10
123
(K10a
121
)
A knot diagram
1
Linearized knot diagam
8 9 10 1 2 3 4 5 6 7
Solving Sequence
1,4 5,7
8 2 9 10 3 6
c
4
c
7
c
1
c
8
c
10
c
3
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
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
1
= hu
3
+ 2u
2
+ b + 2u + 1, a − 1, u
4
+ 3u
3
+ 4u
2
+ 2u + 1i
I
u
2
= hu
3
+ b + 1, a + 1, u
4
− u
3
+ 2u − 1i
I
u
3
= h−6u
9
+ 3u
8
+ 17u
7
− 22u
6
− 19u
5
+ 31u
4
+ 5u
3
− 22u
2
+ 2b + 2u + 6,
6u
9
− 21u
8
+ 13u
7
+ 31u
6
− 48u
5
− 5u
4
+ 36u
3
− 13u
2
+ 2a − 9u + 2,
3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1i
I
u
4
= h18u
9
− 30u
8
− 9u
7
+ 67u
6
− 26u
5
− 41u
4
+ 35u
3
+ 7u
2
+ 2b − 8u, a − 1,
3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1i
I
u
5
= h−2u
9
+ 7u
8
− 14u
7
+ 19u
6
− 27u
5
+ 34u
4
− 40u
3
+ 33u
2
+ 2b − 22u + 6,
− 4u
9
+ 14u
8
− 28u
7
+ 41u
6
− 58u
5
+ 73u
4
− 81u
3
+ 76u
2
+ 6a − 50u + 23,
u
10
− 4u
9
+ 9u
8
− 14u
7
+ 20u
6
− 26u
5
+ 31u
4
− 30u
3
+ 23u
2
− 12u + 3i
I
u
6
= h5u
9
− 20u
8
+ 42u
7
− 61u
6
+ 85u
5
− 109u
4
+ 125u
3
− 114u
2
+ 6b + 79u − 30,
u
9
+ 2u
8
− 9u
7
+ 19u
6
− 22u
5
+ 34u
4
− 41u
3
+ 54u
2
+ 6a − 40u + 24,
u
10
− 4u
9
+ 9u
8
− 14u
7
+ 20u
6
− 26u
5
+ 31u
4
− 30u
3
+ 23u
2
− 12u + 3i
I
u
7
= h−17u
9
− 123u
8
− 488u
7
− 1301u
6
− 2539u
5
− 3687u
4
− 4024u
3
− 3128u
2
+ 144b − 1616u − 496,
u
9
+ 21u
8
+ 118u
7
+ 397u
6
+ 917u
5
+ 1557u
4
+ 1958u
3
+ 1792u
2
+ 96a + 1096u + 416,
u
10
+ 7u
9
+ 28u
8
+ 77u
7
+ 159u
6
+ 251u
5
+ 308u
4
+ 288u
3
+ 200u
2
+ 96u + 32i
I
u
8
= ha
3
u
2
− 2a
2
u
2
+ a
2
u + u
2
a + ba + a
2
− au − a + 1, a
2
u
2
− u
2
a + bu + au + b + a, u
3
a
2
− u
3
a + au − u − 1i
* 7 irreducible components of dim
C
= 0, with total 58 representations.
