12a
0210
(K12a
0210
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 2 5 10 12 4 1 8 11
Solving Sequence
2,5
6 3 7
4,10
8 1 11 9 12
c
5
c
2
c
6
c
3
c
7
c
1
c
10
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
17
+ 3u
15
+ u
14
− 7u
13
− 2u
12
+ 9u
11
+ 5u
10
− 10u
9
− 5u
8
+ 7u
7
+ 6u
6
− 5u
5
− 3u
4
+ u
3
+ 2u
2
+ b,
− u
15
+ 2u
13
+ u
12
− 4u
11
− u
10
+ 3u
9
+ 3u
8
− 3u
7
− u
6
+ u
5
+ 2u
4
− u
3
+ a − u, u
18
− 3u
16
+ ··· + 2u + 1i
I
u
2
= h3u
83
+ 6u
82
+ ··· + b − 1, 7u
83
+ 10u
82
+ ··· + 2a − 11, u
84
+ 3u
83
+ ··· + 2u − 1i
I
u
3
= hb, a + 1, u
3
− u
2
+ 1i
I
u
4
= hb, a
2
− au + 2u
2
− 3u + 2, u
3
− u
2
+ 1i
I
u
5
= hb − 2, a − 1, u + 1i
* 5 irreducible components of dim
C
= 0, with total 112 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−u
17
+3u
15
+· · ·+2u
2
+b, −u
15
+2u
13
+· · ·+a−u, u
18
−3u
16
+· · ·+2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
10
=
u
15
− 2u
13
− u
12
+ 4u
11
+ u
10
− 3u
9
− 3u
8
+ 3u
7
+ u
6
− u
5
− 2u
4
+ u
3
+ u
u
17
− 3u
15
+ ··· − u
3
− 2u
2
a
8
=
−u
16
+ 3u
14
+ ··· − u
2
+ 1
u
16
− 2u
14
+ ··· − u
4
+ 2u
2
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
u
15
− 2u
13
− u
12
+ 4u
11
+ u
10
− 3u
9
− 3u
8
+ 3u
7
+ u
6
− 2u
4
+ u
3
+ u
u
17
− 3u
15
+ ··· + 3u
4
− 2u
2
a
9
=
u
14
− 3u
12
+ ··· + 2u
2
+ 2u
−u
14
+ 2u
12
+ u
11
− 5u
10
− u
9
+ 5u
8
+ 3u
7
− 6u
6
− u
5
+ 3u
4
+ 2u
3
− 2u
2
a
12
=
u
17
− 2u
15
− u
14
+ 4u
13
+ u
12
− 3u
11
− 3u
10
+ 3u
9
+ u
8
− 2u
6
+ u
5
+ 2u
3
−u
15
+ 3u
13
+ ··· − 2u
3
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
17
+ 4u
16
+ 8u
15
− 10u
14
− 24u
13
+ 26u
12
+ 42u
11
− 30u
10
−
66u
9
+ 34u
8
+ 66u
7
− 16u
6
− 66u
5
+ 8u
4
+ 32u
3
+ 8u
2
− 16u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
10
c
12
u
18
+ 6u
17
+ ··· + 2u + 1
c
2
, c
5
, c
8
c
11
u
18
− 3u
16
+ ··· + 2u + 1
c
3
, c
7
u
18
− 2u
17
+ ··· + 4u + 1
c
4
, c
9
u
18
− 6u
17
+ ··· − 24u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
10
c
12
y
18
+ 14y
17
+ ··· + 22y + 1
c
2
, c
5
, c
8
c
11
y
18
− 6y
17
+ ··· − 2y + 1
c
3
, c
7
y
18
− 10y
17
+ ··· − 2y + 1
c
4
, c
9
y
18
+ 8y
17
+ ··· + 256y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.852988 + 0.599070I
a = 1.86967 + 1.04403I
b = −1.54451 + 0.51046I
2.34312 − 4.73471I −7.07668 + 6.82584I
u = 0.852988 − 0.599070I
a = 1.86967 − 1.04403I
b = −1.54451 − 0.51046I
2.34312 + 4.73471I −7.07668 − 6.82584I
u = 0.713575 + 0.772455I
a = −1.68389 + 1.91803I
b = 0.92095 − 1.86302I
5.76795 − 0.42490I −2.62552 + 1.94246I
u = 0.713575 − 0.772455I
