12n
0066
(K12n
0066
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 5 11 8 6 7
Solving Sequence
5,8 6,9,11
12 4 3 2 1 10 7
c
8
c
11
c
4
c
3
c
2
c
1
c
10
c
7
c
5
, c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.30753 × 10
64
u
40
+ 3.75257 × 10
65
u
39
+ ··· + 5.94936 × 10
67
d + 2.30338 × 10
68
,
− 7.99939 × 10
65
u
40
+ 1.44181 × 10
64
u
39
+ ··· + 2.37974 × 10
68
c − 1.93077 × 10
69
,
7.08052 × 10
74
u
40
− 1.75227 × 10
75
u
39
+ ··· + 1.49944 × 10
77
b − 5.67209 × 10
77
,
4.57210 × 10
73
u
40
− 7.88614 × 10
75
u
39
+ ··· + 1.19955 × 10
78
a − 7.69341 × 10
78
,
u
41
− 2u
40
+ ··· + 512u
2
+ 512i
I
u
2
= hc
2
u
2
+ d + 2c − 2, 4u
3
c
2
+ 2c
2
u
2
− 6u
3
c + c
3
+ 10c
2
u − 3u
2
c + 2u
3
+ 2c
2
− 15cu + u
2
− 3c + 5u + 1, b,
a − 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
v
1
= ha, d, c − 1, b − 1, v
2
− v + 1i
I
v
2
= ha, d − 1, c + a, b + 1, v
2
+ v + 1i
I
v
3
= hc, d − 1, b, a − 1, v − 1i
I
v
4
= hc, d − 1, v
2
ba − v
2
b − av + c + v, b
2
v
2
− bv + 1i
* 5 irreducible components of dim
C
= 0, with total 58 representations.
* 1 irreducible components of dim
C
= 1
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−6.31 × 10
64
u
40
+ 3.75 × 10
65
u
39
+ · · · + 5.95 × 10
67
d + 2.30 ×
10
68
, −8.00×10
65
u
40
+1.44× 10
64
u
39
+· · ·+ 2.38 ×10
68
c −1.93 ×10
69
, 7.08×
10
74
u
40
− 1.75 × 10
75
u
39
+ · · · + 1.50 × 10
77
b − 5.67 × 10
77
, 4.57 × 10
73
u
40
−
7.89× 10
75
u
39
+· · ·+ 1.20× 10
78
a − 7.69 ×10
78
, u
41
−2u
40
+· · ·+ 512u
2
+512i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
6
=
−0.0000381150u
40
+ 0.00657423u
39
+ ··· + 3.10866u + 6.41356
−0.00472210u
40
+ 0.0116861u
39
+ ··· − 6.53018u + 3.78280
a
9
=
1
u
2
a
11
=
0.00336145u
40
− 0.0000605866u
39
+ ··· + 6.98697u + 8.11334
0.00106020u
40
− 0.00630753u
39
+ ··· − 0.350233u − 3.87164
a
12
=
0.00416329u
40
− 0.00348782u
39
+ ··· + 8.59128u + 4.01677
0.00344951u
40
− 0.0105481u
39
+ ··· + 5.34083u − 6.53585
a
4
=
u
u
3
+ u
a
3
=
0.00367234u
40
− 0.00715345u
39
+ ··· + 6.07641u − 1.87083
0.00428778u
40
− 0.00271115u
39
+ ··· + 7.55176u + 6.78311
a
2
=
0.00367234u
40
− 0.00715345u
39
+ ··· + 6.07641u − 1.87083
0.00169580u
40
+ 0.00233968u
39
+ ··· + 5.67152u + 6.68520
a
1
=
−0.00488842u
40
+ 0.00771683u
39
+ ··· − 9.65835u + 0.696220
−0.00492654u
40
+ 0.0142911u
39
+ ··· − 6.54969u + 7.10978
a
10
=
0.00442165u
40
− 0.00636811u
39
+ ··· + 6.63674u + 4.24170
0.00106020u
40
− 0.00630753u
39
+ ··· − 0.350233u − 3.87164
a
7
=
0.00158049u
40
+ 0.00495719u
39