* 1 irreducible components of dim
C
= 1
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
= hu
3
+ 2u
2
+ b + 2u + 1, a − 1, u
4
+ 3u
3
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
1
−u
3
− 2u
2
− 2u − 1
a
8
=
−u
3
− 2u
2
− 2u
−u
3
− 2u
2
− 2u − 1
a
2
=
u
2
+ u + 1
−u
3
− u
2
a
9
=
−u
3
− 2u
2
− u
−2u
2
− 2u − 1
a
10
=
u
u
3
+ 2u
2
+ 2u + 1
a
3
=
−u
3
− 2u
2
− u
u
3
+ u
2
+ u
a
6
=
−u
3
− 3u
2
− 2u
u
3
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5u
3
− 10u
2
− 15u − 5
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
u
4
− 3u
3
+ 4u
2
− 2u + 1
c
2
, c
4
, c
6
c
8
, c
10
u
4
+ 3u
3
+ 4u
2
+ 2u + 1
4
(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
7
, c
8
, c
9
c
10
y
4
− y
3
+ 6y
2
+ 4y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.190983 + 0.587785I
a = 1.00000
b = −0.190983 − 0.587785I
1.38939I 0. − 5.87785I
u = −0.190983 − 0.587785I
a = 1.00000
b = −0.190983 + 0.587785I
− 1.38939I 0. + 5.87785I
u = −1.30902 + 0.95106I
a = 1.00000
b = −1.30902 − 0.95106I
17.0857I 0. − 9.51057I
u = −1.30902 − 0.95106I
a = 1.00000
b = −1.30902 + 0.95106I
− 17.0857I 0. + 9.51057I
6
II. I
u
2
= hu
3
+ b + 1, a + 1, u
4
− u
3
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
−1
−u
3
− 1
a
8
=
−u
3
− 2
−u
3
− 1
a
2
=
2u
3
− u
2
− u + 3
u
3
− u
2
+ 2
a
9
=
−u
3
+ u − 2
−1
a
10
=
u
u
3
+ 1
a
3
=
u
3
− u + 2
u
3
− u
2
− u + 2
a
6
=
−u
3
+ u
2
− 2
−u
3
+ u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
+ 5u + 5
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
u
4
+ u
3
− 2u − 1
c
2
, c
4
, c
6
c
8
, c
10
u
4
− u
3
+ 2u − 1
8
(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
7
, c
8
, c
9
c
10
y
4
− y
3
+ 2y
2
− 4y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15372
a = −1.00000
b = 0.535687
−4.48216 −8.44700
u = 0.809017 + 0.981593I
a = −1.00000
b = 0.809017 − 0.981593I
− 9.37207I 0. + 9.81593I
u = 0.809017 − 0.981593I
a = −1.00000
b = 0.809017 + 0.981593I
9.37207I 0. − 9.81593I
u = 0.535687
a = −1.00000
b = −1.15372
4.48216 8.44700
10
III.
I
u
3
= h−6u
9
+3u
8
+· · ·+2b+6, 6u
9
−21u
8
+· · ·+2a+2, 3u
10
−6u
9
+· · ·−5u
2
+1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
−3u
9
+
21
2
u
8
+ ··· +
9
2
u − 1
3u
9
−
3
2
u
8
+ ··· − u − 3
a
8
=
9u
8
− 15u
7
+ ··· +
7
2
u − 4
3u
9
−
3
2
u
8
+ ··· − u − 3
a
2
=
12u
9
−
27
2
u
8
+ ··· − 11u − 3
3
2
u
9
− 3u
8
+ ··· − 3u −
1
2
a
9
=
9u
8
− 15u
7
+ ··· +
9
2
u − 4
3u
9
−
3
2
u
8
+ ··· − u − 3
a
10
=
6u
9
−
9
2
u
8
+ ··· −
5
2
u −
1
2
9
2
u
9
− 6u
8
+ ··· −
7
2
u − 2
a
3
=
−3u
8
+ 3u
7
+ 4u
6
− 10u
5
− 2u
4
+ 8u
3
− 3u
2
− 5u + 1
−
9
2
u
9
+
9
2
u
8
+ ··· + 2u +
5
2
a
6
=
−21u
9
+
75
2
u
8
+ ··· +
21
2
u +
1
2
−6u
9
+
21
2
u
8
+ ··· +
9
2
u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u
