12n
0062
(K12n
0062
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 5 7 8 6 11
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
= h1.37658 × 10
65
u
40
− 4.47424 × 10
65
u
39
+ ··· + 1.06596 × 10
68
d + 6.96533 × 10
67
,
1.14112 × 10
66
u
40
− 3.62494 × 10
66
u
39
+ ··· + 4.26385 × 10
68
c + 2.46764 × 10
68
,
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
= h−u
3
c
2
+ 13c
2
u
2
+ 2u
3
c + 5c
2
u + 12u
2
c + 4u
3
+ 4c
2
+ 9cu + 24u
2
+ 19d − 8c + 18u + 22,
− 4u
3
c
2
− 2c
2
u
2
+ 2u
3
c + c
3
− 10c
2
u + u
2
c + 2u
3
− 2c
2
+ 5cu + 2u
2
+ 3c + 5u + 4, b, a − 1,
u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
v
1
= ha, d + 1, c + a, b − 1, v
2
− v + 1i
I
v
2
= ha, d, c − 1, 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
= h1.38 × 10
65
u
40
− 4.47× 10
65
u
39
+ · · · + 1.07 × 10
68
d +6.97 × 10
67
, 1.14 ×
10
66
u
40
− 3.62 × 10
66
u
39
+ · · · + 4.26 × 10
68
c + 2.47 × 10
68
, 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
=
−0.00267627u
40
+ 0.00850156u
39
+ ··· + 2.32863u − 0.578736
−0.00129140u
40
+ 0.00419737u
39
+ ··· + 1.25599u − 0.653432
a
12
=
0.00393209u
40
− 0.00559798u
39
+ ··· + 9.49704u − 0.508301
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
=
−0.00138487u
40
+ 0.00430419u
39
+ ··· + 1.07263u + 0.0746961
−0.00129140u
40
+ 0.00419737u
39
+ ··· + 1.25599u − 0.653432
a
7
=
−0.00138487u
40
+ 0.00430419u
39
+ ··· + 1.07263u + 0.0746961
0.000383620u
40
− 0.00160154u
39
+ ··· − 0.546942u − 0.132211
(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
u
41
− 8u
40
+ ··· − 8u + 16
c
7
, c
9
, c
10
u
41
+ 8u
40
+ ··· − 8u + 16
c
12
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
y
41
− 10y
40
+ ··· + 2080y − 256
c
7
, c
9
, c
10
y
41
− 50y
40
+ ··· + 8224y − 256
c
12
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 = 0.171620 + 0.881343I
d = −0.419345 + 0.622257I
−1.60252 − 4.55290I −4.51064 + 8.08001I
u = 0.280189 − 0.954581I
a = −0.857033 − 0.817841I
b = −0.265899 + 0.882324I
c = 0.171620 − 0.881343I
d = −0.419345 − 0.622257I
−1.60252 + 4.55290I −4.51064 − 8.08001I
u = 0.942111 + 0.024266I
a = −0.224229 + 1.244680I
b = −0.026109 + 0.791073I
c = 1.54076 + 1.79047I
d = 0.627424 + 0.518765I
0.87865 + 4.07350I −1.48942 − 7.36111I
u = 0.942111 − 0.024266I
a = −0.224229 − 1.244680I
b = −0.026109 − 0.791073I
c = 1.54076 − 1.79047I
d = 0.627424 − 0.518765I
0.87865 − 4.07350I −1.48942 + 7.36111I
u = 0.100000 + 0.892301I
a = −0.052177 − 0.358577I
b = 0.118920 + 0.748261I
c = −0.188847 − 0.591938I
d = −0.730090 − 0.450883I
1.46086 + 1.42227I 3.88823 − 3.83998I
u = 0.100000 − 0.892301I
a = −0.052177 + 0.358577I
b = 0.118920 − 0.748261I
c = −0.188847 + 0.591938I
d = −0.730090 + 0.450883I
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 = −0.709049 − 0.230219I
d = −1.167000 − 0.190055I
2.43397 + 0.55461I 3.61478 + 1.21885I
u = 0.687957 − 0.421229I
a = 0.333750 − 0.336915I
b = 1.03088 − 1.01360I
c = −0.709049 + 0.230219I
d = −1.167000 + 0.190055I
