12n
0495
(K12n
0495
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 12 1 10 3 12 4 7
Solving Sequence
3,10
9 4
1,8
7 12 6 2 5 11
c
9
c
3
c
8
c
7
c
12
c
6
c
2
c
5
c
11
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5u
14
− 18u
13
+ ··· + 32b − 6, 10u
14
− 33u
13
+ ··· + 16a − 24,
u
15
− 3u
14
+ 7u
13
− 11u
12
+ 26u
11
− 40u
10
+ 58u
9
− 56u
8
+ 77u
7
− 59u
6
+ 55u
5
− 15u
4
+ 16u
3
+ 6u
2
+ 2i
I
u
2
= hu
3
+ u
2
+ 2b, u
3
+ 2a + u, u
4
+ u
2
+ 2i
I
u
3
= h−71485u
13
− 71179u
12
+ ··· + 855248b − 1081596,
− 61525u
13
+ 23653u
12
+ ··· + 1710496a + 2423156,
u
14
+ u
13
+ u
12
+ 7u
11
+ 12u
10
+ 12u
9
+ 36u
8
+ 46u
7
+ 51u
6
+ 89u
5
+ 73u
4
+ 57u
3
+ 58u
2
+ 12u + 8i
I
u
4
= h−a
3
u − a
3
+ 2a
2
+ 3au + 2b + a − u − 3, a
4
+ a
3
u − 3a
2
− 2au + 1, u
2
+ 1i
I
u
5
= h−a
2
+ 4b − 3a, a
3
+ 2a
2
+ a + 4, u + 1i
I
u
6
= hu
3
− u
2
+ 2b − u + 1, u
3
+ a, u
4
+ 1i
I
v
1
= ha, b + 1, v −1i
* 7 irreducible components of dim
C
= 0, with total 49 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
= h5u
14
− 18u
13
+ · · · + 32b − 6, 10u
14
− 33u
13
+ · · · + 16a − 24, u
15
−
3u
14
+ · · · + 6u
2
+ 2i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
−
5
8
u
14
+
33
16
u
13
+ ··· −
23
8
u +
3
2
−0.156250u
14
+ 0.562500u
13
+ ··· − 0.312500u + 0.187500
a
8
=
u
2
+ 1
u
2
a
7
=
1
16
u
14
−
1
2
u
13
+ ··· −
7
8
u +
1
8
0.156250u
14
− 0.562500u
13
+ ··· + 0.312500u − 0.187500
a
12
=
−
1
8
u
13
+
3
8
u
12
+ ··· −
5
2
u
2
+
3
4
−u
2
a
6
=
−
9
16
u
14
+
7
4
u
13
+ ··· − 4u +
3
2
1
32
u
14
−
1
8
u
13
+ ··· −
5
16
u +
1
16
a
2
=
−
5
8
u
14
+
33
16
u
13
+ ··· −
23
8
u +
3
2
1
32
u
14
−
1
8
u
13
+ ··· +
15
16
u −
3
16
a
5
=
1
8
u
14
−
3
8
u
13
+ ··· +
3
2
u
3
−
7
4
u
−u
5
− u
3
− u
a
11
=
−
1
8
u
13
+
3
8
u
12
+ ··· −
3
2
u
2
+
3
4
u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
17
8
u
14
−
27
4
u
13
+
125
8
u
12
−
99
4
u
11
+
113
2
u
10
−
181
2
u
9
+
515
4
u
8
−
501
4
u
7
+
1299
8
u
6
−
273
2
u
5
+
927
8
u
4
− 34u
3
+ 20u
2
+
11
4
u −
1
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
+ 18u
13
+ ··· + 1061u + 121
c
2
, c
5
u
15
+ 6u
14
+ ··· + 7u − 11
c
3
, c
4
, c
9
c
11
u
15
+ 3u
14
+ ··· − 6u
2
− 2
c
6
, c
7
, c
12
u
15
− 6u
14
+ ··· − 5u − 11
c
8
, c
10
u
15
+ 5u
14
+ ··· − 24u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ 36y
14
+ ··· + 486357y −14641
c
2
, c
5
y
15
+ 18y
13
+ ··· + 1061y −121
c
3
, c
4
, c
9
c
11
y
15
+ 5y
14
+ ··· − 24y −4
c
6
, c
7
, c
12
y
15
− 24y
14
+ ··· − 459y −121
c
8
, c
10
y
15
+ 45y
14
+ ··· + 768y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697385 + 0.828178I
a = 0.320085 − 1.205310I
b = 0.596828 − 0.784304I
−1.30143 + 4.86126I −1.54571 − 6.09014I