9
+ 6u
8
−64u
7
+ 52u
6
+ 90u
5
−110u
4
−30u
3
+ 86u
2
−4u −24
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
− 7u
9
+ ··· − 96u + 32
c
2
, c
10
u
10
− 4u
9
+ ··· − 12u + 3
c
3
, c
9
3(3u
10
+ 6u
9
− u
8
− 14u
7
− 8u
6
+ 10u
5
+ 11u
4
− 2u
3
− 5u
2
+ 1)
c
4
, c
8
3(3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1)
c
5
, c
7
u
10
+ 4u
9
+ ··· + 12u + 3
c
6
u
10
+ 7u
9
+ ··· + 96u + 32
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
10
+ 7y
9
+ ··· + 3584y + 1024
c
2
, c
5
, c
7
c
10
y
10
+ 2y
9
+ 9y
8
+ 18y
7
+ 36y
6
+ 48y
5
+ 39y
4
+ 22y
3
− 5y
2
− 6y + 9
c
3
, c
4
, c
8
c
9
9(9y
10
− 42y
9
+ ··· − 10y + 1)
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983280 + 0.164908I
a = −0.716079 + 0.118069I
b = 0.724687 − 0.940396I
−3.61397 + 2.21654I −5.38699 − 4.72022I
u = −0.983280 − 0.164908I
a = −0.716079 − 0.118069I
b = 0.724687 + 0.940396I
−3.61397 − 2.21654I −5.38699 + 4.72022I
u = 0.707358 + 0.648629I
a = −0.105697 − 1.232530I
b = 0.684636 − 0.234182I
3.61397 − 2.21654I 5.38699 + 4.72022I
u = 0.707358 − 0.648629I
a = −0.105697 + 1.232530I
b = 0.684636 + 0.234182I
3.61397 + 2.21654I 5.38699 − 4.72022I
u = 0.744942 + 0.201707I
a = 1.81391 + 0.74172I
b = −0.719811 + 1.046890I
−2.49243 − 8.64801I −4.04126 + 7.50135I
u = 0.744942 − 0.201707I
a = 1.81391 − 0.74172I
b = −0.719811 − 1.046890I
−2.49243 + 8.64801I −4.04126 − 7.50135I
u = 1.081500 + 0.798609I
a = −0.893282 − 0.308372I
b = 1.20165 − 0.91842I
2.49243 − 8.64801I 4.04126 + 7.50135I
u = 1.081500 − 0.798609I
a = −0.893282 + 0.308372I
b = 1.20165 + 0.91842I
2.49243 + 8.64801I 4.04126 − 7.50135I
u = −0.550514 + 0.187402I
a = 0.40115 − 1.75920I
b = 0.108840 − 1.043640I
0.806279I 0. − 8.22652I
u = −0.550514 − 0.187402I
a = 0.40115 + 1.75920I
b = 0.108840 + 1.043640I
− 0.806279I 0. + 8.22652I
14
IV. I
u
4
= h18u
9
− 30u
8
+ · · · + 2b − 8u, a − 1, 3u
10
− 6u
9
+ · · · − 5u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
1
−9u
9
+ 15u
8
+ ··· −
7
2
u
2
+ 4u
a
8
=
−9u
9
+ 15u
8
+ ··· + 4u + 1
−9u
9
+ 15u
8
+ ··· −
7
2
u
2
+ 4u
a
2
=
−
3
2
u
9
−
3
2
u
8
+ ··· − 3u +
5
2
3
2
u
9
− 3u
8
+ ··· − 3u −
1
2
a
9
=
−
9
2
u
9
+
15
2
u
8
+ ··· + 3u + 2
−6u
9
+
21
2
u
8
+ ··· +
5
2
u −
1
2
a
10
=
u
−3u
9
+
3
2
u
8
+ ··· + u + 3
a
3
=
−
9
2
u
9
+
15
2
u
8
+ ··· + 3u + 2
−
9
2
u
9
+ 6u
8
+ ··· +
5
2
u +
1
2
a
6
=
−
3
2
u
9
+
3
2
u
8
+ ··· − u −
3
2
3
2
u
9
−
3
2
u
8
+ ··· −
3
2
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u
9
+ 6u
8
−64u
7
+ 52u
6
+ 90u
5
−110u
4
−30u
3
+ 86u
2
−4u −24
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
10
+ 4u
9
+ ··· + 12u + 3
c
2
u
10
+ 7u
9
+ ··· + 96u + 32
c
4
, c
10
3(3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1)
