11n
183
(K11n
183
)
A knot diagram
1
Linearized knot diagam
5 7 1 9 3 9 3 11 5 7 6
Solving Sequence
6,9 3,7
2 5 10 11 1 4 8
c
6
c
2
c
5
c
9
c
10
c
1
c
3
c
8
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, 5u
6
+ 6u
5
+ 13u
4
− 7u
3
+ 29u
2
+ 9a − 11u + 16, u
7
+ u
6
+ 2u
5
− 3u
4
+ 5u
3
− 3u
2
+ 4u − 1i
I
u
2
= hb − u, 54u
5
− 72u
4
− 84u
3
− 80u
2
+ 11a − 85u − 184, u
6
− u
5
− 2u
4
− 2u
3
− 2u
2
− 4u − 1i
I
u
3
= h37u
7
− 61u
6
+ 51u
5
− 60u
4
+ 86u
3
− 191u
2
+ 29b + 214u − 54,
− 41u
7
+ 77u
6
− 62u
5
+ 61u
4
− 100u
3
+ 214u
2
+ 29a − 292u + 81,
u
8
− 2u
7
+ 2u
6
− 2u
5
+ 3u
4
− 6u
3
+ 8u
2
− 4u + 1i
I
u
4
= hu
3
+ 3u
2
+ 3b + 6u + 7, −2u
3
− 21u
2
+ 39a − 57u − 59, u
4
+ 4u
3
+ 9u
2
+ 10u + 13i
I
u
5
= hb − u − 1, a − u − 1, u
2
+ u + 1i
I
u
6
= hb + u, a + 4u − 9, u
2
− 2u − 1i
I
u
7
= hb + u − 1, 3a − 2u + 2, u
2
− u + 3i
I
u
8
= hb + u + 1, a, u
2
+ u + 1i
I
u
9
= hb + 1, a + 1, u − 1i
I
u
10
= hb + u − 1, a − u + 1, u
2
− u + 1i
* 10 irreducible components of dim
C
= 0, with total 36 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
= hb − u, 5u
6
+6u
5
+· · ·+ 9a+16, u
7
+u
6
+2u
5
−3u
4
+5u
3
−3u
2
+4u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
−
5
9
u
6
−
2
3
u
5
+ ··· +
11
9
u −
16
9
u
a
7
=
1
u
2
a
2
=
−
1
3
u
6
−
2
3
u
4
+ ··· +
7
3
u −
5
3
−
1
9
u
6
−
1
3
u
5
+ ··· −
5
9
u +
4
9
a
5
=
1
9
u
6
+
1
3
u
5
+ ··· −
4
9
u +
14
9
−u
2
a
10
=
−
2
9
u
6
−
2
3
u
5
+ ··· −
19
9
u −
1
9
−
1
9
u
6
−
1
3
u
5
+ ··· −
5
9
u +
4
9
a
11
=
−1
−
2
9
u
6
−
2
3
u
5
+ ··· −
19
9
u +
8
9
a
1
=
−
2
9
u
6
−
2
3
u
5
+ ··· −
19
9
u −
1
9
−
2
9
u
6
−
2
3
u
5
+ ··· −
19
9
u +
8
9
a
4
=
−
1
9
u
6
−
1
3
u
5
+ ··· +
4
9
u −
14
9
4
9
u
6
+
1
3
u
5
+ ··· −
7
9
u +
2
9
a
8
=
u
4
9
u
6
+
1
3
u
5
+ ··· −
7
9
u +
2
9
a
8
=
u
4
9
u
6
+
1
3
u
5
+ ··· −
7
9
u +
2
9
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
26
9
u
6
−
8
3
u
5
−
28
9
u
4
+
112
9
u
3
−
86
9
u
2
+
14
9
u −
130
9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
7
+ 4u
6
+ 24u
5
+ 58u
4
+ 139u
3
+ 194u
2
+ 120u + 24
c
2
, c
4
, c
7
c
9
u
7
+ u
6
+ 8u
5
− u
4
+ 12u
3
− 10u
2
− 2u + 2
c
3
, c
5
, c
6
c
8
u
7
− u
6
+ 2u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ 4u + 1
c
11
u
7
+ 7u
6
+ 28u
5
+ 69u
4
+ 106u
3
+ 96u
2
+ 48u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
7
+ 32y
6
+ 390y
5
+ 1996y
4
+ 2385y
3
− 7060y
2
+ 5088y −576
c
2
, c
4
, c
7
c
9
y
7
+ 15y
6
+ 90y
5
+ 207y
4
+ 88y
3
− 144y
2
+ 44y −4
c
3
, c
5
, c
6
c
8
y
7
+ 3y
6
+ 20y
5
+ 25y
4
+ 25y
3
+ 25y
2
+ 10y −1
c
11
y
7
+ 7y
6
+ 30y
5
− 73y
4
+ 564y
3
− 144y
2
+ 768y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.757011 + 0.685123I