+ ··· + 5.61614u + 8.57387
−0.00178096u
40
+ 0.00501777u
39
+ ··· − 1.37083u + 0.460536
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00750642u
40
+ 0.0137245u
39
+ ··· + 0.520985u − 10.6626
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 12u
40
+ ··· + 344u − 16
c
2
, c
5
u
41
+ 2u
40
+ ··· + 16u + 4
c
3
u
41
− 2u
40
+ ··· + 428280u + 66564
c
4
, c
8
u
41
− 2u
40
+ ··· + 512u
2
+ 512
c
6
, c
11
, c
12
u
41
+ 8u
40
+ ··· − 8u + 16
c
7
, c
10
u
41
− 8u
40
+ ··· − 8u + 16
c
9
u
41
+ 10u
40
+ ··· + 2080u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
+ 36y
40
+ ··· + 135968y − 256
c
2
, c
5
y
41
+ 12y
40
+ ··· + 344y − 16
c
3
y
41
+ 60y
40
+ ··· + 44022633912y − 4430766096
c
4
, c
8
y
41
+ 30y
40
+ ··· − 524288y − 262144
c
6
, c
11
, c
12
y
41
− 50y
40
+ ··· + 8224y − 256
c
7
, c
10
y
41
− 10y
40
+ ··· + 2080y − 256
c
9
y
41
+ 50y
40
+ ··· − 663040y − 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280189 + 0.954581I
a = −0.857033 + 0.817841I
b = −0.265899 − 0.882324I
c = 0.46537 + 1.92640I
d = −0.881512 − 0.490480I
−1.60252 − 4.55290I −4.51064 + 8.08001I
u = 0.280189 − 0.954581I
a = −0.857033 − 0.817841I
b = −0.265899 + 0.882324I
c = 0.46537 − 1.92640I
d = −0.881512 + 0.490480I
−1.60252 + 4.55290I −4.51064 − 8.08001I
u = 0.942111 + 0.024266I
a = −0.224229 + 1.244680I
b = −0.026109 + 0.791073I
c = 0.548118 + 0.166539I
d = 0.670232 − 0.507481I
0.87865 + 4.07350I −1.48942 − 7.36111I
u = 0.942111 − 0.024266I
a = −0.224229 − 1.244680I
b = −0.026109 − 0.791073I
c = 0.548118 − 0.166539I
d = 0.670232 + 0.507481I
0.87865 − 4.07350I −1.48942 + 7.36111I
u = 0.100000 + 0.892301I
a = −0.052177 − 0.358577I
b = 0.118920 + 0.748261I
c = 1.00227 − 1.09254I
d = −0.544049 + 0.497019I
1.46086 + 1.42227I 3.88823 − 3.83998I
u = 0.100000 − 0.892301I
a = −0.052177 + 0.358577I
b = 0.118920 − 0.748261I
c = 1.00227 + 1.09254I
d = −0.544049 − 0.497019I
1.46086 − 1.42227I 3.88823 + 3.83998I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687957 + 0.421229I
a = 0.333750 + 0.336915I
b = 1.03088 + 1.01360I
c = 0.722058 − 0.307646I
d = 0.172146 + 0.499414I
2.43397 + 0.55461I 3.61478 + 1.21885I
u = 0.687957 − 0.421229I
a = 0.333750 − 0.336915I
b = 1.03088 − 1.01360I
c = 0.722058 + 0.307646I
d = 0.172146 − 0.499414I
2.43397 − 0.55461I 3.61478 − 1.21885I
u = 0.586118 + 0.499909I
a = −0.491451 + 0.661896I
b = −0.737846 + 0.812570I
c = 0.479205 + 0.060279I
d = 1.054290 − 0.258408I
−3.14860 + 0.97270I −10.27133 − 0.16493I
u = 0.586118 − 0.499909I
a = −0.491451 − 0.661896I