c
5
, c
9
3(3u
10
+ 6u
9
− u
8
− 14u
7
− 8u
6
+ 10u
5
+ 11u
4
− 2u
3
− 5u
2
+ 1)
c
6
, c
8
u
10
− 4u
9
+ ··· − 12u + 3
c
7
u
10
− 7u
9
+ ··· − 96u + 32
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
10
+ 2y
9
+ 9y
8
+ 18y
7
+ 36y
6
+ 48y
5
+ 39y
4
+ 22y
3
− 5y
2
− 6y + 9
c
2
, c
7
y
10
+ 7y
9
+ ··· + 3584y + 1024
c
4
, c
5
, c
9
c
10
9(9y
10
− 42y
9
+ ··· − 10y + 1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983280 + 0.164908I
a = 1.00000
b = −0.127144 − 0.809997I
−3.61397 + 2.21654I −5.38699 − 4.72022I
u = −0.983280 − 0.164908I
a = 1.00000
b = −0.127144 + 0.809997I
−3.61397 − 2.21654I −5.38699 + 4.72022I
u = 0.707358 + 0.648629I
a = 1.00000
b = −1.36087 + 0.66197I
3.61397 − 2.21654I 5.38699 + 4.72022I
u = 0.707358 − 0.648629I
a = 1.00000
b = −1.36087 − 0.66197I
3.61397 + 2.21654I 5.38699 − 4.72022I
u = 0.744942 + 0.201707I
a = 1.00000
b = −0.45427 − 1.55310I
−2.49243 − 8.64801I −4.04126 + 7.50135I
u = 0.744942 − 0.201707I
a = 1.00000
b = −0.45427 + 1.55310I
−2.49243 + 8.64801I −4.04126 − 7.50135I
u = 1.081500 + 0.798609I
a = 1.00000
b = −1.31322 + 1.08050I
2.49243 − 8.64801I 4.04126 + 7.50135I
u = 1.081500 − 0.798609I
a = 1.00000
b = −1.31322 − 1.08050I
2.49243 + 8.64801I 4.04126 − 7.50135I
u = −0.550514 + 0.187402I
a = 1.00000
b = −0.24450 − 1.63857I
0.806279I 0. − 8.22652I
u = −0.550514 − 0.187402I
a = 1.00000
b = −0.24450 + 1.63857I
− 0.806279I 0. + 8.22652I
18
V. I
u
5
=
h−2u
9
+7u
8
+· · ·+2b+6, −4u
9
+14u
8
+· · ·+6a+23, u
10
−4u
9
+· · ·−12u+3i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
2
3
u
9
−
7
3
u
8
+ ··· +
25
3
u −
23
6
u
9
−
7
2
u
8
+ ··· + 11u − 3
a
8
=
5
3
u
9
−
35
6
u
8
+ ··· +
58
3
u −
41
6
u
9
−
7
2
u
8
+ ··· + 11u − 3
a
2
=
−1.11111u
9
+ 3.44444u
8
+ ··· − 11.3889u + 3.83333
−
1
2
u
8
+
3
2
u
7
+ ··· +
9
2
u − 2
a
9
=
2
3
u
9
−
17
6
u
8
+ ··· +
40
3
u −
19
3
1
2
u
9
−
3
2
u
8
+ ··· − 5u
2
+ 2u
a
10
=
−0.111111u
9
+ 0.944444u
8
+ ··· − 6.38889u + 3.33333
−u
9
+ 3u
8
+ ··· −
15
2
u +
5
2
a
3
=
−0.944444u
9
+ 3.27778u
8
+ ··· − 13.0556u + 5.83333
−
1
2
u
9
+ u
8
+ ··· −
3
2
u −
1
2
a
6
=
−0.888889u
9
+ 2.77778u
8
+ ··· − 7.27778u + 2.44444
2
3
u
9
−
5
3
u
8
+ ··· +
17
6
u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
80
9
u
9
−
296
9
u
8
+ 66u
7
−
838
9
u
6
+
1174
9
u
5
−
1504
9
u
4
+
1706
9
u
3
−
496
3
u
2
+
946
9
u −
112
3
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
3(3u
10
+ 6u
9
− u
8
− 14u
7
− 8u
6
+ 10u
5
+ 11u
4
− 2u
3
− 5u
2
+ 1)
c
2
, c
4
u
10
− 4u
9
+ ··· − 12u + 3
c
3
u
10
− 7u
9
+ ··· − 96u + 32
c
6
, c
10
3(3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1)
c
7
, c
9
u
10
+ 4u
9
+ ··· + 12u + 3
c
8
u
10
+ 7u
9
+ ··· + 96u + 32
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