a = 0.681482 − 1.170220I
b = 0.757011 + 0.685123I
−1.68375 − 3.49152I −15.3039 + 5.7802I
u = 0.757011 − 0.685123I
a = 0.681482 + 1.170220I
b = 0.757011 − 0.685123I
−1.68375 + 3.49152I −15.3039 − 5.7802I
u = −0.134406 + 0.899226I
a = 0.516003 + 0.736811I
b = −0.134406 + 0.899226I
10.56250 + 1.19923I −2.68829 − 5.87566I
u = −0.134406 − 0.899226I
a = 0.516003 − 0.736811I
b = −0.134406 − 0.899226I
10.56250 − 1.19923I −2.68829 + 5.87566I
u = 0.285988
a = −1.68483
b = 0.285988
−0.666622 −14.5180
u = −1.26560 + 1.56709I
a = −0.855070 − 0.684725I
b = −1.26560 + 1.56709I
14.4836 + 11.4109I −7.74903 − 4.57488I
u = −1.26560 − 1.56709I
a = −0.855070 + 0.684725I
b = −1.26560 − 1.56709I
14.4836 − 11.4109I −7.74903 + 4.57488I
5
II.
I
u
2
= hb − u, 54u
5
− 72u
4
+ · · · + 11a − 184, u
6
− u
5
− 2u
4
− 2u
3
− 2u
2
− 4u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
−4.90909u
5
+ 6.54545u
4
+ ··· + 7.72727u + 16.7273
u
a
7
=
1
u
2
a
2
=
−4.36364u
5
+ 5.81818u
4
+ ··· + 7.09091u + 15.0909
−0.272727u
5
+ 0.363636u
4
+ ··· + 0.818182u − 0.181818
a
5
=
−1.63636u
5
+ 2.18182u
4
+ ··· + 2.90909u + 5.90909
−u
2
a
10
=
−2.45455u
5
+ 3.27273u
4
+ ··· + 3.36364u + 8.36364
−0.272727u
5
+ 0.363636u
4
+ ··· + 0.818182u − 0.181818
a
11
=
−2.45455u
5
+ 3.27273u
4
+ ··· + 3.36364u + 9.36364
−0.272727u
5
+ 0.363636u
4
+ ··· + 0.818182u − 0.181818
a
1
=
−2.72727u
5
+ 3.63636u
4
+ ··· + 4.18182u + 9.18182
−0.272727u
5
+ 0.363636u
4
+ ··· + 0.818182u − 0.181818
a
4
=
1.63636u
5
− 2.18182u
4
+ ··· − 2.90909u − 5.90909
−0.181818u
5
− 0.0909091u
4
+ ··· + 0.545455u + 0.545455
a
8
=
6.72727u
5
− 8.63636u
4
+ ··· − 10.1818u − 23.1818
−0.181818u
5
− 0.0909091u
4
+ ··· + 0.545455u + 0.545455
a
8
=
6.72727u
5
− 8.63636u
4
+ ··· − 10.1818u − 23.1818
−0.181818u
5
− 0.0909091u
4
+ ··· + 0.545455u + 0.545455
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
84
11
u
5
+
112
11
u
4
+
116
11
u
3
+
188
11
u
2
+
164
11
u +
274
11
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u − 1)
6
c
2
, c
4
, c
7
c
9
(u
3
− u
2
− 1)
2
c
3
, c
5
, c
6
c
8
u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ 4u − 1
c
11
(u
3
− 3u
2
+ 4u − 1)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
6
c
2
, c
4
, c
7
c
9
(y
3
− y
2
− 2y −1)
2
c
3
, c
5
, c
6
c
8
y
6
− 5y
5
− 4y
4
− 6y
3
− 8y
2
− 12y + 1
c
11
(y
3
− y
2
+ 10y −1)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.346535 + 1.017670I
a = 0.040902 − 0.214369I
b = 0.346535 + 1.017670I
1.59057 − 4.74950I −3.95625 + 7.59808I
u = 0.346535 − 1.017670I
a = 0.040902 + 0.214369I
b = 0.346535 − 1.017670I
1.59057 + 4.74950I −3.95625 − 7.59808I
u = −0.920485 + 0.648681I
