11a
291
(K11a
291
)
A knot diagram
1
Linearized knot diagam
8 5 1 9 2 10 11 3 6 7 4
Solving Sequence
6,10
7 11
2,8
1 5 3 9 4
c
6
c
10
c
7
c
1
c
5
c
2
c
9
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h9320183u
20
− 5745909u
19
+ ··· + 120011978b − 47600802,
49214757u
20
− 69440884u
19
+ ··· + 240023956a + 223258849, u
21
− 2u
20
+ ··· + 13u − 4i
I
u
2
= h−u
15
a − 3u
15
+ ··· + 3a − 1, −4u
15
a + 18u
15
+ ··· − 6a + 36,
u
16
− u
15
− 9u
14
+ 8u
13
+ 31u
12
− 22u
11
− 52u
10
+ 22u
9
+ 47u
8
− 2u
7
− 24u
6
− 6u
5
+ 2u
4
+ 6u
3
+ 2u
2
− 1i
I
u
3
= hb + 1, 2a + 3, u
2
+ u − 1i
I
u
4
= hb − a − 1, a
2
+ 2a + 2, u − 1i
* 4 irreducible components of dim
C
= 0, with total 57 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
= h9.32 × 10
6
u
20
− 5.75 × 10
6
u
19
+ · · · + 1.20 × 10
8
b − 4.76 × 10
7
, 4.92 ×
10
7
u
20
−6.94×10
7
u
19
+· · ·+2.40×10
8
a+2.23×10
8
, u
21
−2u
20
+· · ·+13u−4i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
−0.205041u
20
+ 0.289308u
19
+ ··· − 1.57998u − 0.930152
−0.0776604u
20
+ 0.0478778u
19
+ ··· − 0.825434u + 0.396634
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
−0.222415u
20
+ 0.221463u
19
+ ··· − 0.915430u − 0.633782
−0.230117u
20
+ 0.198897u
19
+ ··· + 0.482667u − 0.0496061
a
5
=
0.210965u
20
− 0.285506u
19
+ ··· + 1.46088u + 1.21110
0.145840u
20
− 0.137084u
19
+ ··· + 1.32796u − 0.343964
a
3
=
−0.399042u
20
+ 0.523770u
19
+ ··· − 1.95821u − 1.41205
−0.279364u
20
+ 0.259774u
19
+ ··· − 1.80557u + 0.498910
a
9
=
u
u
a
4
=
0.219932u
20
− 0.302643u
19
+ ··· + 0.964152u + 1.28379
0.154807u
20
− 0.154222u
19
+ ··· + 0.831233u − 0.271279
a
4
=
0.219932u
20
− 0.302643u
19
+ ··· + 0.964152u + 1.28379
0.154807u
20
− 0.154222u
19
+ ··· + 0.831233u − 0.271279
(ii) Obstruction class = −1
(iii) Cusp Shapes =
162514487
240023956
u
20
−
304511969
240023956
u
19
+ ··· +
520499563
60005989
u −
1134730210
60005989
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
4(4u
21
− 2u
20
+ ··· + 6u + 2)
c
2
, c
3
, c
5
c
11
u
21
+ 2u
20
+ ··· + 5u + 1
c
6
, c
7
, c
9
c
10
u
21
+ 2u
20
+ ··· + 13u + 4
c
8
u
21
+ 3u
20
+ ··· + 88u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
16(16y
21
− 76y
20
+ ··· + 76y −4)
c
2
, c
3
, c
5
c
11
y
21
+ 8y
20
+ ··· + 5y −1
c
6
, c
7
, c
9
c
10
y
21
− 24y
20
+ ··· + 273y −16
c
8
y
21
+ 7y
20
+ ··· + 448y −1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.789797 + 0.624633I
a = −1.51457 − 0.44640I
b = −0.546053 + 1.249230I
3.68387 + 11.47460I −9.39826 − 8.82846I
