9
40
(K9a
37
)
A knot diagram
1
Linearized knot diagam
8 7 6 2 1 9 5 4 3
Solving Sequence
3,6 4,9
7 1 2 5 8
c
3
c
6
c
9
c
2
c
5
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, a + 1, u
4
+ 2u
3
+ 2u
2
+ 1i
I
u
2
= hb − u, 4u
3
− 6u
2
+ a + 3u + 6, u
4
− u
3
+ 2u + 1i
I
u
3
= hu
3
+ 3u
2
+ b + 5u + 2, 2u
3
+ 3u
2
+ 7a + 3u − 7, u
4
+ 5u
3
+ 12u
2
+ 14u + 7i
I
u
4
= h2u
3
− 3u
2
+ b + 2u + 4, a + 1, u
4
− u
3
+ 2u + 1i
I
u
5
= hb − u, a + u − 2, u
2
− u + 1i
I
u
6
= hb + u + 1, a + 1, u
2
− u + 1i
I
u
7
= hb + u + 1, 3a + u, u
2
+ 3u + 3i
I
u
8
= hb + u, a + 1, u
4
− u
3
+ u + 1i
I
u
9
= hb − 1, u
3
− 2u
2
+ a + 2u, u
4
− u
3
+ 2u + 1i
I
u
10
= hu
3
− 2u
2
+ b + 2u + 1, −u
3
+ u
2
+ a − 2, u
4
− u
3
+ 2u + 1i
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).
1
I
u
11
= h−a
3
− 2a
2
+ b − 2a + 1, a
4
+ a
3
− 2a + 1, u − 1i
I
u
12
= hb, a + 1, u
2
− u + 1i
I
u
13
= hb − u, a, u
2
− u + 1i
I
u
14
= hb − u, a + 1, u
2
+ u + 1i
I
u
15
= hb + 1, a + 1, u − 1i
I
v
1
= ha, b
2
− b + 1, v −1i
* 16 irreducible components of dim
C
= 0, with total 47 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= hb − u, a + 1, u
4
+ 2u
3
+ 2u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
−1
u
a
7
=
−u
u
2
+ u
a
1
=
−u − 1
u
a
2
=
−u
3
− u
2
+ 1
−u
2
− 1
a
5
=
−u
3
− 2u
2
− u
u
3
+ u
2
+ u
a
8
=
−u
2
− u − 1
u
3
+ 2u
2
+ u + 1
a
8
=
−u
2
− u − 1
u
3
+ 2u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u
2
+ 6u
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
u
4
− 2u
3
+ 2u
2
+ 1
c
2
, c
5
, c
8
u
4
− 2u
3
+ 4u
2
− 2u + 2
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y
4
+ 6y
2
+ 4y + 1
c
2
, c
5
, c
8
y
4
+ 4y
3
+ 12y
2
+ 12y + 4
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.189785 + 0.602803I
a = −1.00000
b = 0.189785 + 0.602803I
−0.10892 − 1.69225I −0.82541 + 4.98965I
u = 0.189785 − 0.602803I
a = −1.00000
b = 0.189785 − 0.602803I
−0.10892 + 1.69225I −0.82541 − 4.98965I
u = −1.18978 + 1.04318I
a = −1.00000
b = −1.18978 + 1.04318I
−4.0034 + 15.0183I −5.17459 − 8.63488I
u = −1.18978 − 1.04318I
a = −1.00000
b = −1.18978 − 1.04318I
−4.0034 − 15.0183I −5.17459 + 8.63488I
6
II. I
u
2
= hb − u, 4u
3
− 6u
2
+ a + 3u + 6, u
4
− u
3
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
−4u
3
+ 6u
2
− 3u − 6
u
a
7
=
7u
3
− 12u
2
+ 8u + 8
u
3
− 2u
2
+ u + 2
a
1
=
−4u
3
+ 6u
2
− 4u − 6
u
a
2
=
−u
2
+ 3u − 3
u
3
− 2u
2
+ u + 1
a
5
=
4u
3
− 8u
2
+ 8u + 4
2u
3
− 2u
2
+ u + 2
a
8
=
−5u
3
+ 8u
2
− 4u − 8
−1
a
8
=
−5u
3
+ 8u
2
− 4u − 8
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12u
3
+ 24u
2
− 12u − 30
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
4
+ u
3
− 2u + 1
c
2
, c
8
(u
2
+ u + 1)
2
c
4
, c
6
u
4
− 5u
3
+ 12u
2
− 14u + 7
c
5
(u
2