a = −1.37622 − 0.47421I
b = −0.920485 + 0.648681I
1.59057 + 4.74950I −3.95625 − 7.59808I
u = −0.920485 − 0.648681I
a = −1.37622 + 0.47421I
b = −0.920485 − 0.648681I
1.59057 − 4.74950I −3.95625 + 7.59808I
u = −0.280929
a = 15.0105
b = −0.280929
−8.11594 21.9130
u = 2.42883
a = 0.660157
b = 2.42883
−8.11594 21.9130
9
III. I
u
3
=
h37u
7
−61u
6
+· · ·+29b−54, −41u
7
+77u
6
+· · ·+29a+81, u
8
−2u
7
+· · ·−4u+1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
1.41379u
7
− 2.65517u
6
+ ··· + 10.0690u − 2.79310
−1.27586u
7
+ 2.10345u
6
+ ··· − 7.37931u + 1.86207
a
7
=
1
u
2
a
2
=
0.482759u
7
− 0.931034u
6
+ ··· + 3.41379u − 0.758621
−u
7
+ 2u
6
− 2u
5
+ 2u
4
− 3u
3
+ 6u
2
− 7u + 2
a
5
=
0.655172u
7
− 1.62069u
6
+ ··· + 6.27586u − 3.17241
−0.551724u
7
+ 1.20690u
6
+ ··· − 4.75862u + 2.72414
a
10
=
0.310345u
7
− 1.24138u
6
+ ··· + 4.55172u − 2.34483
−0.827586u
7
+ 1.31034u
6
+ ··· − 4.13793u + 2.58621
a
11
=
0.379310u
7
− 1.51724u
6
+ ··· + 5.89655u − 4.31034
−0.551724u
7
+ 1.20690u
6
+ ··· − 4.75862u + 2.72414
a
1
=
−0.172414u
7
− 0.310345u
6
+ ··· + 1.13793u − 1.58621
−0.551724u
7
+ 1.20690u
6
+ ··· − 4.75862u + 2.72414
a
4
=
0.655172u
7
− 1.62069u
6
+ ··· + 6.27586u − 3.17241
−0.172414u
7
+ 0.689655u
6
+ ··· − 2.86207u + 2.41379
a
8
=
0.448276u
7
+ 0.206897u
6
+ ··· − 0.758621u + 3.72414
0.172414u
7
− 0.689655u
6
+ ··· + 2.86207u − 2.41379
a
8
=
0.448276u
7
+ 0.206897u
6
+ ··· − 0.758621u + 3.72414
0.172414u
7
− 0.689655u
6
+ ··· + 2.86207u − 2.41379
(ii) Obstruction class = 1
(iii) Cusp Shapes =
48
29
u
7
−
76
29
u
6
+
74
29
u
5
−
70
29
u
4
+
110
29
u
3
−
218
29
u
2
+
298
29
u −
324
29
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
− 2u
3
+ 2)
2
c
2
, c
4
, c
7
c
9
(u
4
+ u
2
− 1)
2
c
3
, c
5
u
8
+ 2u
7
+ 2u
6
+ 2u
5
+ 3u
4
+ 6u
3
+ 8u
2
+ 4u + 1
c
6
, c
8
u
8
− 2u
7
+ 2u
6
− 2u
5
+ 3u
4
− 6u
3
+ 8u
2
− 4u + 1
c
10
(u
4
+ 2u
3
+ 2)
2
c
11
(u
4
− 2u
2
+ 5)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
4
− 4y
3
+ 4y
2
+ 4)
2
c
2
, c
4
, c
7
c
9
(y
2
+ y −1)
4
c
3
, c
5
, c
6
c
8
y
8
+ 2y
6
+ 3y
4
+ 22y
2
+ 1
c
11
(y
2
− 2y + 5)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.415941 + 1.202090I
a = 0.415941 + 0.584059I
b = −0.326993 − 0.326993I
0.82247 − 3.66386I −8.00000 + 2.00000I
u = 0.415941 − 1.202090I
a = 0.415941 − 0.584059I
b = −0.326993 + 0.326993I
0.82247 + 3.66386I −8.00000 − 2.00000I
u = 1.202090 + 0.415941I
a = 1.202090 − 0.202093I
b = 0.945027 + 0.945027I
0.82247 − 3.66386I −8.00000 + 2.00000I
u = 1.202090 − 0.415941I
a = 1.202090 + 0.202093I
b = 0.945027 − 0.945027I
0.82247 + 3.66386I −8.00000 − 2.00000I
u = −0.945027 + 0.945027I
a = −0.945027 − 0.673007I