b = −0.737846 − 0.812570I
c = 0.479205 − 0.060279I
d = 1.054290 + 0.258408I
−3.14860 − 0.97270I −10.27133 + 0.16493I
u = −0.757570 + 0.057431I
a = 0.31675 + 1.45050I
b = 0.104479 + 0.545464I
c = 0.620109 + 0.138172I
d = 0.536344 − 0.342326I
0.834104 − 1.057860I −1.84303 − 1.72199I
u = −0.757570 − 0.057431I
a = 0.31675 − 1.45050I
b = 0.104479 − 0.545464I
c = 0.620109 − 0.138172I
d = 0.536344 + 0.342326I
0.834104 + 1.057860I −1.84303 + 1.72199I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748122 + 0.099272I
a = 0.93330 + 1.08938I
b = 2.35626 + 2.25935I
c = 0.561796 − 0.100209I
d = 0.725119 + 0.307713I
0.52179 − 2.81355I −3.88749 + 5.15717I
u = −0.748122 − 0.099272I
a = 0.93330 − 1.08938I
b = 2.35626 − 2.25935I
c = 0.561796 + 0.100209I
d = 0.725119 − 0.307713I
0.52179 + 2.81355I −3.88749 − 5.15717I
u = 0.004283 + 0.652626I
a = −1.55282 + 0.50485I
b = −2.68614 + 0.95227I
c = 0.461220 + 0.000384I
d = 1.168160 − 0.001807I
−0.70242 − 2.36927I 0.82941 + 4.59716I
u = 0.004283 − 0.652626I
a = −1.55282 − 0.50485I
b = −2.68614 − 0.95227I
c = 0.461220 − 0.000384I
d = 1.168160 + 0.001807I
−0.70242 + 2.36927I 0.82941 − 4.59716I
u = 0.076846 + 0.625583I
a = 1.20268 + 1.29382I
b = −0.275587 − 0.299772I
c = 2.86920 + 1.70110I
d = −0.742119 − 0.152894I
−0.85500 + 1.57570I −0.179374 + 0.776646I
u = 0.076846 − 0.625583I
a = 1.20268 − 1.29382I
b = −0.275587 + 0.299772I
c = 2.86920 − 1.70110I
d = −0.742119 + 0.152894I
−0.85500 − 1.57570I −0.179374 − 0.776646I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01326 + 1.47518I
a = −0.655430 + 0.903143I
b = 0.71376 − 1.96932I
c = 0.270068 − 1.042210I
d = −0.767011 + 0.899123I
5.83509 − 1.34899I 0.977007 + 0.716014I
u = 0.01326 − 1.47518I
a = −0.655430 − 0.903143I
b = 0.71376 + 1.96932I
c = 0.270068 + 1.042210I
d = −0.767011 − 0.899123I
5.83509 + 1.34899I 0.977007 − 0.716014I
u = −0.45410 + 1.44756I
a = 0.692132 + 0.807395I
b = 0.54174 − 2.28917I
c = −0.073099 − 1.252150I
d = −1.046470 + 0.795914I
4.95290 + 7.65933I −2.00000 − 5.62562I
u = −0.45410 − 1.44756I
a = 0.692132 − 0.807395I
b = 0.54174 + 2.28917I
c = −0.073099 + 1.252150I
d = −1.046470 − 0.795914I
4.95290 − 7.65933I −2.00000 + 5.62562I
u = −0.466919
a = −0.0931478
b = −0.579529
c = 0.536246
d = 0.864817
−1.25610 −8.53770
u = −0.35061 + 1.53639I
a = −0.902103 + 0.091854I
b = −0.136075 + 1.212460I
c = 0.001487 − 1.157830I
d = −0.998891 + 0.863682I
6.34261 + 3.42138I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.35061 − 1.53639I
a = −0.902103 − 0.091854I
b = −0.136075 − 1.212460I