2.43397 − 0.55461I 3.61478 − 1.21885I
u = 0.586118 + 0.499909I
a = −0.491451 + 0.661896I
b = −0.737846 + 0.812570I
c = 0.896958 + 0.907467I
d = 0.055470 + 0.479911I
−3.14860 + 0.97270I −10.27133 − 0.16493I
u = 0.586118 − 0.499909I
a = −0.491451 − 0.661896I
b = −0.737846 − 0.812570I
c = 0.896958 − 0.907467I
d = 0.055470 − 0.479911I
−3.14860 − 0.97270I −10.27133 + 0.16493I
u = −0.757570 + 0.057431I
a = 0.31675 + 1.45050I
b = 0.104479 + 0.545464I
c = 2.25474 + 1.86460I
d = 0.677009 + 0.316853I
0.834104 − 1.057860I −1.84303 − 1.72199I
u = −0.757570 − 0.057431I
a = 0.31675 − 1.45050I
b = 0.104479 − 0.545464I
c = 2.25474 − 1.86460I
d = 0.677009 − 0.316853I
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 = −0.756009 + 0.052947I
d = −1.208600 + 0.043942I
0.52179 − 2.81355I −3.88749 + 5.15717I
u = −0.748122 − 0.099272I
a = 0.93330 − 1.08938I
b = 2.35626 − 2.25935I
c = −0.756009 − 0.052947I
d = −1.208600 − 0.043942I
0.52179 + 2.81355I −3.88749 − 5.15717I
u = 0.004283 + 0.652626I
a = −1.55282 + 0.50485I
b = −2.68614 + 0.95227I
c = 0.055598 + 0.216120I
d = −0.573765 + 0.154381I
−0.70242 − 2.36927I 0.82941 + 4.59716I
u = 0.004283 − 0.652626I
a = −1.55282 − 0.50485I
b = −2.68614 − 0.95227I
c = 0.055598 − 0.216120I
d = −0.573765 − 0.154381I
−0.70242 + 2.36927I 0.82941 − 4.59716I
u = 0.076846 + 0.625583I
a = 1.20268 + 1.29382I
b = −0.275587 − 0.299772I
c = 0.281414 + 0.275761I
d = −0.413943 + 0.184853I
−0.85500 + 1.57570I −0.179374 + 0.776646I
u = 0.076846 − 0.625583I
a = 1.20268 − 1.29382I
b = −0.275587 + 0.299772I
c = 0.281414 − 0.275761I
d = −0.413943 − 0.184853I
−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 = −0.266359 − 0.027087I
d = 1.55037 − 0.00630I
5.83509 − 1.34899I 0.977007 + 0.716014I
u = 0.01326 − 1.47518I
a = −0.655430 − 0.903143I
b = 0.71376 + 1.96932I
c = −0.266359 + 0.027087I
d = 1.55037 + 0.00630I
5.83509 + 1.34899I 0.977007 − 0.716014I
u = −0.45410 + 1.44756I
a = 0.692132 + 0.807395I
b = 0.54174 − 2.28917I
c = −0.057340 + 0.859520I
d = 1.53907 + 0.21697I
4.95290 + 7.65933I −2.00000 − 5.62562I
u = −0.45410 − 1.44756I
a = 0.692132 − 0.807395I
b = 0.54174 + 2.28917I
c = −0.057340 − 0.859520I
d = 1.53907 − 0.21697I
4.95290 − 7.65933I −2.00000 + 5.62562I
u = −0.466919
a = −0.0931478
b = −0.579529
c = 1.52928
d = 0.230214
−1.25610 −8.53770
u = −0.35061 + 1.53639I
a = −0.902103 + 0.091854I
b = −0.136075 + 1.212460I
c = −0.137964 − 1.319330I
d = −0.581850 − 1.030240I
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 = −0.137964 + 1.319330I
d = −0.581850 + 1.030240I
6.34261 − 3.42138I 0
u = 0.51610 + 1.49655I
a = −1.048210 − 0.118410I
b = −0.199107 − 1.232920I
c = −0.027761 + 1.384130I
d = −0.474223 + 1.062390I
5.66064 − 9.73522I 0. + 7.05049I
u = 0.51610 − 1.49655I
a = −1.048210 + 0.118410I
b = −0.199107 + 1.232920I
c = −0.027761 − 1.384130I
d = −0.474223 − 1.062390I
5.66064 + 9.73522I 0. − 7.05049I
u = 1.62020 + 0.13077I
a = −0.040113 − 0.941340I
b = 0.59368 − 2.03806I
c = −1.237690 − 0.070746I