− 2u + 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
y
4
− y
3
+ 6y
2
− 4y + 1
c
2
, c
8
(y
2
+ y + 1)
2
c
4
, c
6
y
4
− y
3
+ 18y
2
− 28y + 49
c
5
(y
2
+ 4y + 16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = −1.32516 − 2.80932I
b = −0.621964 + 0.187730I
−3.28987 + 6.08965I −12.0000 − 10.3923I
u = −0.621964 − 0.187730I
a = −1.32516 + 2.80932I
b = −0.621964 − 0.187730I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 1.12196 + 1.05376I
a = 0.825159 − 0.211249I
b = 1.12196 + 1.05376I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 1.12196 − 1.05376I
a = 0.825159 + 0.211249I
b = 1.12196 − 1.05376I
−3.28987 + 6.08965I −12.0000 − 10.3923I
10
III.
I
u
3
= hu
3
+3u
2
+b +5u +2, 2u
3
+3u
2
+7a +3u −7, u
4
+5u
3
+12u
2
+14u +7i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
−
2
7
u
3
−
3
7
u
2
−
3
7
u + 1
−u
3
− 3u
2
− 5u − 2
a
7
=
−
10
7
u
3
−
36
7
u
2
−
64
7
u − 5
−2u
3
− 8u
2
− 14u − 10
a
1
=
5
7
u
3
+
18
7
u
2
+
32
7
u + 3
−u
3
− 3u
2
− 5u − 2
a
2
=
2
7
u
3
−
4
7
u
2
−
18
7
u − 5
4u
3
+ 16u
2
+ 28u + 16
a
5
=
4
7
u
3
+
13
7
u
2
+
20
7
u + 1
u
2
+ 4u + 4
a
8
=
−
9
7
u
3
−
31
7
u
2
−
52
7
u − 4
−u
3
− 6u
2
− 12u − 9
a
8
=
−
9
7
u
3
−
31
7
u
2
−
52
7
u − 4
−u
3
− 6u
2
− 12u − 9
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12u
3
− 48u
2
− 84u − 66
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
4
− 5u
3
+ 12u
2
− 14u + 7
c
2
(u
2
− 2u + 4)
2
c
4
, c
6
, c
7
c
9
u
4
+ u
3
− 2u + 1
c
5
, c
8
(u
2
+ u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
4
− y
3
+ 18y
2
− 28y + 49
c
2
(y
2
+ 4y + 16)
2
c
4
, c
6
, c
7
c
9
y
4
− y
3
+ 6y
2
− 4y + 1
c
5
, c
8
(y
2
+ y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.148400 + 0.632502I
a = 1.137350 − 0.291171I
b = 1.12196 − 1.05376I
−3.28987 + 6.08965I −12.0000 − 10.3923I
u = −1.148400 − 0.632502I
a = 1.137350 + 0.291171I
b = 1.12196 + 1.05376I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = −1.35160 + 1.49853I
a = −0.137346 − 0.291171I
b = −0.621964 − 0.187730I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = −1.35160 − 1.49853I
a = −0.137346 + 0.291171I
b = −0.621964 + 0.187730I
−3.28987 + 6.08965I −12.0000 − 10.3923I
14
IV. I
u
4
= h2u
3
− 3u
2
+ b + 2u + 4, a + 1, u
4
− u
3
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
−1
−2u
3
+ 3u
2
− 2u − 4
a
7
=
−u
u
3
− 2u
2
+ u + 2
a
1
=
2u
3
− 3u
2
+ 2u + 3
−2u
3
+ 3u
2
− 2u − 4
a
2
=
u
3
− u
2
+ 2
u
3
− 2u
2
+ u + 1
a
5
=
u
3
− 2u
2
+ 2u + 1
−2u
3
+ 4u
2
− 2u − 3
a
8
=
2u
3
− 4u
2
+ 2u + 3
−2u
3
+ 3u
2
− 2
a
8
=
2u
3
− 4u
2
+ 2u + 3
−2u
3
+ 3u
2
− 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12u
3
+ 24u
2
− 12u − 30
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
u
4
+ u
3
− 2u + 1
c
2
, c
5
(u
2
+ u + 1)
2
c
7
, c
9
u
4
− 5u
3
+ 12u
2
− 14u + 7
