232090 + 0.392876I
a = −0.092298 − 0.230493I
b = 0.866867 − 0.720237I
5.26692 − 1.41699I −7.20869 + 0.63373I
u = 1.232090 + 0.392876I
a = 0.88708 − 1.64981I
b = −0.02867 + 1.51700I
5.26692 − 1.41699I −7.20869 + 0.63373I
u = 1.232090 − 0.392876I
a = −0.092298 + 0.230493I
b = 0.866867 + 0.720237I
5.26692 + 1.41699I −7.20869 − 0.63373I
u = 1.232090 − 0.392876I
a = 0.88708 + 1.64981I
b = −0.02867 − 1.51700I
5.26692 + 1.41699I −7.20869 − 0.63373I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.317220 + 0.129556I
a = −0.848428 + 0.622696I
b = −0.450568 + 0.155139I
−1.89175 + 2.94672I −13.7994 − 4.1179I
u = −1.317220 + 0.129556I
a = 1.083920 + 0.034152I
b = 0.176110 − 1.143700I
−1.89175 + 2.94672I −13.7994 − 4.1179I
u = −1.317220 − 0.129556I
a = −0.848428 − 0.622696I
b = −0.450568 − 0.155139I
−1.89175 − 2.94672I −13.7994 + 4.1179I
u = −1.317220 − 0.129556I
a = 1.083920 − 0.034152I
b = 0.176110 + 1.143700I
−1.89175 − 2.94672I −13.7994 + 4.1179I
u = −1.304640 + 0.385413I
a = 0.834463 + 0.932370I
b = 0.947680 − 0.541858I
4.72165 + 7.47524I −8.22908 − 5.55460I
u = −1.304640 + 0.385413I
a = −1.53022 − 1.52281I
b = −0.16441 + 1.51556I
4.72165 + 7.47524I −8.22908 − 5.55460I
u = −1.304640 − 0.385413I
a = 0.834463 − 0.932370I
b = 0.947680 + 0.541858I
4.72165 − 7.47524I −8.22908 + 5.55460I
u = −1.304640 − 0.385413I
a = −1.53022 + 1.52281I
b = −0.16441 − 1.51556I
4.72165 − 7.47524I −8.22908 + 5.55460I
u = 0.271947 + 0.385187I
a = 1.176750 + 0.591060I
b = 0.288931 + 0.529428I
2.98514 − 1.13130I −8.01220 + 6.05785I
u = 0.271947 + 0.385187I
a = −1.28240 + 1.91841I
b = −0.021293 − 1.196140I
2.98514 − 1.13130I −8.01220 + 6.05785I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271947 − 0.385187I
a = 1.176750 − 0.591060I
b = 0.288931 − 0.529428I
2.98514 + 1.13130I −8.01220 − 6.05785I
u = 0.271947 − 0.385187I
a = −1.28240 − 1.91841I
b = −0.021293 + 1.196140I
2.98514 + 1.13130I −8.01220 − 6.05785I
12
III. I
u
3
= hu
5
− 2u
3
+ b + u, −u
5
+ 3u
3
− u
2
+ a − 2u + 1, u
6
− 3u
4
+ 2u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
7
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
5
− 3u
3
+ u
2
+ 2u − 1
−u
5
+ 2u
3
− u
a
2
=
u
5
− 3u
3
+ 2u
−u
5
− u
4
+ 2u
3
+ 2u
2
− u
a
4
=
u
5
− 2u
3
+ u
0
a
9
=
−u
4
+ u
3
+ 2u
2
− 2u
1
a
8
=
−u
4
+ u
3
+ 2u
2
− 2u − 1
1
a
8
=
−u
4
+ u
3
+ 2u
2
− 2u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
4
− 8u
2
− 4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
(u
2
+ 1)
3
c
4
, c
6
u
6
+ u
4
+ 2u
2
+ 1
c
5
, c
10
, c
11
u
6
− 3u
4
+ 2u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
(y + 1)
6
c
4
, c
6
(y
3
+ y
2
+ 2y + 1)
2
c
5
, c
10
, c
11
(y
3
− 3y
2
+ 2y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307140 + 0.215080I
a = −0.082503 + 0.684841I
b = − 1.000000I
0.26574 − 2.82812I −7.50976 + 2.97945I
u = 1.307140 − 0.215080I
a = −0.082503 − 0.684841I
b = 1.000000I
0.26574 + 2.82812I −7.50976 − 2.97945I
u = −1.307140 + 0.215080I
a = 1.40722 − 0.43972I
b = − 1.000000I
0.26574 + 2.82812I −7.50976 − 2.97945I
u = −1.307140 − 0.215080I
a = 1.40722 + 0.43972I
b = 1.000000I
0.26574 − 2.82812I −7.50976 + 2.97945I
u = 0.569840I
a = −1.32472 + 1.75488I
b = − 1.000000I
4.40332 −0.980490
u = − 0.569840I
a = −1.32472 − 1.75488I
b = 1.000000I
4.40332 −0.980490
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
((u
2
+ 1)
3
)(u
18
+ 12u
16
+ ··· − 3u − 1)(u
22
− u
21
+ ··· + 6u + 5)
c
4
, c
6
(u
6
+ u
4
+ 2u
2
+ 1)(u
11
− 3u
10
+ ··· − 2u + 1)
2
· (u
18
+ 9u
17
+ ··· + 223u + 26)
c
5
, c
10
, c
11
(u
6
− 3u
4
+ 2u
2
+ 1)
· (u
11
+ u
10
− 4u
9
− 3u
8
+ 6u
7
+ 2u
6
− 2u
5
+ 3u
4
− 3u
3
− 3u
2
+ 2u − 1)
2
· (u
18
− 3u
17
+ ··· − 7u − 2)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
((y + 1)
6
)(y
18
+ 24y
17
+ ··· − 5y + 1)(y
22
+ 19y
21
+ ··· + 24y + 25)
c
4
, c
6
((y
3
+ y
2
+ 2y + 1)
2
)(y
11
+ 11y
10
+ ··· + 6y −1)
2
· (y
18
+ 13y
17
+ ··· − 7609y + 676)
c
5
, c
10
, c
11
((y
3
− 3y
2
+ 2y + 1)
2
)(y
11
− 9y
10
+ ··· − 2y −1)
2
· (y
18
− 15y
17
+ ··· − 41y + 4)
18