9(9y
10
− 42y
9
+ ··· − 10y + 1)
c
2
, c
4
, c
7
c
9
y
10
+ 2y
9
+ 9y
8
+ 18y
7
+ 36y
6
+ 48y
5
+ 39y
4
+ 22y
3
− 5y
2
− 6y + 9
c
3
, c
8
y
10
+ 7y
9
+ ··· + 3584y + 1024
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108840 + 1.043640I
a = 0.123214 + 0.540345I
b = 0.108840 − 1.043640I
0.806279I 0. − 8.22652I
u = 0.108840 − 1.043640I
a = 0.123214 − 0.540345I
b = 0.108840 + 1.043640I
− 0.806279I 0. + 8.22652I
u = 0.724687 + 0.940396I
a = −0.069070 − 0.805418I
b = 0.684636 + 0.234182I
3.61397 + 2.21654I 5.38699 − 4.72022I
u = 0.724687 − 0.940396I
a = −0.069070 + 0.805418I
b = 0.684636 − 0.234182I
3.61397 − 2.21654I 5.38699 + 4.72022I
u = −0.719811 + 1.046890I
a = −1.000260 − 0.345304I
b = 1.20165 + 0.91842I
2.49243 + 8.64801I 4.04126 − 7.50135I
u = −0.719811 − 1.046890I
a = −1.000260 + 0.345304I
b = 1.20165 − 0.91842I
2.49243 − 8.64801I 4.04126 + 7.50135I
u = 0.684636 + 0.234182I
a = −1.359530 + 0.224163I
b = 0.724687 + 0.940396I
−3.61397 − 2.21654I −5.38699 + 4.72022I
u = 0.684636 − 0.234182I
a = −1.359530 − 0.224163I
b = 0.724687 − 0.940396I
−3.61397 + 2.21654I −5.38699 − 4.72022I
u = 1.20165 + 0.91842I
a = 0.472321 − 0.193135I
b = −0.719811 + 1.046890I
−2.49243 − 8.64801I −4.04126 + 7.50135I
u = 1.20165 − 0.91842I
a = 0.472321 + 0.193135I
b = −0.719811 − 1.046890I
−2.49243 + 8.64801I −4.04126 − 7.50135I
22
VI.
I
u
6
= h5u
9
−20u
8
+· · ·+6b−30, u
9
+2u
8
+· · ·+6a+24, u
10
−4u
9
+· · ·−12u+3i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
−
1
6
u
9
−
1
3
u
8
+ ··· +
20
3
u − 4
−
5
6
u
9
+
10
3
u
8
+ ··· −
79
6
u + 5
a
8
=
−u
9
+ 3u
8
+ ··· −
13
2
u + 1
−
5
6
u
9
+
10
3
u
8
+ ··· −
79
6
u + 5
a
2
=
2u
9
−
13
2
u
8
+ ··· + 22u −
15
2
−
1
2
u
8
+
3
2
u
7
+ ··· +
9
2
u − 2
a
9
=
−
2
3
u
9
+
5
3
u
8
+ ··· −
7
3
u − 1
−
4
3
u
9
+
13
3
u
8
+ ··· −
85
6
u + 5
a
10
=
7
6
u
9
−
8
3
u
8
+ ··· +
19
3
u −
1
2
5
6
u
9
−
10
3
u
8
+ ··· +
79
6
u − 5
a
3
=
2
3
u
9
−
17
6
u
8
+ ··· +
40
3
u −
19
3
−u
9
+
19
6
u
8
+ ··· −
19
2
u +
10
3
a
6
=
−
1
2
u
8
+
3
2
u
7
+ ··· + 5u − 2
1
2
u
8
−
3
2
u
7
+ ··· −
9
2
u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
80
9
u
9
−
296
9
u
8
+ 66u
7
−
838
9
u
6
+
1174
9
u
5
−
1504
9
u
4
+
1706
9
u
3
−
496
3
u
2
+
946
9
u −
112
3
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
10
+ 4u
9
+ ··· + 12u + 3
c
2
, c
8
3(3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1)
c
3
, c
7
3(3u
10
+ 6u
9
− u
8
− 14u
7
− 8u
6
+ 10u
5
+ 11u
4
− 2u
3
− 5u
2
+ 1)
c
4
, c
6
u
10
− 4u
9
+ ··· − 12u + 3
c
5
u
10
− 7u
9
+ ··· − 96u + 32
c
10
u
10
+ 7u
9
+ ··· + 96u + 32
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
10
+ 2y
9
+ 9y
8
+ 18y
7
+ 36y
6
+ 48y
5
+ 39y
4
+ 22y
3
− 5y
2
− 6y + 9
c
2
, c
3
, c
7
c
8
9(9y