c
8
(u
2
− 2u + 4)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
4
− y
3
+ 6y
2
− 4y + 1
c
2
, c
5
(y
2
+ y + 1)
2
c
7
, c
9
y
4
− y
3
+ 18y
2
− 28y + 49
c
8
(y
2
+ 4y + 16)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = −1.00000
b = −1.35160 − 1.49853I
−3.28987 + 6.08965I −12.0000 − 10.3923I
u = −0.621964 − 0.187730I
a = −1.00000
b = −1.35160 + 1.49853I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 1.12196 + 1.05376I
a = −1.00000
b = −1.148400 − 0.632502I
−3.28987 − 6.08965I −12.0000 + 10.3923I
u = 1.12196 − 1.05376I
a = −1.00000
b = −1.148400 + 0.632502I
−3.28987 + 6.08965I −12.0000 − 10.3923I
18
V. I
u
5
= hb − u, a + u − 2, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u − 1
a
9
=
−u + 2
u
a
7
=
−3
−u + 1
a
1
=
−2u + 2
u
a
2
=
3u − 2
−u
a
5
=
4u − 4
−u
a
8
=
1
0
a
8
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 6
19
(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
+ u + 1
c
4
, c
6
u
2
− 3u + 3
c
5
(u − 2)
2
20
(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
2
+ y + 1
c
4
, c
6
y
2
− 3y + 9
c
5
(y −4)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.50000 − 0.86603I
b = 0.500000 + 0.866025I
− 6.08965I 0. + 10.39230I
u = 0.500000 − 0.866025I
a = 1.50000 + 0.86603I
b = 0.500000 − 0.866025I
6.08965I 0. − 10.39230I
22
VI. I
u
6
= hb + u + 1, a + 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u − 1
a
9
=
−1
−u − 1
a
7
=
−u
−u + 1
a
1
=
u
−u − 1
a
2
=
0
−u
a
5
=
1
2u − 2
a
8
=
1
u − 3
a
8
=
1
u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
u
2
+ u + 1
c
7
, c
9
u
2
− 3u + 3
c
8
(u − 2)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
y
2
+ y + 1
c
7
, c
9
y
2
− 3y + 9
c
8
(y −4)
2
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = −1.50000 − 0.86603I
− 6.08965I 0. + 10.39230I
u = 0.500000 − 0.866025I
a = −1.00000
b = −1.50000 + 0.86603I
6.08965I 0. − 10.39230I
26
VII. I
u
7
= hb + u + 1, 3a + u, u
2
+ 3u + 3i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
−3u − 3
a
9
=
−
1
3
u
−u − 1
a
7
=
−
2
3
u − 1
−2
a
1
=
2
3
u + 1
−u − 1
a
2
=
4
3
u + 3
4
a
5
=
1
3
u
u + 1
a
8
=
−
4
3
u − 2
−u − 4
a
8
=
−
4
3
u − 2
−u − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12u − 18
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
− 3u + 3
c
2
(u − 2)
2
c
4
, c
5
, c
6
c
7
, c
8
, c
9
u
2
+ u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
2
− 3y + 9
c
2
(y −4)
2
c
4
, c
5
, c
6
c
7
, c
8
, c
9
y
2
+ y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50000 + 0.86603I
a = 0.500000 − 0.288675I
b = 0.500000 − 0.866025I
6.08965I 0. − 10.39230I
u = −1.50000 − 0.86603I
a = 0.500000 + 0.288675I
b = 0.500000 + 0.866025I
− 6.08965I 0. + 10.39230I
30
VIII. I
u
8
= hb + u, a + 1, u
4
− u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
