12a
0195
(K12a
0195
)
A knot diagram
1
Linearized knot diagam
3 5 10 6 2 12 1 11 4 8 9 7
Solving Sequence
4,9 7,10,12
1 3 6 5 2 11 8
c
9
c
12
c
3
c
6
c
4
c
2
c
11
c
8
c
1
, c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.98338 × 10
44
u
32
+ 6.07211 × 10
44
u
31
+ ··· + 8.30969 × 10
46
d + 2.51360 × 10
46
,
7.43844 × 10
44
u
32
+ 1.59524 × 10
45
u
31
+ ··· + 1.66194 × 10
47
c − 9.07104 × 10
46
,
− 2.43633 × 10
45
u
32
− 5.73801 × 10
45
u
31
+ ··· + 8.30969 × 10
46
b − 1.04987 × 10
47
,
− 1.26296 × 10
45
u
32
− 3.00101 × 10
45
u
31
+ ··· + 8.30969 × 10
46
a − 1.12331 × 10
47
,
u
33
+ 3u
32
+ ··· − 32u − 32i
I
u
2
= h−33577974480092u
24
a + 53309187006291u
24
+ ··· + 196002507777016a + 140186694789454,
− 106618374012582u
24
a − 153454383700573u
24
+ ··· − 280373389578908a − 552236032471050,
b − 1, −1.33548 × 10
14
au
24
+ 1.93299 × 10
14
u
24
+ ··· + 1.95694 × 10
15
a + 2.03280 × 10
15
,
u
25
− u
24
+ ··· + 4u + 4i
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
= ha, d + 1, c + a + 1, b − 1, v + 1i
I
v
4
= hc, d + 1, cb + a + 1, −v
2
ba + v
2
c − v
2
b + 2v
2
a − cv − av + 2v
2
+ c − v, b
2
v
2
− 2v
2
b + bv + v
2
− v + 1i
* 5 irreducible components of dim
C
= 0, with total 88 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
= h2.98 × 10
44
u
32
+ 6.07× 10
44
u
31
+ · · · + 8.31 × 10
46
d +2.51 × 10
46
, 7.44 ×
10
44
u
32
+ 1.60 × 10
45
u
31
+ · · · + 1.66 × 10
47
c − 9.07 × 10
46
, −2.44 × 10
45
u
32
−
5.74 × 10
45
u
31
+ · · · + 8.31 × 10
46
b − 1.05 × 10
47
, −1.26 × 10
45
u
32
− 3.00 ×
10
45
u
31
+ · · · + 8.31 × 10
46
a − 1.12 × 10
47
, u
33
+ 3u
32
+ · · · − 32u − 32i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
7
=
0.0151986u
32
+ 0.0361146u
31
+ ··· − 0.765502u + 1.35181
0.0293192u
32
+ 0.0690520u
31
+ ··· − 1.79735u + 1.26343
a
10
=
1
u
2
a
12
=
−0.00447577u
32
− 0.00959870u
31
+ ··· + 0.258096u + 0.545811
−0.00359025u
32
− 0.00730726u
31
+ ··· + 0.166618u − 0.302490
a
1
=
−0.0150061u
32
− 0.0352289u
31
+ ··· + 1.12333u − 0.0633242
−0.0275000u
32
− 0.0663276u
31
+ ··· + 1.81369u − 1.26434
a
3
=
u
u
3
+ u
a
6
=
0.0197140u
32
+ 0.0451970u
31
+ ··· − 0.857293u + 1.51428
0.0347201u
32
+ 0.0804259u
31
+ ··· − 1.98062u + 1.57761
a
5
=
0.0254851u
32
+ 0.0825348u
31
+ ··· − 2.53688u − 1.85413
0.0263436u
32
+ 0.101429u
31
+ ··· − 2.69293u − 2.59143
a
2
=
−0.0169811u
32
− 0.0390647u
31
+ ··· + 1.30794u − 0.509563
−0.0254461u
32
− 0.0623905u
31
+ ··· + 2.00195u − 1.64373
a
11
=
−0.000885519u
32
− 0.00229144u
31
+ ··· + 0.0914785u + 0.848301
−0.00359025u
32
− 0.00730726u
31
+ ··· + 0.166618u − 0.302490
a
8
=
−0.000885519u
32
− 0.00229144u
31
+ ··· + 0.0914785u + 0.848301
0.00540092u
32
+ 0.0113739u
31
+ ··· − 0.183270u + 0.314174
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0605080u
32
+ 0.0513753u
31
+ ··· + 7.44134u + 11.1534