c = 0.001487 + 1.157830I
d = −0.998891 − 0.863682I
6.34261 − 3.42138I 0
u = 0.51610 + 1.49655I
a = −1.048210 − 0.118410I
b = −0.199107 − 1.232920I
c = −0.132300 + 1.210890I
d = −1.089170 − 0.816098I
5.66064 − 9.73522I 0. + 7.05049I
u = 0.51610 − 1.49655I
a = −1.048210 + 0.118410I
b = −0.199107 + 1.232920I
c = −0.132300 − 1.210890I
d = −1.089170 + 0.816098I
5.66064 + 9.73522I 0. − 7.05049I
u = 1.62020 + 0.13077I
a = −0.040113 − 0.941340I
b = 0.59368 − 2.03806I
c = 0.422272 + 0.213562I
d = 0.885797 − 0.953734I
8.89854 + 0.19005I 0
u = 1.62020 − 0.13077I
a = −0.040113 + 0.941340I
b = 0.59368 + 2.03806I
c = 0.422272 − 0.213562I
d = 0.885797 + 0.953734I
8.89854 − 0.19005I 0
u = −1.59450 + 0.33027I
a = −0.066671 + 1.013570I
b = 0.54013 + 2.15152I
c = 0.416106 − 0.187734I
d = 0.996781 + 0.900887I
8.54414 − 6.61454I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59450 − 0.33027I
a = −0.066671 − 1.013570I
b = 0.54013 − 2.15152I
c = 0.416106 + 0.187734I
d = 0.996781 − 0.900887I
8.54414 + 6.61454I 0
u = 0.23388 + 1.65276I
a = −0.028955 − 0.573985I
b = 0.54769 + 2.08324I
c = 0.052963 + 1.047860I
d = −0.951888 − 0.951893I
9.70458 − 3.47853I 0
u = 0.23388 − 1.65276I
a = −0.028955 + 0.573985I
b = 0.54769 − 2.08324I
c = 0.052963 − 1.047860I
d = −0.951888 + 0.951893I
9.70458 + 3.47853I 0
u = −0.86658 + 1.51028I
a = 1.022730 − 0.213320I
b = 0.25996 − 2.32316I
c = −0.410043 − 1.126980I
d = −1.28510 + 0.78359I
12.2320 + 15.1490I 0
u = −0.86658 − 1.51028I
a = 1.022730 + 0.213320I
b = 0.25996 + 2.32316I
c = −0.410043 + 1.126980I
d = −1.28510 − 0.78359I
12.2320 − 15.1490I 0
u = 0.78943 + 1.61251I
a = 0.798911 + 0.089727I
b = 0.30028 + 2.26529I
c = −0.326045 + 1.083060I
d = −1.25486 − 0.84659I
13.5026 − 8.6555I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.78943 − 1.61251I
a = 0.798911 − 0.089727I
b = 0.30028 − 2.26529I
c = −0.326045 − 1.083060I
d = −1.25486 + 0.84659I
13.5026 + 8.6555I 0
u = 0.64330 + 1.72758I
a = −0.985622 − 0.148269I
b = 0.50633 − 1.68069I
c = 0.289772 − 0.691736I
d = −0.484819 + 1.229830I
14.7932 − 7.9945I 0
u = 0.64330 − 1.72758I
a = −0.985622 + 0.148269I
b = 0.50633 + 1.68069I
c = 0.289772 + 0.691736I
d = −0.484819 − 1.229830I
14.7932 + 7.9945I 0
u = −0.48873 + 1.82349I
a = −0.848856 + 0.042762I
b = 0.50243 + 1.74679I
c = 0.241355 + 0.733667I
d = −0.595396 − 1.229910I
15.6167 + 1.2657I 0
u = −0.48873 − 1.82349I
a = −0.848856 − 0.042762I
b = 0.50243 − 1.74679I
c = 0.241355 − 0.733667I
d = −0.595396 + 1.229910I
15.6167 − 1.2657I 0
11
II.