a = −1.68389 − 1.91803I
b = 0.92095 + 1.86302I
5.76795 + 0.42490I −2.62552 − 1.94246I
u = −0.680242 + 0.830816I
a = 1.80309 + 1.05417I
b = −1.63673 − 1.25883I
3.89996 − 5.56871I −4.31829 + 2.06139I
u = −0.680242 − 0.830816I
a = 1.80309 − 1.05417I
b = −1.63673 + 1.25883I
3.89996 + 5.56871I −4.31829 − 2.06139I
u = 1.088500 + 0.110069I
a = −0.751912 + 0.070278I
b = −1.65982 + 0.10721I
−9.12746 − 5.02050I −18.4222 + 4.8342I
u = 1.088500 − 0.110069I
a = −0.751912 − 0.070278I
b = −1.65982 − 0.10721I
−9.12746 + 5.02050I −18.4222 − 4.8342I
u = −1.012600 + 0.591290I
a = −0.91949 − 1.13440I
b = 0.066057 + 0.911088I
−3.35551 + 7.83027I −12.5543 − 7.9398I
u = −1.012600 − 0.591290I
a = −0.91949 + 1.13440I
b = 0.066057 − 0.911088I
−3.35551 − 7.83027I −12.5543 + 7.9398I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.997184 + 0.703282I
a = 1.01150 − 3.14671I
b = 1.47517 + 2.11590I
4.02002 − 10.78450I −6.41328 + 8.53348I
u = 0.997184 − 0.703282I
a = 1.01150 + 3.14671I
b = 1.47517 − 2.11590I
4.02002 + 10.78450I −6.41328 − 8.53348I
u = −0.623040 + 0.431726I
a = −0.237344 + 0.890114I
b = 0.157083 + 0.325898I
−0.68211 + 1.26711I −9.25343 − 4.35410I
u = −0.623040 − 0.431726I
a = −0.237344 − 0.890114I
b = 0.157083 − 0.325898I
−0.68211 − 1.26711I −9.25343 + 4.35410I
u = −1.029700 + 0.727727I
a = −0.09346 − 2.99952I
b = −2.04495 + 1.32035I
1.7668 + 17.2595I −7.77898 − 11.27344I
u = −1.029700 − 0.727727I
a = −0.09346 + 2.99952I
b = −2.04495 − 1.32035I
1.7668 − 17.2595I −7.77898 + 11.27344I
u = −0.306671 + 0.477938I
a = 0.001829 + 0.467096I
b = −0.233244 + 0.353264I
−0.520477 + 1.222060I −5.55737 − 4.78188I
u = −0.306671 − 0.477938I
a = 0.001829 − 0.467096I
b = −0.233244 − 0.353264I
−0.520477 − 1.222060I −5.55737 + 4.78188I
6
II. I
u
2
=
h3u
83
+6u
82
+· · · +b−1, 7u
83
+10u
82
+· · · +2a−11, u
84
+3u
83
+· · · +2u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
10
=
−
7
2
u
83
− 5u
82
+ ··· − 3u +
11
2
−3u
83
− 6u
82
+ ··· − 3u + 1
a
8
=
−
1
2
u
83
−
3
2
u
82
+ ··· −
15
2
u
2
−
9
2
u
u
19
− 3u
17
+ ··· + 4u
2
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
−12.5000u
83
− 28.5000u
82
+ ··· − 28.5000u + 15.5000
8u
83
+ 16u
82
+ ··· + 9u −
9
2
a
9
=
−
21
2
u
83
− 23u
82
+ ··· − 21u +
25
2
5u
83
+ 10u
82
+ ··· + 5u − 3
a
12
=
u
83
+ 3u
82
+ ··· + 6u +
1
2
−
1
2
u
83
− u
82
+ ··· − u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
33
2
u
82
−
35
2
u
81
+ ··· −
97
2
u +
21
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
10
c
12
u
84
+ 27u
83
+ ··· + 20u + 1
c
2
, c
5