u = 0.697385 − 0.828178I
a = 0.320085 + 1.205310I
b = 0.596828 + 0.784304I
−1.30143 − 4.86126I −1.54571 + 6.09014I
u = −0.568338 + 1.053040I
a = 0.458588 − 0.214607I
b = 0.355345 + 0.509744I
2.62859 − 6.17338I 5.25348 + 7.15560I
u = −0.568338 − 1.053040I
a = 0.458588 + 0.214607I
b = 0.355345 − 0.509744I
2.62859 + 6.17338I 5.25348 − 7.15560I
u = −0.059276 + 0.727915I
a = −1.94701 − 0.12490I
b = −1.037900 + 0.063892I
4.57881 + 2.95035I 8.93827 − 0.98271I
u = −0.059276 − 0.727915I
a = −1.94701 + 0.12490I
b = −1.037900 − 0.063892I
4.57881 − 2.95035I 8.93827 + 0.98271I
u = 0.142281 + 0.483742I
a = 1.39721 − 0.99957I
b = 0.178761 − 0.047955I
−1.49033 − 1.08782I −1.21432 + 1.45793I
u = 0.142281 − 0.483742I
a = 1.39721 + 0.99957I
b = 0.178761 + 0.047955I
−1.49033 + 1.08782I −1.21432 − 1.45793I
u = 1.18615 + 1.00645I
a = −1.46570 − 0.18514I
b = −0.570924 − 0.788977I
6.77956 + 6.79736I 4.43994 − 4.51085I
u = 1.18615 − 1.00645I
a = −1.46570 + 0.18514I
b = −0.570924 + 0.788977I
6.77956 − 6.79736I 4.43994 + 4.51085I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423770
a = −0.380234
b = −0.682622
0.948533 11.8010
u = −0.90624 + 1.36309I
a = 1.16372 − 1.52636I
b = 0.36666 − 2.75118I
16.2386 − 13.6992I 2.92416 + 5.89399I
u = −0.90624 − 1.36309I
a = 1.16372 + 1.52636I
b = 0.36666 + 2.75118I
16.2386 + 13.6992I 2.92416 − 5.89399I
u = 1.21992 + 1.30757I
a = 0.76322 + 1.95846I
b = −0.04746 + 2.68598I
18.1501 + 4.1175I 4.30382 − 1.81660I
u = 1.21992 − 1.30757I
a = 0.76322 − 1.95846I
b = −0.04746 − 2.68598I
18.1501 − 4.1175I 4.30382 + 1.81660I
6
II. I
u
2
= hu
3
+ u
2
+ 2b, u
3
+ 2a + u, u
4
+ u
2
+ 2i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
−
1
2
u
3
−
1
2
u
−
1
2
u
3
−
1
2
u
2
a
8
=
u
2
+ 1
u
2
a
7
=
−
1
2
u
3
+ u
2
−
1
2
u + 1
−
1
2
u
3
+
1
2
u
2
a
12
=
−u
2
− 1
−u
2
a
6
=
−
1
2
u
3
−
1
2
u
−
1
2
u
3
−
1
2
u
2
a
2
=
−
1
2
u
3
−
1
2
u
−
1
2
u
3
−
1
2
u
2
+ u
a
5
=
0
−u
a
11
=
−1
−u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
(u − 1)
4
c
2
, c
12
(u + 1)
4
c
3
, c
4
, c
9
c
11
u
4
+ u
2
+ 2
c
8
, c
10
(u
2
− u + 2)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y −1)
4
c
3
, c
4
, c
9
c
11
(y
2
+ y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.676097 + 0.978318I
a = 0.478073 − 0.691776I
b = 1.066120 − 0.864054I
0.82247 + 5.33349I 2.00000 − 5.29150I
u = 0.676097 − 0.978318I
a = 0.478073 + 0.691776I
b = 1.066120 + 0.864054I
0.82247 − 5.33349I 2.00000 + 5.29150I
u = −0.676097 + 0.978318I
a = −0.478073 − 0.691776I
b = −0.566121 + 0.458821I
0.82247 − 5.33349I 2.00000 + 5.29150I
u = −0.676097 − 0.978318I
a = −0.478073 + 0.691776I
b = −0.566121 − 0.458821I
0.82247 + 5.33349I 2.00000 − 5.29150I
10
III.