I
u
2
= hc
2
u
2
+d+2c−2, 4u
3
c
2
−6u
3
c+· · ·−3c+1, b, a−1, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
6
=
1
0
a
9
=
1
u
2
a
11
=
c
−c
2
u
2
− 2c + 2
a
12
=
−c
2
u
2
− c + 2
−c
2
u
2
− 2c + 2
a
4
=
u
u
3
+ u
a
3
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
a
1
=
−u
2
− 1
−u
2
a
10
=
−c
2
u
2
− c + 2
−c
2
u
2
− 2c + 2
a
7
=
c
2
u
2
+ u
2
c + 3c − 2
c
2
u
2
+ u
2
c + 2c − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
c
2
, c
5
(u
4
+ u
3
+ u
2
+ 1)
3
c
3
(u
4
− u
3
+ 5u
2
+ u + 2)
3
c
6
, c
7
, c
10
c
11
, c
12
u
12
− 4u
10
+ ··· − 2u + 1
c
9
u
12
+ 8u
11
+ ··· − 10u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
c
2
, c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
c
3
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
3
c
6
, c
7
, c
10
c
11
, c
12
y
12
− 8y
11
+ ··· + 10y + 1
c
9
y
12
− 8y
11
+ ··· − 78y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 1.00000
b = 0
c = 0.937473 + 0.363729I
d = −0.072869 − 0.359716I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = 1.00000
b = 0
c = 0.477428 − 0.036931I
d = 1.082100 + 0.161058I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = 1.00000
b = 0
c = −0.23342 − 5.02292I
d = −1.009230 + 0.198659I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = 1.00000
b = 0
c = 0.937473 − 0.363729I
d = −0.072869 + 0.359716I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = 1.00000
b = 0
c = 0.477428 + 0.036931I
d = 1.082100 − 0.161058I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = 1.00000
b = 0
c = −0.23342 + 5.02292I
d = −1.009230 − 0.198659I
−0.21101 − 1.41510I −1.82674 + 4.90874I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = 1.00000
b = 0
c = 0.266059 + 0.958153I
d = −0.730940 − 0.968963I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 + 1.55249I
a = 1.00000
b = 0
c = 0.166080 − 1.061830I
d = −0.856215 + 0.919282I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 + 1.55249I
a = 1.00000
b = 0
c = 0.386383 − 0.007420I
d = 1.58715 + 0.04968I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 1.00000
b = 0
c = 0.266059 − 0.958153I
d = −0.730940 + 0.968963I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.10488 − 1.55249I
a = 1.00000
b = 0
c = 0.166080 + 1.061830I
d = −0.856215 − 0.919282I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.10488 − 1.55249I
a = 1.00000
b = 0
c = 0.386383 + 0.007420I
d = 1.58715 − 0.04968I
6.79074 − 3.16396I 1.82674 + 2.56480I
16
III. I
v
1
= ha, d, c − 1, b − 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
6
=
0
1
a
9
=
1
0
a
11
=
1
0
a
12
=
1
−1
a
4
=
v
0
a
3
=
v
−v
a
2
=
v − 1
−v
a
1
=
0
−1
a
10
=
1
0
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
(u + 1)
2
c
11
, c
12
(u − 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = 1.00000
d = 0
1.64493 − 2.02988I 3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 1.00000
d = 0
1.64493 + 2.02988I 3.00000 − 3.46410I
20
IV. I
v
2
= ha, d − 1, c + a, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
6
=
0
−1
a
9
=
1
0
a
11
=
0
1
a
12
=
0
1