, c
8
c
11
u
84
+ 3u
83
+ ··· + 2u − 1
c
3
, c
7
u
84
− 3u
83
+ ··· + 76888u − 5953
c
4
, c
9
(u
42
+ 3u
41
+ ··· − 36u − 8)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
10
c
12
y
84
+ 61y
83
+ ··· − 492y + 1
c
2
, c
5
, c
8
c
11
y
84
− 27y
83
+ ··· − 20y + 1
c
3
, c
7
y
84
+ y
83
+ ··· − 880217508y + 35438209
c
4
, c
9
(y
42
+ 21y
41
+ ··· + 304y + 64)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.712297 + 0.693306I
a = 2.23429 − 0.72427I
b = −1.31799 + 1.19951I
−0.0807684 + 0.0270051I 0
u = 0.712297 − 0.693306I
a = 2.23429 + 0.72427I
b = −1.31799 − 1.19951I
−0.0807684 − 0.0270051I 0
u = −0.981209 + 0.106389I
a = −1.063230 + 0.239722I
b = −1.31799 + 1.19951I
−0.0807684 + 0.0270051I 0
u = −0.981209 − 0.106389I
a = −1.063230 − 0.239722I
b = −1.31799 − 1.19951I
−0.0807684 − 0.0270051I 0
u = −1.013640 + 0.084832I
a = 1.108450 − 0.126642I
b = 1.84271 − 1.22555I
−0.87551 + 5.31550I 0
u = −1.013640 − 0.084832I
a = 1.108450 + 0.126642I
b = 1.84271 + 1.22555I
−0.87551 − 5.31550I 0
u = −0.672327 + 0.781209I
a = 1.046300 + 0.176265I
b = −1.139890 − 0.738004I
1.33500 − 3.00337I 0
u = −0.672327 − 0.781209I
a = 1.046300 − 0.176265I
b = −1.139890 + 0.738004I
1.33500 + 3.00337I 0
u = −0.622637 + 0.740255I
a = −0.917148 + 0.701158I
b = 0.958255 + 0.174252I
−0.916866 + 0.809895I 0
u = −0.622637 − 0.740255I
a = −0.917148 − 0.701158I
b = 0.958255 − 0.174252I
−0.916866 − 0.809895I 0
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.693162 + 0.769076I
a = 2.10791 − 2.00976I
b = −1.18015 + 1.94588I
4.93754 + 5.19661I 0
u = 0.693162 − 0.769076I
a = 2.10791 + 2.00976I
b = −1.18015 − 1.94588I
4.93754 − 5.19661I 0
u = −0.648818 + 0.814325I
a = −1.87305 − 0.13963I
b = 1.66800 + 0.67324I
−2.74884 − 5.46887I 0
u = −0.648818 − 0.814325I
a = −1.87305 + 0.13963I
b = 1.66800 − 0.67324I
−2.74884 + 5.46887I 0
u = 1.048020 + 0.087930I
a = 0.740915 + 0.375139I
b = 0.938320 − 0.000865I
−4.65419 − 2.84221I 0
u = 1.048020 − 0.087930I
a = 0.740915 − 0.375139I
b = 0.938320 + 0.000865I
−4.65419 + 2.84221I 0
u = −0.761114 + 0.735215I
a = 0.528661 + 0.102908I
b = 0.294442 + 0.779185I
6.06758 + 3.93578I 0
u = −0.761114 − 0.735215I
a = 0.528661 − 0.102908I
b = 0.294442 − 0.779185I
6.06758 − 3.93578I 0
u = −0.749660 + 0.749510I
a = −0.377620 + 0.179779I
b = −0.382925 − 0.879824I
6.42114 − 2.03089I 0
u = −0.749660 − 0.749510I
a = −0.377620 − 0.179779I
b = −0.382925 + 0.879824I
6.42114 + 2.03089I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958216 + 0.461454I
a = −0.29023 + 1.63234I