u = −0.789797 − 0.624633I
a = −1.51457 + 0.44640I
b = −0.546053 − 1.249230I
3.68387 − 11.47460I −9.39826 + 8.82846I
u = 0.758227 + 0.411195I
a = −0.698370 + 0.278847I
b = 0.041928 − 0.594017I
−0.315718 − 0.478711I −14.5208 + 0.8983I
u = 0.758227 − 0.411195I
a = −0.698370 − 0.278847I
b = 0.041928 + 0.594017I
−0.315718 + 0.478711I −14.5208 − 0.8983I
u = −0.179300 + 0.815897I
a = 0.030732 + 0.642646I
b = −0.442140 − 1.177470I
5.53762 − 6.70880I −6.60250 + 5.49950I
u = −0.179300 − 0.815897I
a = 0.030732 − 0.642646I
b = −0.442140 + 1.177470I
5.53762 + 6.70880I −6.60250 − 5.49950I
u = 0.506129 + 0.654446I
a = 0.657349 − 1.025090I
b = 0.372085 + 0.842002I
0.34108 − 3.49247I −11.9725 + 8.3783I
u = 0.506129 − 0.654446I
a = 0.657349 + 1.025090I
b = 0.372085 − 0.842002I
0.34108 + 3.49247I −11.9725 − 8.3783I
u = 1.209060 + 0.446540I
a = 0.070327 + 0.349474I
b = −0.345184 + 1.020620I
1.29592 + 2.27858I −10.67873 − 5.63740I
u = 1.209060 − 0.446540I
a = 0.070327 − 0.349474I
b = −0.345184 − 1.020620I
1.29592 − 2.27858I −10.67873 + 5.63740I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.639776 + 0.168175I
a = 1.34866 + 0.57840I
b = 1.079910 + 0.285594I
−2.83019 + 0.37915I −14.9029 − 12.5783I
u = −0.639776 − 0.168175I
a = 1.34866 − 0.57840I
b = 1.079910 − 0.285594I
−2.83019 − 0.37915I −14.9029 + 12.5783I
u = −1.56702 + 0.20612I
a = 1.206150 + 0.091091I
b = 0.510228 − 1.044980I
−6.63082 + 6.65001I −13.3056 − 6.2387I
u = −1.56702 − 0.20612I
a = 1.206150 − 0.091091I
b = 0.510228 + 1.044980I
−6.63082 − 6.65001I −13.3056 + 6.2387I
u = 1.59922 + 0.05529I
a = 1.76881 − 0.60078I
b = 1.291780 − 0.473779I
−10.58370 − 1.26080I −14.0233 + 4.6800I
u = 1.59922 − 0.05529I
a = 1.76881 + 0.60078I
b = 1.291780 + 0.473779I
−10.58370 + 1.26080I −14.0233 − 4.6800I
u = 1.63963 + 0.18902I
a = −1.69792 − 0.35423I
b = −0.63892 − 1.29044I
−4.5325 − 14.5799I −12.0752 + 7.7299I
u = 1.63963 − 0.18902I
a = −1.69792 + 0.35423I
b = −0.63892 + 1.29044I
−4.5325 + 14.5799I −12.0752 − 7.7299I
u = −1.68983 + 0.00575I
a = −0.819332 − 0.396829I
b = −0.450400 − 0.614576I
−9.51673 − 1.46421I −13.5665 + 4.8534I
u = −1.68983 − 0.00575I
a = −0.819332 + 0.396829I
b = −0.450400 + 0.614576I
−9.51673 + 1.46421I −13.5665 − 4.8534I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.306916
a = −0.953646
b = 0.253532
−0.600717 −16.6570
7
II. I
u
2
= h−u
15
a − 3u
15
+ · · · + 3a − 1, −4u
15
a + 18u
15
+ · · · − 6a +
36, u
16
− u
15
+ · · · + 2u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
2
=
