11a
87
(K11a
87
)
A knot diagram
1
Linearized knot diagam
6 1 9 8 2 3 11 4 5 7 10
Solving Sequence
1,6
2 3 7
5,10
9 11 8 4
c
1
c
2
c
6
c
5
c
9
c
11
c
7
c
4
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.76827 × 10
20
u
65
− 3.94428 × 10
20
u
64
+ ··· + 3.38827 × 10
20
b − 3.37636 × 10
20
,
1.46899 × 10
21
u
65
+ 7.18335 × 10
20
u
64
+ ··· + 2.03296 × 10
21
a − 4.01396 × 10
21
, u
66
+ 2u
65
+ ··· + 9u + 3i
I
u
2
= hb − 1, a
2
− 2au + 2a + u − 2, u
2
− u + 1i
I
u
3
= hb − 1, a + u + 1, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 72 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−2.77×10
20
u
65
−3.94×10
20
u
64
+· · ·+3.39×10
20
b−3.38×10
20
, 1.47×
10
21
u
65
+7.18×10
20
u
64
+· · ·+2.03×10
21
a−4.01×10
21
, u
66
+2u
65
+· · ·+9u+3i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
10
=
−0.722586u
65
− 0.353344u
64
+ ··· + 4.62019u + 1.97444
0.817018u
65
+ 1.16410u
64
+ ··· + 3.14431u + 0.996486
a
9
=
−0.240968u
65
+ 0.706381u
64
+ ··· + 8.22401u + 3.27525
0.769366u
65
+ 0.828277u
64
+ ··· + 1.85375u − 0.0148534
a
11
=
0.621466u
65
+ 1.92904u
64
+ ··· + 12.3901u + 5.69831
0.738277u
65
+ 0.691862u
64
+ ··· + 0.186232u − 1.40925
a
8
=
0.00495114u
65
+ 0.779268u
64
+ ··· + 4.72824u + 1.89831
1.18832u
65
+ 1.94777u
64
+ ··· + 5.44396u + 0.722904
a
4
=
1.01619u
65
+ 2.39037u
64
+ ··· + 8.96868u + 4.74556
0.357982u
65
− 0.423891u
64
+ ··· − 4.40018u − 3.04858
a
4
=
1.01619u
65
+ 2.39037u
64
+ ··· + 8.96868u + 4.74556
0.357982u
65
− 0.423891u
64
+ ··· − 4.40018u − 3.04858
(ii) Obstruction class = −1
(iii) Cusp Shapes =
637819945328403808339
338826759075039659107
u
65
+
1108465925103697174201
338826759075039659107
u
64
+ ··· +
3852435380313220749703
338826759075039659107
u +
473140454884407107541
338826759075039659107
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
66
− 2u
65
+ ··· − 9u + 3
c
2
u
66
+ 32u
65
+ ··· + 33u + 9
c
3
, c
4
, c
8
u
66
+ u
65
+ ··· + 16u + 4
c
6
u
66
+ 2u
65
+ ··· + 9195u + 2391
c
7
, c
10
u
66
− 3u
65
+ ··· − 16u + 3
c
9
u
66
− u
65
+ ··· − 64u + 548
c
11
u
66
− 33u
65
+ ··· − 4u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
66
+ 32y
65
+ ··· + 33y + 9
c
2
y
66
+ 8y
65
+ ··· + 873y + 81
c
3
, c
4
, c
8
y
66
+ 61y
65
+ ··· − 128y + 16
c
6
y
66
− 16y
65
+ ··· − 60107223y + 5716881
c
7
, c
10
y
66
− 33y
65
+ ··· − 4y + 9
c
9
y
66
+ y
65
+ ··· − 1284224y + 300304
c
11
y
66
+ 7y
65
+ ··· − 2176y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755953 + 0.642253I
a = −1.50344 − 0.99906I
b = 0.91082 + 1.08246I
7.19005 + 6.79978I 5.09513 − 6.93835I
u = 0.755953 − 0.642253I
a = −1.50344 + 0.99906I
b = 0.91082 − 1.08246I
7.19005 − 6.79978I 5.09513 + 6.93835I
u = 0.381443 + 0.962354I
a = 1.84405 − 1.05401I
b = 0.434581 − 0.385324I
5.19371 + 1.45398I 0
u = 0.381443 − 0.962354I
a = 1.84405 + 1.05401I
b = 0.434581 + 0.385324I
5.19371 − 1.45398I 0
u = −0.673098 + 0.678865I
a = −1.193220 + 0.537398I
b = 0.813918 − 0.796640I
1.97562 − 3.83931I 0.43158 + 7.99484I
u = −0.673098 − 0.678865I