b = −1.202090 + 0.415941I
0.82247 + 3.66386I −8.00000 − 2.00000I
u = −0.945027 − 0.945027I
a = −0.945027 + 0.673007I
b = −1.202090 − 0.415941I
0.82247 − 3.66386I −8.00000 + 2.00000I
u = 0.326993 + 0.326993I
a = 0.32699 + 1.94503I
b = −0.415941 − 1.202090I
0.82247 − 3.66386I −8.00000 + 2.00000I
u = 0.326993 − 0.326993I
a = 0.32699 − 1.94503I
b = −0.415941 + 1.202090I
0.82247 + 3.66386I −8.00000 − 2.00000I
13
IV. I
u
4
=
hu
3
+3u
2
+3b+6u+7, −2u
3
−21u
2
+39a−57u−59, u
4
+4u
3
+9u
2
+10u+13i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
0.0512821u
3
+ 0.538462u
2
+ 1.46154u + 1.51282
−
1
3
u
3
− u
2
− 2u −
7
3
a
7
=
1
u
2
a
2
=
0.0512821u
3
+ 1.53846u
2
+ 3.46154u + 3.51282
−
7
3
u
3
− 8u
2
− 12u −
46
3
a
5
=
0.230769u
3
+ 0.923077u
2
+ 1.07692u + 0.307692
−
2
3
u
3
− u
2
− 2u +
1
3
a
10
=
−0.307692u
3
− 1.23077u
2
− 3.76923u − 5.07692
−
4
3
u
3
− 3u
2
+ u −
10
3
a
11
=
0.0256410u
3
− 0.230769u
2
− 0.769231u − 1.74359
1
a
1
=
0.0256410u
3
− 0.230769u
2
− 0.769231u − 0.743590
1
a
4
=
−0.230769u
3
− 0.923077u
2
− 1.07692u − 0.307692
−
1
3
u
3
− u
2
− u −
1
3
a
8
=
0.435897u
3
+ 1.07692u
2
+ 0.923077u − 1.64103
−
1
3
u
3
− u
2
− u −
1
3
a
8
=
0.435897u
3
+ 1.07692u
2
+ 0.923077u − 1.64103
−
1
3
u
3
− u
2
− u −
1
3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
− 2u + 10)
2
c
2
, c
4
, c
7
c
9
(u
2
− u + 7)
2
c
3
, c
5
, c
6
c
8
u
4
− 4u
3
+ 9u
2
− 10u + 13
c
11
(u + 1)
4
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
2
+ 16y + 100)
2
c
2
, c
4
, c
7
c
9
(y
2
+ 13y + 49)
2
c
3
, c
5
, c
6
c
8
y
4
+ 2y
3
+ 27y
2
+ 134y + 169
c
11
(y −1)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13397 + 1.50000I
a = 0.16139 + 1.80695I
b = −0.13397 − 1.50000I
13.1595 −6.00000
u = −0.13397 − 1.50000I
a = 0.16139 − 1.80695I
b = −0.13397 + 1.50000I
13.1595 −6.00000
u = −1.86603 + 1.50000I
a = −0.238314 − 0.191568I
b = −1.86603 − 1.50000I
13.1595 −6.00000
u = −1.86603 − 1.50000I
a = −0.238314 + 0.191568I
b = −1.86603 + 1.50000I
13.1595 −6.00000
17
V. I
u
5
= hb − u − 1, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
u + 1
u + 1
a
7
=
1
−u − 1
a
2
=
3u + 2
2
a
5
=
−u + 1
−u
a
10
=
−3u − 3
−2
a
11
=
−1
−2u − 1
a
1
=
−2u − 2
−2u − 1
a
4
=
−u + 1
2
a
8
=
u
−2
a
8
=
u
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ u + 7
c
2
, c
4
, c
7
c
9
, c
11
u
2
+ 3
c
3
, c
5
u
2
− u + 1
c
6
, c
8
u
2
+ u + 1
c
10
u
2
− u + 7
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
2
+ 13y + 49
c
2
, c
4
, c
7
c
9
, c
11
(y + 3)
2
c
3
, c
5
, c
6
c
8
y
2
+ y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 + 0.866025I
9.86960 −9.00000