b = 0.958255 + 0.174252I
−0.916866 + 0.809895I 0
u = −0.958216 − 0.461454I
a = −0.29023 − 1.63234I
b = 0.958255 − 0.174252I
−0.916866 − 0.809895I 0
u = −0.674263 + 0.839731I
a = −2.12227 − 1.06881I
b = 1.83778 + 1.26952I
2.85235 − 11.39960I 0
u = −0.674263 − 0.839731I
a = −2.12227 + 1.06881I
b = 1.83778 − 1.26952I
2.85235 + 11.39960I 0
u = 1.078220 + 0.052470I
a = −0.355684 − 0.249586I
b = −0.803714 + 0.656750I
−6.62757 + 1.48268I 0
u = 1.078220 − 0.052470I
a = −0.355684 + 0.249586I
b = −0.803714 − 0.656750I
−6.62757 − 1.48268I 0
u = 0.791471 + 0.735596I
a = −0.975220 + 0.562204I
b = 0.633168 − 0.948263I
3.25378 − 1.67585I 0
u = 0.791471 − 0.735596I
a = −0.975220 − 0.562204I
b = 0.633168 + 0.948263I
3.25378 + 1.67585I 0
u = 1.071840 + 0.149484I
a = 1.208950 − 0.123740I
b = 1.66800 + 0.67324I
−2.74884 − 5.46887I 0
u = 1.071840 − 0.149484I
a = 1.208950 + 0.123740I
b = 1.66800 − 0.67324I
−2.74884 + 5.46887I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.914052 + 0.017611I
a = 0.28796 + 2.10554I
b = 0.029606 + 0.357540I
1.30504 − 2.96740I −16.6019 + 3.9985I
u = 0.914052 − 0.017611I
a = 0.28796 − 2.10554I
b = 0.029606 − 0.357540I
1.30504 + 2.96740I −16.6019 − 3.9985I
u = 1.087550 + 0.152734I
a = −1.157320 + 0.302919I
b = −1.97161 − 0.66469I
−3.89961 − 11.18750I 0
u = 1.087550 − 0.152734I
a = −1.157320 − 0.302919I
b = −1.97161 + 0.66469I
−3.89961 + 11.18750I 0
u = −0.999343 + 0.459478I
a = 0.30537 − 1.95122I
b = −1.345570 − 0.027761I
−2.06219 − 4.61435I 0
u = −0.999343 − 0.459478I
a = 0.30537 + 1.95122I
b = −1.345570 + 0.027761I
−2.06219 + 4.61435I 0
u = 0.926856 + 0.616107I
a = −1.48117 − 1.93854I
b = 1.95814
2.04966 0
u = 0.926856 − 0.616107I
a = −1.48117 + 1.93854I
b = 1.95814
2.04966 0
u = −0.971842 + 0.584202I
a = 0.378274 + 1.128680I
b = 0.110057 − 0.403021I
−1.77536 + 3.05903I 0
u = −0.971842 − 0.584202I
a = 0.378274 − 1.128680I
b = 0.110057 + 0.403021I
−1.77536 − 3.05903I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.004520 + 0.529184I
a = −0.37789 − 1.78426I
b = −0.803714 + 0.656750I
−6.62757 + 1.48268I 0
u = −1.004520 − 0.529184I
a = −0.37789 + 1.78426I
b = −0.803714 − 0.656750I
−6.62757 − 1.48268I 0
u = 0.822047 + 0.815086I
a = 0.503520 + 0.685512I
b = −0.382925 − 0.879824I
6.42114 − 2.03089I 0
u = 0.822047 − 0.815086I
a = 0.503520 − 0.685512I
b = −0.382925 + 0.879824I
6.42114 + 2.03089I 0
u = 0.929297 + 0.706689I
a = −0.162531 + 1.378400I
b = −0.897351 − 0.739849I
2.82931 − 3.82448I 0
u = 0.929297 − 0.706689I
a = −0.162531 − 1.378400I
b = −0.897351 + 0.739849I