−1
−u
a
7
=
−u
−u
2
+ u
a
1
=
u − 1
−u
a
2
=
u
3
− u
2
+ 1
−u
3
+ u
2
− u − 1
a
5
=
−u
3
+ 2u
2
− u
u
3
− u
2
+ u
a
8
=
−u
2
+ u − 1
1
a
8
=
−u
2
+ u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
− 3u
2
+ 3u − 3
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
u
4
+ u
3
− u + 1
c
2
, c
5
, c
8
u
4
+ u
2
+ 2
c
3
, c
6
, c
9
u
4
− u
3
+ u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y
4
− y
3
+ 4y
2
− y + 1
c
2
, c
5
, c
8
(y
2
+ y + 2)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566121 + 0.458821I
a = −1.00000
b = 0.566121 − 0.458821I
−2.46740 − 5.33349I −4.50000 + 3.96863I
u = −0.566121 − 0.458821I
a = −1.00000
b = 0.566121 + 0.458821I
−2.46740 + 5.33349I −4.50000 − 3.96863I
u = 1.066120 + 0.864054I
a = −1.00000
b = −1.066120 − 0.864054I
−2.46740 − 5.33349I −4.50000 + 3.96863I
u = 1.066120 − 0.864054I
a = −1.00000
b = −1.066120 + 0.864054I
−2.46740 + 5.33349I −4.50000 − 3.96863I
34
IX. I
u
9
= hb − 1, u
3
− 2u
2
+ a + 2u, u
4
− u
3
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
−u
3
+ 2u
2
− 2u
1
a
7
=
−4u
3
+ 7u
2
− 5u − 5
−u
3
+ 2u
2
− u − 1
a
1
=
−u
3
+ 2u
2
− 2u − 1
1
a
2
=
−4u
3
+ 6u
2
− 3u − 6
−u
3
+ 2u
2
− u − 2
a
5
=
−2u
3
+ 3u
2
− 2u − 3
−u
3
+ 2u
2
− 1
a
8
=
−2u
3
+ 4u
2
− 3u − 2
−u
a
8
=
−2u
3
+ 4u
2
− 3u − 2
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 8u
2
− 4u − 18
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
u
4
+ u
3
− 2u + 1
c
2
, c
5
, c
8
(u
2
+ u + 1)
2
c
7
, c
9
(u + 1)
4
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
4
− y
3
+ 6y
2
− 4y + 1
c
2
, c
5
, c
8
(y
2
+ y + 1)
2
c
7
, c
9
(y −1)
4
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = 2.12196 − 1.05376I
b = 1.00000
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.621964 − 0.187730I
a = 2.12196 + 1.05376I
b = 1.00000
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 1.12196 + 1.05376I
a = 0.378036 − 0.187730I
b = 1.00000
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 1.12196 − 1.05376I
a = 0.378036 + 0.187730I
b = 1.00000
−3.28987 + 2.02988I −12.00000 − 3.46410I
38
X. I
u
10
= hu
3
− 2u
2
+ b + 2u + 1, −u
3
+ u
2
+ a − 2, u
4
− u
3
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u
2
a
9
=
u
3
− u
2
+ 2
−u
3
+ 2u
2
− 2u − 1
a
7
=
u
3
− u
2
+ 2
−u
3
+ 2u
2
− u − 1
a
1
=
2u
3
− 3u
2
+ 2u + 3
−u
3
+ 2u
2
− 2u − 1
a
2
=
−u
3
+ 2u
2
− 2u
−u
3
+ 2u
2
− u − 2
a
5
=
u
3
− 2u
2
+ 2u + 1
u
3
− u
2
+ u + 2
a
8
=
2u
3
− 3u
2
+ u + 3
−u
3
+ u
2
− u
a
8
=
2u
3
− 3u
2
+ u + 3
−u
3
+ u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 8u
2
− 4u − 18
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
9
u
4
+ u
3
− 2u + 1
c
2
, c
5
, c
8
(u
2
+ u + 1)
2
c
4
, c
6
(u + 1)
4
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