10
− 42y
9
+ ··· − 10y + 1)
c
5
, c
10
y
10
+ 7y
9
+ ··· + 3584y + 1024
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.108840 + 1.043640I
a = 1.52900 + 0.39374I
b = −0.550514 − 0.187402I
0.806279I 0. − 8.22652I
u = 0.108840 − 1.043640I
a = 1.52900 − 0.39374I
b = −0.550514 + 0.187402I
− 0.806279I 0. + 8.22652I
u = 0.724687 + 0.940396I
a = 0.475042 + 0.501279I
b = −0.983280 − 0.164908I
3.61397 + 2.21654I 5.38699 − 4.72022I
u = 0.724687 − 0.940396I
a = 0.475042 − 0.501279I
b = −0.983280 + 0.164908I
3.61397 − 2.21654I 5.38699 + 4.72022I
u = −0.719811 + 1.046890I
a = −0.804739 + 0.987238I
b = 0.744942 + 0.201707I
2.49243 + 8.64801I 4.04126 − 7.50135I
u = −0.719811 − 1.046890I
a = −0.804739 − 0.987238I
b = 0.744942 − 0.201707I
2.49243 − 8.64801I 4.04126 + 7.50135I
u = 0.684636 + 0.234182I
a = −2.07561 − 0.25693I
b = 0.707358 − 0.648629I
−3.61397 − 2.21654I −5.38699 + 4.72022I
u = 0.684636 − 0.234182I
a = −2.07561 + 0.25693I
b = 0.707358 + 0.648629I
−3.61397 + 2.21654I −5.38699 − 4.72022I
u = 1.20165 + 0.91842I
a = −1.123690 − 0.040350I
b = 1.081500 − 0.798609I
−2.49243 − 8.64801I −4.04126 + 7.50135I
u = 1.20165 − 0.91842I
a = −1.123690 + 0.040350I
b = 1.081500 + 0.798609I
−2.49243 + 8.64801I −4.04126 − 7.50135I
26
VII. I
u
7
= h−17u
9
− 123u
8
+ · · · + 144b − 496, u
9
+ 21u
8
+ · · · + 96a +
416, u
10
+ 7u
9
+ · · · + 96u + 32i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
−0.0104167u
9
− 0.218750u
8
+ ··· − 11.4167u − 4.33333
0.118056u
9
+ 0.854167u
8
+ ··· + 11.2222u + 3.44444
a
8
=
31
288
u
9
+
61
96
u
8
+ ··· −
7
36
u −
8
9
0.118056u
9
+ 0.854167u
8
+ ··· + 11.2222u + 3.44444
a
2
=
−
1
48
u
9
−
7
48
u
8
+ ··· −
23
4
u −
7
3
1
24
u
8
+
5
24
u
7
+ ··· +
4
3
u −
2
3
a
9
=
−0.0381944u
9
− 0.302083u
8
+ ··· − 3.52778u − 0.555556
41
144
u
9
+
89
48
u
8
+ ··· +
71
9
u +
7
9
a
10
=
−
1
16
u
9
−
7
16
u
8
+ ··· −
23
4
u − 1
1
24
u
9
+
1
4
u
8
+ ··· +
2
3
u −
2
3
a
3
=
1
8
u
9
+
11
16
u
8
+ ··· +
5
2
u +
1
2
−
1
16
u
9
−
5
16
u
8
+ ··· +
5
2
u + 2
a
6
=
0.0138889u
9
− 0.0208333u
8
+ ··· − 5.94444u − 1.38889
0.159722u
9
+ 1.10417u
8
+ ··· + 8.38889u + 1.77778
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
4
27
u
9
−
11
18
u
8
−
173
54
u
7
−
331
27
u
6
−
1765
54
u
5
−
1103
18
u
4
−
4645
54
u
3
−
2239
27
u
2
−
1420
27
u −
554
27
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
3(3u
10
+ 6u
9
− u
8
− 14u
7
− 8u
6
+ 10u
5
+ 11u
4
− 2u
3
− 5u
2
+ 1)
c
2
, c
6
3(3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1)
c
3
, c
5
u
10
+ 4u
9
+ ··· + 12u + 3
c
4
u
10
+ 7u
9
+ ··· + 96u + 32
c
8
, c
10
u
10
− 4u
9
+ ··· − 12u + 3
c
9
u
10
− 7u
9
+ ··· − 96u + 32
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
9(9y
10
− 42y
9
+ ··· − 10y + 1)
c