2.82931 + 3.82448I 0
u = −0.830789
a = −0.529711
b = −0.524897
−1.36262 −6.28990
u = 0.835882 + 0.822680I
a = −0.705257 − 0.359402I
b = 0.488855 + 0.663264I
5.77020 − 7.57055I 0
u = 0.835882 − 0.822680I
a = −0.705257 + 0.359402I
b = 0.488855 − 0.663264I
5.77020 + 7.57055I 0
u = −0.952690 + 0.699025I
a = −1.161850 + 0.128348I
b = −0.383270 + 0.555402I
5.47969 + 1.54222I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.952690 − 0.699025I
a = −1.161850 − 0.128348I
b = −0.383270 − 0.555402I
5.47969 − 1.54222I 0
u = 0.879439 + 0.791896I
a = 0.143018 + 0.204296I
b = 0.029606 + 0.357540I
1.30504 − 2.96740I 0
u = 0.879439 − 0.791896I
a = 0.143018 − 0.204296I
b = 0.029606 − 0.357540I
1.30504 + 2.96740I 0
u = 0.974010 + 0.672846I
a = −0.13241 − 2.73914I
b = 1.84271 + 1.22555I
−0.87551 − 5.31550I 0
u = 0.974010 − 0.672846I
a = −0.13241 + 2.73914I
b = 1.84271 − 1.22555I
−0.87551 + 5.31550I 0
u = −0.962485 + 0.705411I
a = 1.230370 + 0.245638I
b = 0.488855 − 0.663264I
5.77020 + 7.57055I 0
u = −0.962485 − 0.705411I
a = 1.230370 − 0.245638I
b = 0.488855 + 0.663264I
5.77020 − 7.57055I 0
u = −0.431386 + 0.666039I
a = −0.225386 − 1.395600I
b = 0.110057 + 0.403021I
−1.77536 − 3.05903I −9.76833 + 2.76622I
u = −0.431386 − 0.666039I
a = −0.225386 + 1.395600I
b = 0.110057 − 0.403021I
−1.77536 + 3.05903I −9.76833 − 2.76622I
u = 0.987595 + 0.710734I
a = −1.11733 + 2.72417I
b = −1.18015 − 1.94588I
4.93754 − 5.19661I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.987595 − 0.710734I
a = −1.11733 − 2.72417I
b = −1.18015 + 1.94588I
4.93754 + 5.19661I 0
u = 0.937037 + 0.779487I
a = −1.369200 + 0.010031I
b = 0.294442 − 0.779185I
6.06758 − 3.93578I 0
u = 0.937037 − 0.779487I
a = −1.369200 − 0.010031I
b = 0.294442 + 0.779185I
6.06758 + 3.93578I 0
u = −1.015290 + 0.678143I
a = 0.593516 − 0.877102I
b = −1.345570 + 0.027761I
−2.06219 + 4.61435I 0
u = −1.015290 − 0.678143I
a = 0.593516 + 0.877102I
b = −1.345570 − 0.027761I
−2.06219 − 4.61435I 0
u = 0.930205 + 0.791978I
a = 1.228620 + 0.396768I
b = −0.383270 + 0.555402I
5.47969 + 1.54222I 0
u = 0.930205 − 0.791978I
a = 1.228620 − 0.396768I
b = −0.383270 − 0.555402I
5.47969 − 1.54222I 0
u = −1.010270 + 0.702765I
a = 0.06764 + 1.52585I
b = 1.40467 − 0.62102I
0.31756 + 8.62089I 0
u = −1.010270 − 0.702765I
a = 0.06764 − 1.52585I
b = 1.40467 + 0.62102I
0.31756 − 8.62089I 0
u = −1.029790 + 0.708012I
a = 0.48664 − 2.20279I
b = −1.97161 + 0.66469I
−3.89961 + 11.18750I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.029790 − 0.708012I
a = 0.48664 + 2.20279I