9
y
4
− y
3
+ 6y
2
− 4y + 1
c
2
, c
5
, c
8
(y
2
+ y + 1)
2
c
4
, c
6
(y −1)
4
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621964 + 0.187730I
a = 1.47356 + 0.44477I
b = 1.12196 − 1.05376I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = −0.621964 − 0.187730I
a = 1.47356 − 0.44477I
b = 1.12196 + 1.05376I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 1.12196 + 1.05376I
a = −0.473561 + 0.444772I
b = −0.621964 − 0.187730I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 1.12196 − 1.05376I
a = −0.473561 − 0.444772I
b = −0.621964 + 0.187730I
−3.28987 + 2.02988I −12.00000 − 3.46410I
42
XI. I
u
11
= h−a
3
− 2a
2
+ b − 2a + 1, a
4
+ a
3
− 2a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
4
=
1
1
a
9
=
a
a
3
+ 2a
2
+ 2a − 1
a
7
=
−a
2
−a
3
− 2a
2
− a + 2
a
1
=
−a
3
− 2a
2
− a + 1
a
3
+ 2a
2
+ 2a − 1
a
2
=
a
−a
3
− 2a
2
− a + 1
a
5
=
−a
3
− 2a
2
− a + 2
2a
3
+ 3a
2
+ 2a − 2
a
8
=
−a
3
− 2a
2
+ 1
a
a
8
=
−a
3
− 2a
2
+ 1
a
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4a
3
+ 8a
2
+ 4a − 18
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u + 1)
4
c
2
, c
5
, c
8
(u
2
+ u + 1)
2
c
4
, c
6
, c
7
c
9
u
4
+ u
3
− 2u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
, c
5
, c
8
(y
2
+ y + 1)
2
c
4
, c
6
, c
7
c
9
y
4
− y
3
+ 6y
2
− 4y + 1
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.621964 + 0.187730I
b = 1.12196 + 1.05376I
−3.28987 − 2.02988I −12.00000 + 3.46410I
u = 1.00000
a = 0.621964 − 0.187730I
b = 1.12196 − 1.05376I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 1.00000
a = −1.12196 + 1.05376I
b = −0.621964 + 0.187730I
−3.28987 + 2.02988I −12.00000 − 3.46410I
u = 1.00000
a = −1.12196 − 1.05376I
b = −0.621964 − 0.187730I
−3.28987 − 2.02988I −12.00000 + 3.46410I
46
XII. I
u
12
= hb, a + 1, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u − 1
a
9
=
−1
0
a
7
=
−u
u
a
1
=
−1
0
a
2
=
−u + 2
u − 1
a
5
=
−u
u
a
8
=
−u
u
a
8
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
47
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
u
2
+ u + 1
c
7
, c
9
u
2
c
8
u
2
− u + 1
48
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
8
y
2
+ y + 1
c
7
, c
9
y
2
49
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.00000
b = 0
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = −1.00000
b = 0
2.02988I 0. − 3.46410I
50
XIII. I
u
13
= hb − u, a, u
2
− u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
u − 1
a
9
=
0
u
a
7
=
0
u
a
1
=
−u
u
a
2
=
1
u − 1
a
5
=
1
u − 1
a
8
=
−u
u + 1
a
8
=
−u
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
51
(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
+ u + 1
c
4
, c
6
u
2
c
5
u
2
− u + 1
52
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
7
, c
8
c
9
y
2
+ y + 1
c
4
, c