d = −1.61926 − 0.06175I
8.89854 + 0.19005I 0
u = 1.62020 − 0.13077I
a = −0.040113 + 0.941340I
b = 0.59368 + 2.03806I
c = −1.237690 + 0.070746I
d = −1.61926 + 0.06175I
8.89854 − 0.19005I 0
u = −1.59450 + 0.33027I
a = −0.066671 + 1.013570I
b = 0.54013 + 2.15152I
c = −1.226210 + 0.179294I
d = −1.60824 + 0.15639I
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 = −1.226210 − 0.179294I
d = −1.60824 − 0.15639I
8.54414 + 6.61454I 0
u = 0.23388 + 1.65276I
a = −0.028955 − 0.573985I
b = 0.54769 + 2.08324I
c = 0.106730 − 0.375749I
d = 1.63512 − 0.11031I
9.70458 − 3.47853I 0
u = 0.23388 − 1.65276I
a = −0.028955 + 0.573985I
b = 0.54769 − 2.08324I
c = 0.106730 + 0.375749I
d = 1.63512 + 0.11031I
9.70458 + 3.47853I 0
u = −0.86658 + 1.51028I
a = 1.022730 − 0.213320I
b = 0.25996 − 2.32316I
c = 0.437465 + 1.236920I
d = 1.57759 + 0.41592I
12.2320 + 15.1490I 0
u = −0.86658 − 1.51028I
a = 1.022730 + 0.213320I
b = 0.25996 + 2.32316I
c = 0.437465 − 1.236920I
d = 1.57759 − 0.41592I
12.2320 − 15.1490I 0
u = 0.78943 + 1.61251I
a = 0.798911 + 0.089727I
b = 0.30028 + 2.26529I
c = 0.449091 − 1.082320I
d = 1.62479 − 0.37558I
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 = 0.449091 + 1.082320I
d = 1.62479 + 0.37558I
13.5026 + 8.6555I 0
u = 0.64330 + 1.72758I
a = −0.985622 − 0.148269I
b = 0.50633 − 1.68069I
c = 0.444320 − 0.855033I
d = 1.67606 − 0.30300I
14.7932 − 7.9945I 0
u = 0.64330 − 1.72758I
a = −0.985622 + 0.148269I
b = 0.50633 + 1.68069I
c = 0.444320 + 0.855033I
d = 1.67606 + 0.30300I
14.7932 + 7.9945I 0
u = −0.48873 + 1.82349I
a = −0.848856 + 0.042762I
b = 0.50243 + 1.74679I
c = 0.453903 + 0.630306I
d = 1.71830 + 0.22835I
15.6167 + 1.2657I 0
u = −0.48873 − 1.82349I
a = −0.848856 − 0.042762I
b = 0.50243 − 1.74679I
c = 0.453903 − 0.630306I
d = 1.71830 − 0.22835I
15.6167 − 1.2657I 0
11
II. I
u
2
= h−u
3
c
2
+ 2u
3
c + · · · − 8c + 22, −4u
3
c
2
+ 2u
3
c + · · · + 3c + 4, 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
0.0526316c
2
u
3
− 0.105263cu
3
+ ··· + 0.421053c − 1.15789
a
12
=
−0.0526316c
2
u
3
+ 0.105263cu
3
+ ··· + 0.578947c + 1.15789
0.0526316c
2
u
3
− 0.105263cu
3
+ ··· + 0.421053c − 1.15789
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
=
−0.0526316c
2
u
3
+ 0.105263cu
3
+ ··· + 0.578947c + 1.15789
0.0526316c
2
u
3
− 0.105263cu
3
+ ··· + 0.421053c − 1.15789
a
7
=
−0.0526316c
2
u
3
+ 0.105263cu
3
+ ··· + 0.578947c + 1.15789
−0.368421c
2
u
3
− 0.263158cu
3
+ ··· − 0.947368c + 0.105263
(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
9
c
10
, c
11
u
12
− 4u
10
+ ··· − 2u + 1
c
12
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
9
c
10
, c
11
y
12
− 8y
11
+ ··· + 10y + 1
c
12
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 = 0.765020 − 0.640647I
d = −0.072869 − 0.359716I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = 1.00000
b = 0
c = −0.516348 + 0.247391I
d = −1.009230 + 0.198659I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = 1.00000
b = 0
c = −1.43015 + 5.08937I