I
u
3
= h−7.15 × 10
4
u
13
− 7.12 × 10
4
u
12
+ · · · + 8.55 × 10
5
b − 1.08 × 10
6
, −6.15 ×
10
4
u
13
+2.37×10
4
u
12
+· · · +1.71×10
6
a+2.42×10
6
, u
14
+u
13
+· · · +12u +8i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
0.0359691u
13
− 0.0138282u
12
+ ··· − 0.612814u − 1.41664
0.0835839u
13
+ 0.0832262u
12
+ ··· + 2.37555u + 1.26466
a
8
=
u
2
+ 1
u
2
a
7
=
−0.0716091u
13
− 0.0864036u
12
+ ··· − 2.69890u − 0.496032
0.0256803u
13
+ 0.0829128u
12
+ ··· + 3.52899u + 1.16024
a
12
=
0.0423257u
13
+ 0.0196119u
12
+ ··· + 0.694498u − 1.67568
−0.00489683u
13
− 0.000238527u
12
+ ··· − 0.0660393u + 1.18171
a
6
=
−0.0923358u
13
− 0.177850u
12
+ ··· − 4.80626u − 2.20422
0.0564421u
13
+ 0.128466u
12
+ ··· + 5.94481u + 2.59514
a
2
=
0.0359691u
13
− 0.0138282u
12
+ ··· − 0.612814u − 1.41664
0.105884u
13
+ 0.0653296u
12
+ ··· + 2.68537u + 1.66304
a
5
=
−0.120342u
13
− 0.180647u
12
+ ··· − 6.00953u − 1.46083
0.0761440u
13
+ 0.0459726u
12
+ ··· + 5.11046u + 0.860223
a
11
=
0.0374289u
13
+ 0.0193733u
12
+ ··· + 0.628459u − 1.49397
−0.0700990u
13
− 0.0120106u
12
+ ··· − 0.148804u + 1.32616
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
133137
213812
u
13
−
52127
213812
u
12
+ ··· −
496203
53453
u +
335445
53453
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
− 2u
6
+ 15u
5
− 35u
4
+ 11u
3
+ 20u
2
+ 13u + 9)
2
c
2
, c
5
(u
7
− 2u
6
+ 3u
5
− u
4
+ 5u
3
+ 2u
2
− u − 3)
2
c
3
, c
4
, c
9
c
11
u
14
− u
13
+ ··· − 12u + 8
c
6
, c
7
, c
12
(u
7
+ 2u
6
− 5u
5
− 9u
4
+ 9u
3
+ 14u
2
+ 3u − 3)
2
c
8
, c
10
u
14
+ u
13
+ ··· + 784u + 64
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
+ 26y
6
+ 107y
5
− 789y
4
+ 1947y
3
+ 516y
2
− 191y −81)
2
c
2
, c
5
(y
7
+ 2y
6
+ 15y
5
+ 35y
4
+ 11y
3
− 20y
2
+ 13y −9)
2
c
3
, c
4
, c
9
c
11
y
14
+ y
13
+ ··· + 784y + 64
c
6
, c
7
, c
12
(y
7
− 14y
6
+ 79y
5
− 221y
4
+ 315y
3
− 196y
2
+ 93y −9)
2
c
8
, c
10
y
14
+ 21y
13
+ ··· − 209664y + 4096
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.189350 + 1.052410I
a = 0.100138 − 0.556568I
b = 1.64987 + 0.29513I
−4.30745 −7.31983 + 0.I
u = 0.189350 − 1.052410I
a = 0.100138 + 0.556568I
b = 1.64987 − 0.29513I
−4.30745 −7.31983 + 0.I
u = 0.009734 + 1.144270I
a = 0.482951 − 0.115663I
b = −0.207824 + 0.900142I
−2.06755 − 1.45738I 4.50826 + 4.10370I
u = 0.009734 − 1.144270I
a = 0.482951 + 0.115663I
b = −0.207824 − 0.900142I
−2.06755 + 1.45738I 4.50826 − 4.10370I
u = −1.185310 + 0.249865I