3
, c
5
, c
8
c
10
y
10
+ 2y
9
+ 9y
8
+ 18y
7
+ 36y
6
+ 48y
5
+ 39y
4
+ 22y
3
− 5y
2
− 6y + 9
c
4
, c
9
y
10
+ 7y
9
+ ··· + 3584y + 1024
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −0.127144 + 0.809997I
a = 0.99601 − 1.05102I
b = −0.983280 − 0.164908I
3.61397 + 2.21654I 5.38699 − 4.72022I
u = −0.127144 − 0.809997I
a = 0.99601 + 1.05102I
b = −0.983280 + 0.164908I
3.61397 − 2.21654I 5.38699 + 4.72022I
u = −1.36087 + 0.66197I
a = −0.474516 − 0.058738I
b = 0.707358 + 0.648629I
−3.61397 + 2.21654I −5.38699 − 4.72022I
u = −1.36087 − 0.66197I
a = −0.474516 + 0.058738I
b = 0.707358 − 0.648629I
−3.61397 − 2.21654I −5.38699 + 4.72022I
u = −0.45427 + 1.55310I
a = −0.496066 + 0.608563I
b = 0.744942 − 0.201707I
2.49243 − 8.64801I 4.04126 + 7.50135I
u = −0.45427 − 1.55310I
a = −0.496066 − 0.608563I
b = 0.744942 + 0.201707I
2.49243 + 8.64801I 4.04126 − 7.50135I
u = −0.24450 + 1.63857I
a = 0.613351 − 0.157946I
b = −0.550514 − 0.187402I
0.806279I 0. − 8.22652I
u = −0.24450 − 1.63857I
a = 0.613351 + 0.157946I
b = −0.550514 + 0.187402I
− 0.806279I 0. + 8.22652I
u = −1.31322 + 1.08050I
a = −0.888779 − 0.031915I
b = 1.081500 + 0.798609I
−2.49243 + 8.64801I −4.04126 − 7.50135I
u = −1.31322 − 1.08050I
a = −0.888779 + 0.031915I
b = 1.081500 − 0.798609I
−2.49243 − 8.64801I −4.04126 + 7.50135I
30
VIII. I
u
8
=
ha
3
u
2
−2a
2
u
2
+· · ·−a+1, a
2
u
2
−u
2
a+bu+au+b+a, u
3
a
2
−u
3
a+au−u−1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
7
=
a
b
a
8
=
b + a
b
a
2
=
a
3
u
2
− 2a
2
u
2
+ 2a
2
u + u
2
a − b
2
+ a
2
− 2au − a + 1
a
3
u
2
− a
2
u
2
+ a
2
u − b
2
+ a
2
− au + u
a
9
=
a
2
u
2
− u
2
a + au + b + 2a − u − 1
u
3
a − u
3
+ b + u
a
10
=
a
2
u
−a
2
u
2
+ u
2
a − au − a + u + 1
a
3
=
−a
3
u
2
+ a
2
u
2
− a
2
+ 1
a
3
u
2
− a
2
u
2
+ a
2
u − u
2
a + a
2
− au + u
2
− 1
a
6
=
−a
3
u
2
+ 2a
2
u
2
− u
2
a + b + 2a
a
2
u
2
− 2u
2
a + u
2
+ b + a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
31
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
32
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
9
9(u
4
− 3u
3
+ ··· − 2u + 1)(u
4
+ u
3
− 2u − 1)(u
10
− 7u
9
+ ··· − 96u + 32)
· (u
10
+ 4u
9
+ ··· + 12u + 3)
2
· (3u
10
+ 6u
9
− u
8
− 14u
7
− 8u
6
+ 10u
5
+ 11u
4
− 2u
3
− 5u
2
+ 1)
2
c
2
, c
4
, c
6
c
8
, c
10
9(u
4
− u
3
+ 2u − 1)(u
4
+ 3u
3
+ 4u
2
+ 2u + 1)
· ((u
10
− 4u
9
+ ··· − 12u + 3)
2
)(u
10
+ 7u
9
+ ··· + 96u + 32)
· (3u
10
− 6u
9
− u
8
+ 14u
7
− 8u
6
− 10u
5
+ 11u
4
+ 2u
3
− 5u
2
+ 1)
2
33
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
81(y
4
− y
3
+ 2y
2
− 4y + 1)(y
4
− y
3
+ 6y
2
+ 4y + 1)
· (y
10
+ 2y
9
+ 9y
8
+ 18y
7
+ 36y
6
+ 48y
5
+ 39y
4
+ 22y
3
− 5y
2
− 6y + 9)
2
· (y
10
+ 7y
9
+ ··· + 3584y + 1024)(9y
10
− 42y
9
+ ··· − 10y + 1)
2
34