a
1
2
u
15
a +
3
2
u
15
+ ··· −
3
2
a +
1
2
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
15
a + 2u
15
+ ··· − a + 1
1
2
u
15
a +
3
2
u
15
+ ··· −
1
2
a +
1
2
a
5
=
3
2
u
15
a −
7
2
u
15
+ ··· +
1
2
a −
11
2
−
1
2
u
15
a +
1
2
u
15
+ ··· −
1
2
a −
1
2
a
3
=
−u
15
+ 8u
13
− 22u
11
+ 22u
9
− 2u
7
− 6u
5
+ 6u
3
−u
15
+ 9u
13
− 30u
11
+ 45u
9
− 30u
7
+ 8u
5
+ 2u
3
− u
a
9
=
u
u
a
4
=
3
2
u
15
a −
5
2
u
15
+ ··· +
1
2
a −
5
2
−
1
2
u
15
a +
3
2
u
15
+ ··· −
1
2
a +
5
2
a
4
=
3
2
u
15
a −
5
2
u
15
+ ··· +
1
2
a −
5
2
−
1
2
u
15
a +
3
2
u
15
+ ··· −
1
2
a +
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
13
− 32u
11
+ 92u
9
+ 4u
8
− 112u
7
− 20u
6
+ 56u
5
+ 28u
4
− 12u
3
− 8u
2
− 12u − 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
32
− 3u
31
+ ··· + 52u + 17
c
2
, c
3
, c
5
c
11
u
32
− 5u
31
+ ··· − 11u + 2
c
6
, c
7
, c
9
c
10
(u
16
+ u
15
+ ··· + 2u
2
− 1)
2
c
8
(u
16
− u
15
+ ··· + 2u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
32
+ 11y
31
+ ··· + 14534y + 289
c
2
, c
3
, c
5
c
11
y
32
+ 19y
31
+ ··· + 59y + 4
c
6
, c
7
, c
9
c
10
(y
16
− 19y
15
+ ··· − 4y + 1)
2
c
8
(y
16
+ 5y
15
+ ··· − 4y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.752457 + 0.456573I
a = −0.862515 − 0.499116I
b = −0.965256 − 0.143588I
0.28749 + 6.07197I −12.6157 − 7.0281I
u = −0.752457 + 0.456573I
a = 1.61525 + 0.23701I
b = 0.562596 − 1.228100I
0.28749 + 6.07197I −12.6157 − 7.0281I
u = −0.752457 − 0.456573I
a = −0.862515 + 0.499116I
b = −0.965256 + 0.143588I
0.28749 − 6.07197I −12.6157 + 7.0281I
u = −0.752457 − 0.456573I
a = 1.61525 − 0.23701I
b = 0.562596 + 1.228100I
0.28749 − 6.07197I −12.6157 + 7.0281I
u = 0.790211 + 0.368636I
a = −0.861711 − 0.010777I
b = 0.058639 − 0.741860I
−0.311107 − 0.489680I −14.3561 + 1.4314I
u = 0.790211 + 0.368636I
a = −0.580679 + 0.527896I
b = −0.071737 − 0.398232I
−0.311107 − 0.489680I −14.3561 + 1.4314I
u = 0.790211 − 0.368636I
a = −0.861711 + 0.010777I
b = 0.058639 + 0.741860I
−0.311107 + 0.489680I −14.3561 − 1.4314I
u = 0.790211 − 0.368636I
a = −0.580679 − 0.527896I
b = −0.071737 + 0.398232I
−0.311107 + 0.489680I −14.3561 − 1.4314I
u = −0.452620 + 0.425410I
a = 0.223204 − 0.029590I
b = −0.325222 − 1.319700I
5.17692 + 1.52971I −5.27263 − 5.08772I
u = −0.452620 + 0.425410I
a = −2.28305 − 0.32185I
b = −0.511738 + 1.137200I
5.17692 + 1.52971I −5.27263 − 5.08772I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.452620 − 0.425410I
a = 0.223204 + 0.029590I
b = −0.325222 + 1.319700I
5.17692 − 1.52971I −5.27263 + 5.08772I