b = −1.97161 − 0.66469I
−3.89961 − 11.18750I 0
u = −1.023700 + 0.726192I
a = 0.28327 + 2.73696I
b = 1.83778 − 1.26952I
2.85235 + 11.39960I 0
u = −1.023700 − 0.726192I
a = 0.28327 − 2.73696I
b = 1.83778 + 1.26952I
2.85235 − 11.39960I 0
u = −0.284139 + 0.668066I
a = −1.170660 − 0.642188I
b = 0.938320 + 0.000865I
−4.65419 + 2.84221I −12.59242 − 3.99568I
u = −0.284139 − 0.668066I
a = −1.170660 + 0.642188I
b = 0.938320 − 0.000865I
−4.65419 − 2.84221I −12.59242 + 3.99568I
u = −0.193209 + 0.694467I
a = −1.71483 + 0.37751I
b = 1.40467 − 0.62102I
0.31756 + 8.62089I −6.58174 − 7.44305I
u = −0.193209 − 0.694467I
a = −1.71483 − 0.37751I
b = 1.40467 + 0.62102I
0.31756 − 8.62089I −6.58174 + 7.44305I
u = −0.181530 + 0.663240I
a = 1.289870 − 0.508739I
b = −1.139890 + 0.738004I
1.33500 + 3.00337I −4.59894 − 2.71098I
u = −0.181530 − 0.663240I
a = 1.289870 + 0.508739I
b = −1.139890 − 0.738004I
1.33500 − 3.00337I −4.59894 + 2.71098I
u = 0.210352 + 0.417710I
a = 2.58989 + 0.96746I
b = −0.897351 − 0.739849I
2.82931 − 3.82448I −1.91908 + 4.03755I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210352 − 0.417710I
a = 2.58989 − 0.96746I
b = −0.897351 + 0.739849I
2.82931 + 3.82448I −1.91908 − 4.03755I
u = 0.122077 + 0.444395I
a = −2.03594 − 1.04124I
b = 0.633168 + 0.948263I
3.25378 + 1.67585I −1.01897 − 2.48260I
u = 0.122077 − 0.444395I
a = −2.03594 + 1.04124I
b = 0.633168 − 0.948263I
3.25378 − 1.67585I −1.01897 + 2.48260I
u = 0.212119
a = 3.37531
b = −0.524897
−1.36262 −6.28990
18
III. I
u
3
= hb, a + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
7
=
−u
2
+ 1
u
2
a
4
=
1
0
a
10
=
−1
0
a
8
=
−2u
2
+ 1
u
2
a
1
=
u
2
− 1
−u
2
a
11
=
−u − 2
−u
2
+ u + 1
a
9
=
−1
0
a
12
=
−2u
2
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u − 12
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
10
u
3
− u
2
+ 2u − 1
c
2
, c
8
u
3
+ u
2
− 1
c
4
, c
9
u
3
c
5
, c
11
u
3
− u
2
+ 1
c
6
, c
12
u
3
+ u
2
+ 2u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
y
3
+ 3y
2
+ 2y − 1
c
2
, c
5
, c
8
c
11
y
3
− y
2
+ 2y − 1
c
4
, c
9
y
3
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −1.00000
b = 0
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.877439 − 0.744862I
a = −1.00000
b = 0
6.04826 + 5.65624I −4.98049 − 5.95889I
u = −0.754878
a = −1.00000
b = 0
−2.22691 −18.0390
22
IV. I
u
4
= hb, a
2
− au + 2u
2
− 3u + 2, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
7
=
−u
2
+ 1
u
2
a
4
=
1
0
a
10
=
a
0
a
8
=
−u
2
a + a − 2u + 2
u
2
a
1
=
u
2
− 1
−u
2
a
11
=
au + 2a
u
2
a − au − a