6
y
2
53
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
u = 0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
2.02988I 0. − 3.46410I
54
XIV. I
u
14
= hb − u, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
4
=
1
−u − 1
a
9
=
−1
u
a
7
=
−u
−1
a
1
=
−u − 1
u
a
2
=
u + 1
1
a
5
=
u + 1
0
a
8
=
0
−1
a
8
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3
55
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
u
2
− u + 1
c
2
, c
5
, c
8
(u − 1)
2
56
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y
2
+ y + 1
c
2
, c
5
, c
8
(y −1)
2
57
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = −0.500000 + 0.866025I
3.28987 3.00000
u = −0.500000 − 0.866025I
a = −1.00000
b = −0.500000 − 0.866025I
3.28987 3.00000
58
XV. I
u
15
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
1
a
4
=
1
1
a
9
=
−1
−1
a
7
=
−1
0
a
1
=
0
−1
a
2
=
1
0
a
5
=
0
1
a
8
=
−1
−1
a
8
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
59
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
u + 1
c
2
, c
5
, c
8
u
c
3
, c
6
, c
9
u − 1
60
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y −1
c
2
, c
5
, c
8
y
61
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
15
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−3.28987 −12.0000
62
XVI. I
v
1
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
1
0
a
4
=
1
0
a
9
=
0
b
a
7
=
1
b − 1
a
1
=
−b
b
a
2
=
b
−b
a
5
=
−b + 2
b − 1
a
8
=
−b
b
a
8
=
−b
b
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4b − 2
63
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
c
2
u
2
− u + 1
c
4
, c
5
, c
6
c
7
, c
8
, c
9
u
2
+ u + 1
64
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
2
c
2
, c
4
, c
5
c
6
, c
7
, c
8
c
9
y
2
+ y + 1
65
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
− 2.02988I 0. + 3.46410I
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
2.02988I 0. − 3.46410I
66
XVII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
u
2
(u + 1)
5
(u
2
− 3u + 3)(u
2
− u + 1)(u
2
+ u + 1)
4
· (u
4
− 5u
3
+ ··· − 14u + 7)(u
4
− 2u
3
+ 2u
2
+ 1)(u
4
+ u
3
− 2u + 1)
4
· (u
4
+ u
3
− u + 1)
c
2
, c
5
, c
8
u(u − 2)
2
(u − 1)
2
(u
2
− 2u + 4)
2
(u
2
− u + 1)(u
2
+ u + 1)
14
(u
4
+ u
2
+ 2)
· (u
4
− 2u
3
+ 4u
2
− 2u + 2)
c
3
, c
6
, c
9
u
2
(u − 1)(u + 1)
4
(u
2
− 3u + 3)(u
2
− u + 1)(u
2
+ u + 1)
4
· (u
4
− 5u
3
+ 12u
2
− 14u + 7)(u
4
− 2u
3
+ 2u
2
+ 1)(u
4
− u
3
+ u + 1)
· (u
4
+ u
3
− 2u + 1)
4
67
XVIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
y
2
(y −1)
5
(y
2
− 3y + 9)(y
2
+ y + 1)
5
(y
4
+ 6y
2
+ 4y + 1)
· (y
4
− y
3
+ 4y
2
− y + 1)(y
4
− y
3
+ 6y
2
− 4y + 1)
4
· (y
4
− y
3
+ 18y
2
− 28y + 49)
c
2
, c
5
, c
8
y(y −4)
2
(y −1)
2
(y
2
+ y + 1)
15
(y
2
+ y + 2)
2
(y
2
+ 4y + 16)
2
· (y
4
+ 4y
3
+ 12y
2
+ 12y + 4)
68