a = −1.193220 − 0.537398I
b = 0.813918 + 0.796640I
1.97562 + 3.83931I 0.43158 − 7.99484I
u = 0.638302 + 0.703727I
a = 1.149350 + 0.463060I
b = −0.200847 − 0.267724I
4.99477 + 2.60395I 2.08066 − 2.86296I
u = 0.638302 − 0.703727I
a = 1.149350 − 0.463060I
b = −0.200847 + 0.267724I
4.99477 − 2.60395I 2.08066 + 2.86296I
u = −0.316058 + 1.015530I
a = −0.80720 − 1.18230I
b = 1.59297 − 0.23810I
4.37513 − 0.91344I 0
u = −0.316058 − 1.015530I
a = −0.80720 + 1.18230I
b = 1.59297 + 0.23810I
4.37513 + 0.91344I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629972 + 0.864578I
a = 0.282045 − 0.437369I
b = 0.105832 + 0.332549I
4.56888 + 2.29703I 0
u = 0.629972 − 0.864578I
a = 0.282045 + 0.437369I
b = 0.105832 − 0.332549I
4.56888 − 2.29703I 0
u = −0.827182 + 0.359098I
a = −1.48252 − 1.13505I
b = 1.00026 + 1.36192I
5.59217 + 9.84151I 4.35993 − 5.90567I
u = −0.827182 − 0.359098I
a = −1.48252 + 1.13505I
b = 1.00026 − 1.36192I
5.59217 − 9.84151I 4.35993 + 5.90567I
u = −0.615669 + 0.911613I
a = 0.149118 − 1.152950I
b = 0.719356 + 0.533955I
1.29731 − 1.14051I 0
u = −0.615669 − 0.911613I
a = 0.149118 + 1.152950I
b = 0.719356 − 0.533955I
1.29731 + 1.14051I 0
u = 0.484610 + 1.022030I
a = −0.59263 + 1.37966I
b = 1.48883 − 0.30554I
1.07785 + 3.02843I 0
u = 0.484610 − 1.022030I
a = −0.59263 − 1.37966I
b = 1.48883 + 0.30554I
1.07785 − 3.02843I 0
u = 0.789237 + 0.311182I
a = −1.14249 + 0.91939I
b = 0.83658 − 1.26862I
0.08192 − 6.09483I 0.06758 + 5.72110I
u = 0.789237 − 0.311182I
a = −1.14249 − 0.91939I
b = 0.83658 + 1.26862I
0.08192 + 6.09483I 0.06758 − 5.72110I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772578 + 0.300651I
a = 1.43595 + 0.47376I
b = −0.606077 − 0.508848I
3.05327 + 4.56939I 1.49874 − 2.48258I
u = −0.772578 − 0.300651I
a = 1.43595 − 0.47376I
b = −0.606077 + 0.508848I
3.05327 − 4.56939I 1.49874 + 2.48258I
u = −0.327983 + 1.126830I
a = 0.973843 + 0.583016I
b = 0.256425 + 1.074870I
−2.37023 − 1.02641I 0
u = −0.327983 − 1.126830I
a = 0.973843 − 0.583016I
b = 0.256425 − 1.074870I
−2.37023 + 1.02641I 0
u = 0.666510 + 0.972232I
a = 0.23112 + 1.62158I
b = 0.834491 − 0.957996I
6.21106 − 1.42535I 0
u = 0.666510 − 0.972232I
a = 0.23112 − 1.62158I
b = 0.834491 + 0.957996I
6.21106 + 1.42535I 0
u = −0.254618 + 1.152190I
a = 0.308382 − 0.112718I
b = −0.492338 − 0.741909I
−1.45645 + 1.57837I 0
u = −0.254618 − 1.152190I
a = 0.308382 + 0.112718I
b = −0.492338 + 0.741909I
−1.45645 − 1.57837I 0
u = 0.530812 + 1.055770I
a = −1.34138 + 2.03995I
b = 0.816422 + 0.889494I
6.42459 + 4.74081I 0
u = 0.530812 − 1.055770I
a = −1.34138 − 2.03995I
b = 0.816422 − 0.889494I
6.42459 − 4.74081I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.241965 + 1.161020I
a = 0.593783 − 0.497940I
b = 0.56461 − 1.30292I
−4.56064 − 3.10867I 0
u = 0.241965 − 1.161020I
a = 0.593783 + 0.497940I
b = 0.56461 + 1.30292I
−4.56064 + 3.10867I 0
u = −0.179712 + 1.178530I
a = 0.312033 + 0.454932I
b = 0.80836 + 1.39012I
0.48993 + 7.02185I 0
u = −0.179712 − 1.178530I