a
9
=
a
0
a
12
=
−3u
2
a + au + 2u
2
+ 3a − 3u
2u
2
a − u
2
− a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
a + u
2
− 5
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
7
c
10
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
8
(u
3
+ u
2
− 1)
2
c
4
, c
9
u
6
c
5
, c
11
(u
3
− u
2
+ 1)
2
c
6
, c
12
(u
3
+ u
2
+ 2u + 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
2
, c
5
, c
8
c
11
(y
3
− y
2
+ 2y − 1)
2
c
4
, c
9
y
6
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.947279 + 0.320410I
b = 0
6.04826 −4.56984 + 0.I
u = 0.877439 + 0.744862I
a = −0.069840 + 0.424452I
b = 0
1.91067 − 2.82812I −4.21508 + 1.30714I
u = 0.877439 − 0.744862I
a = 0.947279 − 0.320410I
b = 0
6.04826 −4.56984 + 0.I
u = 0.877439 − 0.744862I
a = −0.069840 − 0.424452I
b = 0
1.91067 + 2.82812I −4.21508 − 1.30714I
u = −0.754878
a = −0.37744 + 2.29387I
b = 0
1.91067 + 2.82812I −4.21508 − 1.30714I
u = −0.754878
a = −0.37744 − 2.29387I
b = 0
1.91067 − 2.82812I −4.21508 + 1.30714I
26
V. I
u
5
= hb − 2, a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
7
=
0
1
a
4
=
1
1
a
10
=
1
2
a
8
=
−1
−1
a
1
=
−1
−1
a
11
=
0
1
a
9
=
0
1
a
12
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
u + 1
c
4
, c
9
u − 1
28
(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
, c
11
, c
12
y − 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.00000
b = 2.00000
−4.93480 −18.0000
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u + 1)(u
3
− u
2
+ 2u − 1)
3
(u
18
+ 6u
17
+ ··· + 2u + 1)
· (u
84
+ 27u
83
+ ··· + 20u + 1)
c
2
, c
8
(u + 1)(u
3
+ u
2
− 1)
3
(u
18
− 3u
16
+ ··· + 2u + 1)
· (u
84
+ 3u
83
+ ··· + 2u − 1)
c
3
, c
7
(u + 1)(u
3
− u
2
+ 2u − 1)
3
(u
18
− 2u
17
+ ··· + 4u + 1)
· (u
84
− 3u
83
+ ··· + 76888u − 5953)
c
4
, c
9
u
9
(u − 1)(u
18
− 6u
17
+ ··· − 24u + 8)(u
42
+ 3u
41
+ ··· − 36u − 8)
2
c
5
, c
11
(u + 1)(u
3
− u
2
+ 1)
3
(u
18
− 3u
16
+ ··· + 2u + 1)
· (u
84
+ 3u
83
+ ··· + 2u − 1)
c
6
, c
12
(u + 1)(u
3
+ u
2
+ 2u + 1)
3
(u
18
+ 6u
17
+ ··· + 2u + 1)
· (u
84
+ 27u
83
+ ··· + 20u + 1)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
10
c
12
(y − 1)(y
3
+ 3y
2
+ 2y − 1)
3
(y
18
+ 14y
17
+ ··· + 22y + 1)
· (y
84
+ 61y
83
+ ··· − 492y + 1)
c
2
, c
5
, c
8
c
11
(y − 1)(y
3
− y
2
+ 2y − 1)
3
(y
18
− 6y
17
+ ··· − 2y + 1)
· (y
84
− 27y
83
+ ··· − 20y + 1)
c
3
, c
7
(y − 1)(y
3
+ 3y
2
+ 2y − 1)
3
(y
18
− 10y
17
+ ··· − 2y + 1)
· (y
84
+ y
83
+ ··· − 880217508y + 35438209)
c
4
, c
9
y
9
(y − 1)(y
18
+ 8y
17
+ ··· + 256y + 64)
· (y
42
+ 21y
41
+ ··· + 304y + 64)
2
32