a
4
=
v
0
a
3
=
v
−v
a
2
=
v + 1
−v
a
1
=
0
1
a
10
=
1
1
a
7
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 11
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
8
c
11
, c
12
u
2
c
7
, c
9
(u − 1)
2
c
10
(u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
8
c
11
, c
12
y
2
c
7
, c
9
, c
10
(y − 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
c = 0
d = 1.00000
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 0
d = 1.00000
−1.64493 − 2.02988I −9.00000 + 3.46410I
24
V. I
v
3
= hc, d − 1, b, a − 1, v − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
1
0
a
6
=
1
0
a
9
=
1
0
a
11
=
0
1
a
12
=
1
1
a
4
=
1
0
a
3
=
1
0
a
2
=
1
0
a
1
=
1
0
a
10
=
1
1
a
7
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
u
c
6
, c
7
, c
9
u − 1
c
10
, c
11
, c
12
u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
y
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y − 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
28
VI. I
v
4
= hc, d − 1, v
2
ba − v
2
b − av + c + v, b
2
v
2
− bv + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
6
=
1
b
a
9
=
1
0
a
11
=
0
1
a
12
=
1
b + 1
a
4
=
v
0
a
3
=
−bv + v
−b
2
v
a
2
=
v
2
b − bv
−b
2
v
a
1
=
−1
−b
a
10
=
1
1
a
7
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −b
3
v + 4bv + v
2
− 4
(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.
29
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
− 2.02988I −0.70149 + 4.98668I
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
· (u
41
+ 12u
40
+ ··· + 344u − 16)
c
2
u(u
2
+ u + 1)
2
(u
4
+ u
3
+ u
2
+ 1)
3
(u
41
+ 2u
40
+ ··· + 16u + 4)
c
3
u(u
2
− u + 1)
2
(u
4
− u
3
+ 5u
2
+ u + 2)
3
· (u
41
− 2u
40
+ ··· + 428280u + 66564)
c
4
, c
8
u
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
(u
41
− 2u
40
+ ··· + 512u
2
+ 512)
c
5
u(u
2
− u + 1)
2
(u
4
+ u
3
+ u
2
+ 1)
3
(u
41
+ 2u
40
+ ··· + 16u + 4)
c
6
u
2
(u − 1)(u + 1)
2
(u
12
− 4u
10
+ ··· − 2u + 1)(u
41
+ 8u
40
+ ··· − 8u + 16)
c
7
u
2
(u − 1)
3
(u
12
− 4u
10
+ ··· − 2u + 1)(u
41
− 8u
40
+ ··· − 8u + 16)
c
9
u
2
(u − 1)
3
(u
12
+ 8u
11
+ ··· − 10u + 1)
· (u
41
+ 10u
40
+ ··· + 2080u + 256)
c
10
u
2
(u + 1)
3
(u
12
− 4u
10
+ ··· − 2u + 1)(u
41
− 8u
40
+ ··· − 8u + 16)
c
11
, c
12
u
2
(u − 1)
2
(u + 1)(u
12
− 4u
10
+ ··· − 2u + 1)(u
41
+ 8u
40
+ ··· − 8u + 16)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
3
· (y
41
+ 36y
40
+ ··· + 135968y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
3
· (y
41
+ 12y
40
+ ··· + 344y − 16)
c
3
y(y
2
+ y + 1)
2
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
3
· (y
41
+ 60y
40
+ ··· + 44022633912y − 4430766096)
c
4
, c
8
y
5
(y
4
+ 5y
3
+ ··· + 2y + 1)
3
(y
41
+ 30y
40
+ ··· − 524288y − 262144)
c
6
, c
11
, c
12
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 10y + 1)
· (y
41
− 50y
40
+ ··· + 8224y − 256)
c
7
, c
10
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 10y + 1)
· (y
41
− 10y
40
+ ··· + 2080y − 256)
c
9
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· − 78y + 1)
· (y
41
+ 50y
40
+ ··· − 663040y − 65536)
32