a = 1.21841 + 0.75477I
b = 0.108273 + 0.365843I
5.47090 + 1.03782I 5.54723 − 0.70964I
u = −1.185310 − 0.249865I
a = 1.21841 − 0.75477I
b = 0.108273 − 0.365843I
5.47090 − 1.03782I 5.54723 + 0.70964I
u = 0.74851 + 1.30026I
a = −0.883878 + 0.746918I
b = −0.98455 + 1.12797I
5.47090 + 1.03782I 5.54723 − 0.70964I
u = 0.74851 − 1.30026I
a = −0.883878 − 0.746918I
b = −0.98455 − 1.12797I
5.47090 − 1.03782I 5.54723 + 0.70964I
u = −0.062057 + 0.426068I
a = −1.313380 − 0.130369I
b = 1.048580 + 0.721441I
−2.06755 + 1.45738I 4.50826 − 4.10370I
u = −0.062057 − 0.426068I
a = −1.313380 + 0.130369I
b = 1.048580 − 0.721441I
−2.06755 − 1.45738I 4.50826 + 4.10370I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48947 + 0.77264I
a = −1.17405 + 2.01302I
b = −0.15440 + 2.28010I
18.4896 + 5.2126I 4.60442 − 1.93466I
u = −1.48947 − 0.77264I
a = −1.17405 − 2.01302I
b = −0.15440 − 2.28010I
18.4896 − 5.2126I 4.60442 + 1.93466I
u = 1.28924 + 1.19882I
a = −1.43019 − 1.69938I
b = −0.45995 − 2.46137I
18.4896 + 5.2126I 4.60442 − 1.93466I
u = 1.28924 − 1.19882I
a = −1.43019 + 1.69938I
b = −0.45995 + 2.46137I
18.4896 − 5.2126I 4.60442 + 1.93466I
15
IV.
I
u
4
= h−a
3
u − a
3
+ 2a
2
+ 3au + 2b +a − u − 3, a
4
+ a
3
u − 3a
2
− 2au + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
9
=
1
−1
a
4
=
u
0
a
1
=
a
1
2
a
3
u −
3
2
au + ··· −
1
2
a +
3
2
a
8
=
0
−1
a
7
=
a
2
−
1
2
a
3
u +
3
2
au + ··· +
1
2
a −
3
2
a
12
=
−a
3
+ a
1
a
6
=
a
3
u − a
2
− 2au + 1
−
1
2
a
3
u +
3
2
au + ··· +
3
2
a −
3
2
a
2
=
a
1
2
a
3
u −
3
2
au + ··· −
3
2
a +
3
2
a
5
=
a
3
u − au
−u
a
11
=
−a
3
+ a + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
u + 4a
2
+ 12au − 8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
2
, c
5
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
c
3
, c
4
, c
9
c
11
(u
2
+ 1)
4
c
6
, c
7
, c
12
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
c
8
, c
10
(u − 1)
8
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
5
(y
4
− y
3
+ 3y
2
− 2y + 1)
2
c
3
, c
4
, c
9
c
11
(y + 1)
8
c
6
, c
7
, c
12
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
c
8
, c
10
(y −1)
8
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.506844 − 0.395123I
b = 0.620943 + 0.162823I
−3.50087 − 1.41510I −3.82674 + 4.90874I
u = 1.000000I
a = −0.506844 − 0.395123I
b = 1.23497 + 0.98948I
−3.50087 + 1.41510I −3.82674 − 4.90874I
u = 1.000000I
a = 1.55249 − 0.10488I
b = 0.391114 + 0.016070I