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 − 0.866025I
9.86960 −9.00000
21
VI. I
u
6
= hb + u, a + 4u − 9, u
2
− 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
−4u + 9
−u
a
7
=
1
2u + 1
a
2
=
−3u + 8
2u + 1
a
5
=
u − 3
−2u − 1
a
10
=
−2u + 4
−2u − 1
a
11
=
−2u + 5
0
a
1
=
−2u + 5
0
a
4
=
u − 3
−u
a
8
=
5u − 12
u
a
8
=
5u − 12
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −52
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
2
c
2
, c
4
, c
7
c
9
u
2
− 2
c
3
, c
5
u
2
+ 2u − 1
c
6
, c
8
u
2
− 2u − 1
c
10
(u − 1)
2
c
11
u
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
2
c
2
, c
4
, c
7
c
9
(y −2)
2
c
3
, c
5
, c
6
c
8
y
2
− 6y + 1
c
11
y
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.414214
a = 10.6569
b = 0.414214
−8.22467 −52.0000
u = 2.41421
a = −0.656854
b = −2.41421
−8.22467 −52.0000
25
VII. I
u
7
= hb + u − 1, 3a − 2u + 2, u
2
− u + 3i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
2
3
u −
2
3
−u + 1
a
7
=
1
u − 3
a
2
=
5
3
u +
1
3
−2u − 5
a
5
=
−
2
3
u −
1
3
u + 2
a
10
=
1
3
u +
8
3
2u − 7
a
11
=
1
3
u +
2
3
−1
a
1
=
1
3
u −
1
3
−1
a
4
=
2
3
u +
1
3
1
a
8
=
2
3
u −
5
3
1
a
8
=
2
3
u −
5
3
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u + 2)
2
c
2
, c
4
, c
7
c
9
u
2
+ 3u + 5
c
3
, c
5
, c
6
c
8
u
2
+ u + 3
c
11
(u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −4)
2
c
2
, c
4
, c
7
c
9
y
2
+ y + 25
c
3
, c
5
, c
6
c
8
y
2
+ 5y + 9
c
11
(y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.65831I
a = −0.333333 + 1.105540I
b = 0.50000 − 1.65831I
3.28987 −6.00000
u = 0.50000 − 1.65831I
a = −0.333333 − 1.105540I
b = 0.50000 + 1.65831I
3.28987 −6.00000
29
VIII. I
u
8
= hb + u + 1, a, u
2
+ u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
0
−u − 1
a
7
=
1
−u − 1
a
2
=
−u − 1
−1
a
5
=
1
−u
a
10
=
−u
−1
a
11
=
−u
−1
a
1
=
−u − 1
−1
a
4
=
−1
−1
a
8
=
1
−1
a
8
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
u
2
− u + 1
c
11
(u − 1)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
2
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
y
2
+ y + 1
c
11
(y −1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
3.28987 −6.00000
u = −0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
3.28987 −6.00000
33
IX. I
u
9
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
1
a
3
=
−1
−1
a
7
=
1
1
a
2
=
−1
−1
a
5
=
0
−1
a
10
=
0
1
a
11
=
−1
0
a
1
=
−1
0
a
4
=
0
−1
a
8
=
1
1
a
8
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u − 1
c
2
, c
4
, c
7
c
9
, c
11
u
c
3
, c
5
, c
10
u + 1
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
8
, c
10
y −1
c
2
, c
4
, c
7
c
9
, c
11
y
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−3.28987 −12.0000