a = 0.312033 − 0.454932I
b = 0.80836 − 1.39012I
0.48993 − 7.02185I 0
u = 0.337552 + 1.150340I
a = 0.029903 + 0.280018I
b = −0.229833 + 0.947989I
−5.71596 + 2.27676I 0
u = 0.337552 − 1.150340I
a = 0.029903 − 0.280018I
b = −0.229833 − 0.947989I
−5.71596 − 2.27676I 0
u = −0.441361 + 1.120500I
a = 1.302260 + 0.531091I
b = −0.196410 + 0.826154I
−2.36959 − 1.62048I 0
u = −0.441361 − 1.120500I
a = 1.302260 − 0.531091I
b = −0.196410 − 0.826154I
−2.36959 + 1.62048I 0
u = −0.539438 + 1.080200I
a = −0.58267 − 1.65912I
b = 1.64758 + 0.62868I
5.95344 − 5.84050I 0
u = −0.539438 − 1.080200I
a = −0.58267 + 1.65912I
b = 1.64758 − 0.62868I
5.95344 + 5.84050I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.416062 + 1.153030I
a = −0.417211 − 0.486945I
b = 0.078553 − 1.146340I
−2.51166 − 6.30368I 0
u = −0.416062 − 1.153030I
a = −0.417211 + 0.486945I
b = 0.078553 + 1.146340I
−2.51166 + 6.30368I 0
u = −0.529988 + 1.122110I
a = −1.43472 − 1.07430I
b = 0.70216 − 1.23357I
−0.97780 − 6.67256I 0
u = −0.529988 − 1.122110I
a = −1.43472 + 1.07430I
b = 0.70216 + 1.23357I
−0.97780 + 6.67256I 0
u = 0.515018 + 1.137380I
a = 1.42983 − 0.56620I
b = −0.550564 − 0.698729I
−4.51086 + 5.70416I 0
u = 0.515018 − 1.137380I
a = 1.42983 + 0.56620I
b = −0.550564 + 0.698729I
−4.51086 − 5.70416I 0
u = 0.595919 + 0.445110I
a = −1.71034 − 0.58122I
b = 1.032560 − 0.749088I
8.21032 − 0.24162I 6.87319 + 1.62100I
u = 0.595919 − 0.445110I
a = −1.71034 + 0.58122I
b = 1.032560 + 0.749088I
8.21032 + 0.24162I 6.87319 − 1.62100I
u = −0.634539 + 0.386396I
a = −2.62691 + 0.09834I
b = 1.45210 − 0.62541I
7.96080 + 1.22074I 6.79923 − 0.85488I
u = −0.634539 − 0.386396I
a = −2.62691 − 0.09834I
b = 1.45210 + 0.62541I
7.96080 − 1.22074I 6.79923 + 0.85488I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.495446 + 0.549605I
a = −1.81945 + 0.43460I
b = 1.158230 + 0.508717I
2.51441 + 1.02533I 3.07736 + 2.06010I
u = 0.495446 − 0.549605I
a = −1.81945 − 0.43460I
b = 1.158230 − 0.508717I
2.51441 − 1.02533I 3.07736 − 2.06010I
u = −0.279936 + 0.676376I
a = 0.982603 − 0.117408I
b = −0.148031 − 0.060354I
−0.280767 − 1.133580I −3.39541 + 6.11783I
u = −0.279936 − 0.676376I
a = 0.982603 + 0.117408I
b = −0.148031 + 0.060354I
−0.280767 + 1.133580I −3.39541 − 6.11783I
u = −0.560271 + 1.138380I
a = 1.48877 + 0.66169I
b = −0.742454 + 0.556217I
0.59224 − 9.57146I 0
u = −0.560271 − 1.138380I
a = 1.48877 − 0.66169I
b = −0.742454 − 0.556217I
0.59224 + 9.57146I 0
u = 0.702291 + 0.195645I
a = 1.088270 − 0.495569I
b = −0.323516 + 0.616413I
−1.84194 − 1.10470I −3.59487 + 1.11336I
u = 0.702291 − 0.195645I
a = 1.088270 + 0.495569I
b = −0.323516 − 0.616413I
−1.84194 + 1.10470I −3.59487 − 1.11336I
u = −0.673885 + 0.269171I
a = −0.765242 − 0.266085I
b = 0.709105 + 0.972863I
1.45545 + 2.02266I 2.54801 − 0.95165I
u = −0.673885 − 0.269171I
a = −0.765242 + 0.266085I
b = 0.709105 − 0.972863I
1.45545 − 2.02266I 2.54801 + 0.95165I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.568245 + 1.141590I
a = −1.88642 + 0.84516I