u = −0.452620 − 0.425410I
a = −2.28305 + 0.32185I
b = −0.511738 − 1.137200I
5.17692 − 1.52971I −5.27263 + 5.08772I
u = −0.071750 + 0.572783I
a = −0.393981 − 0.880662I
b = 0.338699 + 1.140160I
2.27257 − 2.57669I −8.69244 + 2.71681I
u = −0.071750 + 0.572783I
a = −0.152598 − 0.881762I
b = −0.658604 + 0.021898I
2.27257 − 2.57669I −8.69244 + 2.71681I
u = −0.071750 − 0.572783I
a = −0.393981 + 0.880662I
b = 0.338699 − 1.140160I
2.27257 + 2.57669I −8.69244 − 2.71681I
u = −0.071750 − 0.572783I
a = −0.152598 + 0.881762I
b = −0.658604 − 0.021898I
2.27257 + 2.57669I −8.69244 − 2.71681I
u = 0.508466
a = 6.38440 + 5.02047I
b = 0.074040 − 1.008190I
2.52578 −17.0940
u = 0.508466
a = 6.38440 − 5.02047I
b = 0.074040 + 1.008190I
2.52578 −17.0940
u = 1.52559 + 0.07425I
a = −0.185891 + 0.863663I
b = −0.18841 + 1.53021I
−1.40970 − 3.12434I −9.94060 + 3.66013I
u = 1.52559 + 0.07425I
a = −1.91032 − 0.81582I
b = −0.793946 − 1.008570I
−1.40970 − 3.12434I −9.94060 + 3.66013I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52559 − 0.07425I
a = −0.185891 − 0.863663I
b = −0.18841 − 1.53021I
−1.40970 + 3.12434I −9.94060 − 3.66013I
u = 1.52559 − 0.07425I
a = −1.91032 + 0.81582I
b = −0.793946 + 1.008570I
−1.40970 + 3.12434I −9.94060 − 3.66013I
u = −1.57280
a = 1.97074 + 0.61509I
b = 0.237438 − 1.081260I
−4.71670 −16.1480
u = −1.57280
a = 1.97074 − 0.61509I
b = 0.237438 + 1.081260I
−4.71670 −16.1480
u = 1.62338 + 0.13130I
a = −1.49404 + 0.52581I
b = −1.144250 + 0.248239I
−7.82454 − 8.28859I −14.5771 + 5.2713I
u = 1.62338 + 0.13130I
a = 1.68539 + 0.55122I
b = 0.72433 + 1.27550I
−7.82454 − 8.28859I −14.5771 + 5.2713I
u = 1.62338 − 0.13130I
a = −1.49404 − 0.52581I
b = −1.144250 − 0.248239I
−7.82454 + 8.28859I −14.5771 − 5.2713I
u = 1.62338 − 0.13130I
a = 1.68539 − 0.55122I
b = 0.72433 − 1.27550I
−7.82454 + 8.28859I −14.5771 − 5.2713I
u = −1.63018 + 0.10414I
a = −1.297790 + 0.134879I
b = −0.436027 + 0.931326I
−8.61070 + 2.28357I −15.9247 − 0.3083I
u = −1.63018 + 0.10414I
a = 0.643588 + 0.194017I
b = 0.599447 + 0.332807I
−8.61070 + 2.28357I −15.9247 − 0.3083I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63018 − 0.10414I
a = −1.297790 − 0.134879I
b = −0.436027 − 0.931326I
−8.61070 − 2.28357I −15.9247 + 0.3083I
u = −1.63018 − 0.10414I
a = 0.643588 − 0.194017I
b = 0.599447 − 0.332807I
−8.61070 − 2.28357I −15.9247 + 0.3083I
14
III. I
u
3
= hb + 1, 2a + 3, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u + 1
a
11
=
−u
−u + 1
a
2
=
−1.5
−1
a
8
=
u