37
X. I
u
10
= hb + u − 1, a − u + 1, u
2
− u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
u − 1
−u + 1
a
7
=
1
u − 1
a
2
=
u
0
a
5
=
−u + 1
u
a
10
=
u − 1
0
a
11
=
−1
1
a
1
=
0
1
a
4
=
u − 1
0
a
8
=
u
0
a
8
=
u
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −9
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
8
, c
10
u
2
+ u + 1
c
2
, c
4
, c
7
c
9
, c
11
(u + 1)
2
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
8
, c
10
y
2
+ y + 1
c
2
, c
4
, c
7
c
9
, c
11
(y −1)
2
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 − 0.866025I
0 −9.00000
u = 0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 + 0.866025I
0 −9.00000
41
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
7
(u + 1)
2
(u + 2)
2
(u
2
− 2u + 10)
2
(u
2
+ u + 1)(u
2
+ u + 7)
· ((u
4
− 2u
3
+ 2)
2
)(u
7
+ 4u
6
+ ··· + 120u + 24)
c
2
, c
4
, c
7
c
9
u(u + 1)
2
(u
2
− 2)(u
2
+ 3)(u
2
− u + 1)(u
2
− u + 7)
2
(u
2
+ 3u + 5)
· ((u
3
− u
2
− 1)
2
)(u
4
+ u
2
− 1)
2
(u
7
+ u
6
+ ··· − 2u + 2)
c
3
, c
5
(u + 1)(u
2
− u + 1)
2
(u
2
+ u + 1)(u
2
+ u + 3)(u
2
+ 2u − 1)
· (u
4
− 4u
3
+ 9u
2
− 10u + 13)(u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ 4u − 1)
· (u
7
− u
6
+ 2u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ 4u + 1)
· (u
8
+ 2u
7
+ 2u
6
+ 2u
5
+ 3u
4
+ 6u
3
+ 8u
2
+ 4u + 1)
c
6
, c
8
(u − 1)(u
2
− 2u − 1)(u
2
− u + 1)(u
2
+ u + 1)
2
(u
2
+ u + 3)
· (u
4
− 4u
3
+ 9u
2
− 10u + 13)(u
6
+ u
5
− 2u
4
+ 2u
3
− 2u
2
+ 4u − 1)
· (u
7
− u
6
+ 2u
5
+ 3u
4
+ 5u
3
+ 3u
2
+ 4u + 1)
· (u
8
− 2u
7
+ 2u
6
− 2u
5
+ 3u
4
− 6u
3
+ 8u
2
− 4u + 1)
c
10
u
2
(u − 1)
8
(u + 1)(u + 2)
2
(u
2
− 2u + 10)
2
(u
2
− u + 7)(u
2
+ u + 1)
· ((u
4
+ 2u
3
+ 2)
2
)(u
7
+ 4u
6
+ ··· + 120u + 24)
c
11
u
3
(u − 1)
4
(u + 1)
6
(u
2
+ 3)(u
3
− 3u
2
+ 4u − 1)
2
(u
4
− 2u
2
+ 5)
2
· (u
7
+ 7u
6
+ 28u
5
+ 69u
4
+ 106u
3
+ 96u
2
+ 48u + 8)
42
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
2
(y −4)
2
(y −1)
9
(y
2
+ y + 1)(y
2
+ 13y + 49)(y
2
+ 16y + 100)
2
· (y
4
− 4y
3
+ 4y
2
+ 4)
2
· (y
7
+ 32y
6
+ 390y
5
+ 1996y
4
+ 2385y
3
− 7060y
2
+ 5088y −576)
c
2
, c
4
, c
7
c
9
y(y −2)
2
(y −1)
2
(y + 3)
2
(y
2
+ y −1)
4
(y
2
+ y + 1)(y
2
+ y + 25)
· (y
2
+ 13y + 49)
2
(y
3
− y
2
− 2y −1)
2
· (y
7
+ 15y
6
+ 90y
5
+ 207y
4
+ 88y
3
− 144y
2
+ 44y −4)
c
3
, c
5
, c
6
c
8
(y −1)(y
2
− 6y + 1)(y
2
+ y + 1)
3
(y
2
+ 5y + 9)
· (y
4
+ 2y
3
+ 27y
2
+ 134y + 169)(y
6
− 5y
5
+ ··· − 12y + 1)
· (y
7
+ 3y
6
+ 20y
5
+ 25y
4
+ 25y
3
+ 25y
2
+ 10y −1)
· (y
8
+ 2y
6
+ 3y
4
+ 22y
2
+ 1)
c
11
y
3
(y −1)
10
(y + 3)
2
(y
2
− 2y + 5)
4
(y
3
− y
2
+ 10y −1)
2
· (y
7
+ 7y
6
+ 30y
5
− 73y
4
+ 564y
3
− 144y
2
+ 768y −64)
43