b = 0.87554 + 1.41049I
−2.37082 + 11.17440I 0
u = 0.568245 − 1.141590I
a = −1.88642 − 0.84516I
b = 0.87554 − 1.41049I
−2.37082 − 11.17440I 0
u = −0.596220 + 1.140020I
a = −2.20616 − 0.82618I
b = 1.03862 − 1.45053I
3.2588 − 15.1381I 0
u = −0.596220 − 1.140020I
a = −2.20616 + 0.82618I
b = 1.03862 + 1.45053I
3.2588 + 15.1381I 0
u = −0.694677 + 0.021213I
a = 0.410694 − 0.577612I
b = 0.112167 + 0.890796I
0.77779 + 2.28714I 0.68771 − 3.78757I
u = −0.694677 − 0.021213I
a = 0.410694 + 0.577612I
b = 0.112167 − 0.890796I
0.77779 − 2.28714I 0.68771 + 3.78757I
11
II. I
u
2
= hb − 1, a
2
− 2au + 2a + u − 2, u
2
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u + 1
a
3
=
u
−u + 1
a
7
=
1
0
a
5
=
−u
u − 1
a
10
=
a
1
a
9
=
u − 1
au + 2
a
11
=
a + 1
1
a
8
=
−a
−1
a
4
=
−au + u − 1
au − a + 2u − 1
a
4
=
−au + u − 1
au − a + 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 8
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
2
c
7
, c
11
(u − 1)
4
c
10
(u + 1)
4
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y + 2)
4
c
7
, c
10
, c
11
(y −1)
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.724745 + 0.158919I
b = 1.00000
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 0.500000 + 0.866025I
a = −1.72474 + 1.57313I
b = 1.00000
6.57974 + 2.02988I 6.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.724745 − 0.158919I
b = 1.00000
6.57974 − 2.02988I 6.00000 + 3.46410I
u = 0.500000 − 0.866025I
a = −1.72474 − 1.57313I
b = 1.00000
6.57974 − 2.02988I 6.00000 + 3.46410I
15
III. I
u
3
= hb − 1, a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
7
=
−1
0
a
5
=
−u
u + 1
a
10
=
−u − 1
1
a
9
=
−u − 1
1
a
11
=
−u
1
a
8
=
−u − 1
1
a
4
=
−u
u + 1
a
4
=
−u
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
(u + 1)
2
c
10
, c
11
(u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 1.00000
1.64493 − 2.02988I 0. + 3.46410I
u = −0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 1.00000
1.64493 + 2.02988I 0. − 3.46410I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
66
− 2u
65
+ ··· − 9u + 3)
c
2
((u
2
+ u + 1)
3
)(u
66
+ 32u
65
+ ··· + 33u + 9)
c
3
, c
4
, c
8
u
2
(u
2
+ 2)
2
(u
66
+ u
65
+ ··· + 16u + 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
66
− 2u
65
+ ··· − 9u + 3)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
66
+ 2u
65
+ ··· + 9195u + 2391)
c
7
((u − 1)
4
)(u + 1)
2
(u
66
− 3u
65
+ ··· − 16u + 3)
c
9
u
2
(u
2
+ 2)
2
(u
66
− u
65
+ ··· − 64u + 548)
c
10
((u − 1)
2
)(u + 1)
4
(u
66
− 3u
65
+ ··· − 16u + 3)
c
11
((u − 1)
6
)(u
66
− 33u
65
+ ··· − 4u + 9)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
66
+ 32y
65
+ ··· + 33y + 9)
c
2
((y
2
+ y + 1)
3
)(y
66
+ 8y
65
+ ··· + 873y + 81)
c
3
, c
4
, c
8
y
2
(y + 2)
4
(y
66
+ 61y
65
+ ··· − 128y + 16)
c
6
((y
2
+ y + 1)
3
)(y
66
− 16y
65
+ ··· − 6.01072 × 10
7
y + 5716881)
c
7
, c
10
((y −1)
6
)(y
66
− 33y
65
+ ··· − 4y + 9)
c
9
y
2
(y + 2)
4
(y
66
+ y
65
+ ··· − 1284224y + 300304)
c
11
((y −1)
6
)(y
66
+ 7y
65
+ ··· − 2176y + 81)
21