3.50087 − 3.16396I −0.17326 + 2.56480I
u = 1.000000I
a = −1.55249 − 0.10488I
b = −1.74703 + 0.33163I
3.50087 + 3.16396I −0.17326 − 2.56480I
u = − 1.000000I
a = 0.506844 + 0.395123I
b = 0.620943 − 0.162823I
−3.50087 + 1.41510I −3.82674 − 4.90874I
u = − 1.000000I
a = −0.506844 + 0.395123I
b = 1.23497 − 0.98948I
−3.50087 − 1.41510I −3.82674 + 4.90874I
u = − 1.000000I
a = 1.55249 + 0.10488I
b = 0.391114 − 0.016070I
3.50087 + 3.16396I −0.17326 − 2.56480I
u = − 1.000000I
a = −1.55249 + 0.10488I
b = −1.74703 − 0.33163I
3.50087 − 3.16396I −0.17326 + 2.56480I
19
V. I
u
5
= h−a
2
+ 4b − 3a, a
3
+ 2a
2
+ a + 4, u + 1i
(i) Arc colorings
a
3
=
0
−1
a
10
=
1
0
a
9
=
1
1
a
4
=
−1
−2
a
1
=
a
1
4
a
2
+
3
4
a
a
8
=
2
1
a
7
=
−
1
2
a
2
−
1
2
a
−
1
4
a
2
−
3
4
a
a
12
=
0
−1
a
6
=
−
1
2
a
2
−
1
2
a
−
3
4
a
2
−
5
4
a
a
2
=
a
1
4
a
2
+
7
4
a
a
5
=
2
3
a
11
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 2u
2
+ u + 4
c
2
, c
5
, c
6
c
7
, c
12
u
3
− u + 2
c
3
, c
4
, c
8
c
9
, c
10
, c
11
(u − 1)
3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 2y
2
− 15y −16
c
2
, c
5
, c
6
c
7
, c
12
y
3
− 2y
2
+ y −4
c
3
, c
4
, c
8
c
9
, c
10
, c
11
(y −1)
3
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.157298 + 1.305150I
b = −0.301696 + 1.081510I
1.64493 6.00000
u = −1.00000
a = 0.157298 − 1.305150I
b = −0.301696 − 1.081510I
1.64493 6.00000
u = −1.00000
a = −2.31460
b = −0.396608
1.64493 6.00000
23
VI. I
u
6
= hu
3
− u
2
+ 2b − u + 1, u
3
+ a, u
4
+ 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
4
=
u
u
3
+ u
a
1
=
−u
3
−
1
2
u
3
+
1
2
u
2
+
1
2
u −
1
2
a
8
=
u
2
+ 1
u
2
a
7
=
u
3
+ u
2
+ 1
1
2
u
3
+
1
2
u
2
−
1
2
u +
1
2
a
12
=
u
2
+ 1
u
2
a
6
=
u
3
1
2
u
3
−
1
2
u
2
−
1
2
u +
1
2
a
2
=
−u
3
−
1
2
u
3
+
1
2
u
2
+
3
2
u −
1
2
a
5
=
0
u
a
11
=
u
2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
(u − 1)
4
c
3
, c
4
, c
9
c
11
u
4
+ 1
c
5
, c
6
, c
7
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
(y −1)
4
c
3
, c
4
, c
9
c
11
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = 0.707107 − 0.707107I
b = 0.207107 + 0.500000I
1.64493 4.00000
u = 0.707107 − 0.707107I
a = 0.707107 + 0.707107I
b = 0.207107 − 0.500000I
1.64493 4.00000
u = −0.707107 + 0.707107I
a = −0.707107 − 0.707107I
b = −1.207110 − 0.500000I
1.64493 4.00000
u = −0.707107 − 0.707107I
a = −0.707107 + 0.707107I
b = −1.207110 + 0.500000I
1.64493 4.00000
27
VII. I
v
1
= ha, b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