d = 1.082100 + 0.161058I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = 1.00000
b = 0
c = 0.765020 + 0.640647I
d = −0.072869 + 0.359716I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = 1.00000
b = 0
c = −0.516348 − 0.247391I
d = −1.009230 − 0.198659I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = 1.00000
b = 0
c = −1.43015 − 5.08937I
d = 1.082100 − 0.161058I
−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 = −0.423593 + 1.133540I
d = −0.856215 + 0.919282I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 + 1.55249I
a = 1.00000
b = 0
c = −0.291061 − 1.215200I
d = −0.730940 − 0.968963I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 + 1.55249I
a = 1.00000
b = 0
c = −0.103867 + 0.192761I
d = 1.58715 + 0.04968I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 1.00000
b = 0
c = −0.423593 − 1.133540I
d = −0.856215 − 0.919282I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.10488 − 1.55249I
a = 1.00000
b = 0
c = −0.291061 + 1.215200I
d = −0.730940 + 0.968963I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.10488 − 1.55249I
a = 1.00000
b = 0
c = −0.103867 − 0.192761I
d = 1.58715 − 0.04968I
6.79074 − 3.16396I 1.82674 + 2.56480I
16
III. I
v
1
= 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 + 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
6
, c
8
c
11
, c
12
u
2
c
7
(u + 1)
2
c
9
, c
10
(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
6
, c
8
c
11
, c
12
y
2
c
7
, c
9
, c
10
(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 = 0
d = −1.00000
1.64493 − 2.02988I 3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
1.64493 + 2.02988I 3.00000 − 3.46410I
20
IV. I
v
2
= 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 − 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
7
, c
8
c
9
, c
10
u
2
c
6
(u − 1)
2
c
11
, c
12
(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
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(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 = 1.00000
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 1.00000
d = 0
−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
12
u + 1
c
9
, c
10
, c
11
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 −3.94751 + 3.47096I
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)
2
(u + 1)(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
, c
10
u
2
(u − 1)
3
(u
12
− 4u
10
+ ··· − 2u + 1)(u
41
+ 8u
40
+ ··· − 8u + 16)
c
11
u
2
(u − 1)(u + 1)
2
(u
12
− 4u
10
+ ··· − 2u + 1)(u
41
− 8u
40
+ ··· − 8u + 16)
c
12
u
2
(u + 1)
3
(u
12
+ 8u
11
+ ··· − 10u + 1)
· (u
41
+ 10u
40
+ ··· + 2080u + 256)
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
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 10y + 1)
· (y
41
− 10y
40
+ ··· + 2080y − 256)
c
7
, c
9
, c
10
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 10y + 1)
· (y
41
− 50y
40
+ ··· + 8224y − 256)
c
12
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· − 78y + 1)
· (y
41
+ 50y
40
+ ··· − 663040y − 65536)
32