u
a
1
=
−
1
2
u − 1
−
1
2
u −
1
2
a
5
=
−0.5
−1
a
3
=
−2
−2
a
9
=
u
u
a
4
=
1
2
u − 1
1
2
u −
3
2
a
4
=
1
2
u − 1
1
2
u −
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
15
4
u −
39
4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
2
− 2u − 1)
c
2
, c
11
(u − 1)
2
c
3
, c
5
(u + 1)
2
c
4
4(4u
2
+ 2u − 1)
c
6
, c
7
u
2
+ u − 1
c
8
u
2
c
9
, c
10
u
2
− u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
16(16y
2
− 12y + 1)
c
2
, c
3
, c
5
c
11
(y −1)
2
c
6
, c
7
, c
9
c
10
y
2
− 3y + 1
c
8
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −1.50000
b = −1.00000
−2.63189 −7.43240
u = −1.61803
a = −1.50000
b = −1.00000
−10.5276 −15.8180
18
IV. I
u
4
= hb − a − 1, a
2
+ 2a + 2, u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
1
a
7
=
1
1
a
11
=
−1
0
a
2
=
a
a + 1
a
8
=
0
1
a
1
=
a
1
a
5
=
a + 3
1
a
3
=
−a − 1
0
a
9
=
1
1
a
4
=
1
−a − 1
a
4
=
1
−a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 2u + 2
c
2
, c
3
, c
5
c
8
, c
11
u
2
+ 1
c
4
u
2
− 2u + 2
c
6
, c
7
(u − 1)
2
c
9
, c
10
(u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
2
+ 4
c
2
, c
3
, c
5
c
8
, c
11
(y + 1)
2
c
6
, c
7
, c
9
c
10
(y −1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000 + 1.00000I
b = 1.000000I
1.64493 −8.00000
u = 1.00000
a = −1.00000 − 1.00000I
b = − 1.000000I
1.64493 −8.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(u
2
+ 2u + 2)(4u
2
− 2u − 1)(4u
21
− 2u
20
+ ··· + 6u + 2)
· (u
32
− 3u
31
+ ··· + 52u + 17)
c
2
, c
11
((u − 1)
2
)(u
2
+ 1)(u
21
+ 2u
20
+ ··· + 5u + 1)(u
32
− 5u
31
+ ··· − 11u + 2)
c
3
, c
5
((u + 1)
2
)(u
2
+ 1)(u
21
+ 2u
20
+ ··· + 5u + 1)(u
32
− 5u
31
+ ··· − 11u + 2)
c
4
16(u
2
− 2u + 2)(4u
2
+ 2u − 1)(4u
21
− 2u
20
+ ··· + 6u + 2)
· (u
32
− 3u
31
+ ··· + 52u + 17)
c
6
, c
7
((u − 1)
2
)(u
2
+ u − 1)(u
16
+ u
15
+ ··· + 2u
2
− 1)
2
· (u
21
+ 2u
20
+ ··· + 13u + 4)
c
8
u
2
(u
2
+ 1)(u
16
− u
15
+ ··· + 2u − 1)
2
(u
21
+ 3u
20
+ ··· + 88u + 32)
c
9
, c
10
((u + 1)
2
)(u
2
− u − 1)(u
16
+ u
15
+ ··· + 2u
2
− 1)
2
· (u
21
+ 2u
20
+ ··· + 13u + 4)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
256(y
2
+ 4)(16y
2
− 12y + 1)(16y
21
− 76y
20
+ ··· + 76y −4)
· (y
32
+ 11y
31
+ ··· + 14534y + 289)
c
2
, c
3
, c
5
c
11
((y −1)
2
)(y + 1)
2
(y
21
+ 8y
20
+ ··· + 5y −1)
· (y
32
+ 19y
31
+ ··· + 59y + 4)
c
6
, c
7
, c
9
c
10
((y −1)
2
)(y
2
− 3y + 1)(y
16
− 19y
15
+ ··· − 4y + 1)
2
· (y
21
− 24y
20
+ ··· + 273y −16)
c
8
y
2
(y + 1)
2
(y
16
+ 5y
15
+ ··· − 4y + 1)
2
· (y
21
+ 7y
20
+ ··· + 448y −1024)
24