1
0
a
9
=
1
0
a
4
=
1
0
a
1
=
0
−1
a
8
=
1
0
a
7
=
1
1
a
12
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
5
=
1
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
u
c
5
, c
6
, c
7
u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
12
y − 1
c
3
, c
4
, c
8
c
9
, c
10
, c
11
y
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
0 0
31
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
3
+ 2u
2
+ u + 4)(u
4
− u
3
+ 3u
2
− 2u + 1)
2
· (u
7
− 2u
6
+ 15u
5
− 35u
4
+ 11u
3
+ 20u
2
+ 13u + 9)
2
· (u
15
+ 18u
13
+ ··· + 1061u + 121)
c
2
(u − 1)
5
(u + 1)
4
(u
3
− u + 2)
· (u
7
− 2u
6
+ 3u
5
− u
4
+ 5u
3
+ 2u
2
− u − 3)
2
(u
8
− u
6
+ 3u
4
− 2u
2
+ 1)
· (u
15
+ 6u
14
+ ··· + 7u − 11)
c
3
, c
4
, c
9
c
11
u(u − 1)
3
(u
2
+ 1)
4
(u
4
+ 1)(u
4
+ u
2
+ 2)(u
14
− u
13
+ ··· − 12u + 8)
· (u
15
+ 3u
14
+ ··· − 6u
2
− 2)
c
5
(u − 1)
4
(u + 1)
5
(u
3
− u + 2)
· (u
7
− 2u
6
+ 3u
5
− u
4
+ 5u
3
+ 2u
2
− u − 3)
2
(u
8
− u
6
+ 3u
4
− 2u
2
+ 1)
· (u
15
+ 6u
14
+ ··· + 7u − 11)
c
6
, c
7
(u − 1)
4
(u + 1)
5
(u
3
− u + 2)
· (u
7
+ 2u
6
− 5u
5
− 9u
4
+ 9u
3
+ 14u
2
+ 3u − 3)
2
· (u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)(u
15
− 6u
14
+ ··· − 5u − 11)
c
8
, c
10
u(u − 1)
11
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
14
+ u
13
+ ··· + 784u + 64)
· (u
15
+ 5u
14
+ ··· − 24u − 4)
c
12
(u − 1)
5
(u + 1)
4
(u
3
− u + 2)
· (u
7
+ 2u
6
− 5u
5
− 9u
4
+ 9u
3
+ 14u
2
+ 3u − 3)
2
· (u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)(u
15
− 6u
14
+ ··· − 5u − 11)
32
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
9
(y
3
− 2y
2
− 15y − 16)(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
· (y
7
+ 26y
6
+ 107y
5
− 789y
4
+ 1947y
3
+ 516y
2
− 191y − 81)
2
· (y
15
+ 36y
14
+ ··· + 486357y − 14641)
c
2
, c
5
(y − 1)
9
(y
3
− 2y
2
+ y − 4)(y
4
− y
3
+ 3y
2
− 2y + 1)
2
· (y
7
+ 2y
6
+ 15y
5
+ 35y
4
+ 11y
3
− 20y
2
+ 13y − 9)
2
· (y
15
+ 18y
13
+ ··· + 1061y − 121)
c
3
, c
4
, c
9
c
11
y(y − 1)
3
(y + 1)
8
(y
2
+ 1)
2
(y
2
+ y + 2)
2
· (y
14
+ y
13
+ ··· + 784y + 64)(y
15
+ 5y
14
+ ··· − 24y − 4)
c
6
, c
7
, c
12
(y − 1)
9
(y
3
− 2y
2
+ y − 4)(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
· (y
7
− 14y
6
+ 79y
5
− 221y
4
+ 315y
3
− 196y
2
+ 93y − 9)
2
· (y
15
− 24y
14
+ ··· − 459y − 121)
c
8
, c
10
y(y − 1)
11
(y + 1)
4
(y
2
+ 3y + 4)
2
· (y
14
+ 21y
13
+ ··· − 209664y + 4096)(y
15
+ 45y
14
+ ··· + 768y − 16)
33