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
33
+ 11u
32
+ ··· + 8u − 16
c
2
, c
5
u
33
+ u
32
+ ··· − 12u + 4
c
3
, c
9
u
33
− 3u
32
+ ··· − 32u + 32
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
33
+ 5u
32
+ ··· − 7u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
33
+ 23y
32
+ ··· − 14304y − 256
c
2
, c
5
y
33
+ 11y
32
+ ··· + 8y − 16
c
3
, c
9
y
33
+ 15y
32
+ ··· − 6144y − 1024
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
33
− 39y
32
+ ··· − 14y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979372 + 0.273800I
a = −1.96498 − 0.53087I
b = −4.30037 − 1.10323I
c = −0.881800 + 0.153170I
d = −1.312830 + 0.129109I
4.01193 − 3.40996I 6.93635 + 3.61829I
u = −0.979372 − 0.273800I
a = −1.96498 + 0.53087I
b = −4.30037 + 1.10323I
c = −0.881800 − 0.153170I
d = −1.312830 − 0.129109I
4.01193 + 3.40996I 6.93635 − 3.61829I
u = −0.581985 + 0.777781I
a = −0.007920 − 0.444148I
b = −0.601205 + 0.151913I
c = 0.549449 − 1.043340I
d = −0.117441 − 0.653397I
−3.19812 + 2.28214I −2.55468 − 4.65224I
u = −0.581985 − 0.777781I
a = −0.007920 + 0.444148I
b = −0.601205 − 0.151913I
c = 0.549449 + 1.043340I
d = −0.117441 + 0.653397I
−3.19812 − 2.28214I −2.55468 + 4.65224I
u = 0.342726 + 1.062970I
a = −0.156749 + 0.042002I
b = −0.772312 − 0.554016I
c = 0.138173 + 1.013650I
d = −0.419652 + 0.727712I
2.46500 − 1.75021I 7.36804 + 3.35767I
u = 0.342726 − 1.062970I
a = −0.156749 − 0.042002I
b = −0.772312 + 0.554016I
c = 0.138173 − 1.013650I
d = −0.419652 − 0.727712I
2.46500 + 1.75021I 7.36804 − 3.35767I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16826
a = −1.85589
b = −4.05777
c = −0.988324
d = −1.40425
7.47395 12.4850
u = −0.464136 + 1.103860I
a = −0.232978 − 0.137172I
b = −0.849884 + 0.432403I
c = 0.189734 − 1.130300I
d = −0.355294 − 0.806119I
1.74788 + 7.33440I 5.47919 − 8.14278I
u = −0.464136 − 1.103860I
a = −0.232978 + 0.137172I
b = −0.849884 − 0.432403I
c = 0.189734 + 1.130300I
d = −0.355294 + 0.806119I
1.74788 − 7.33440I 5.47919 + 8.14278I
u = −0.635877 + 0.397843I
a = 0.450608 − 1.006370I
b = −0.324141 − 0.199030I
c = 1.07971 − 0.93923I
d = 0.155830 − 0.448444I
−0.42221 − 2.98824I −0.68495 + 3.66701I
u = −0.635877 − 0.397843I
a = 0.450608 + 1.006370I
b = −0.324141 + 0.199030I
c = 1.07971 + 0.93923I
d = 0.155830 + 0.448444I
−0.42221 + 2.98824I −0.68495 − 3.66701I
u = 0.239228 + 0.607577I
a = 0.467370 + 0.141887I
b = −0.118760 − 0.290085I
c = 0.499292 + 0.509831I
d = −0.251234 + 0.318679I
0.292144 − 0.942663I 5.66111 + 7.03214I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.239228 − 0.607577I
a = 0.467370 − 0.141887I
b = −0.118760 + 0.290085I
c = 0.499292 − 0.509831I
d = −0.251234 − 0.318679I
0.292144 + 0.942663I 5.66111 − 7.03214I
u = −0.351447 + 1.312440I
a = 1.33782 − 2.18315I
b = −3.47360 + 0.63971I
c = −0.402867 + 0.835349I
d = 1.47320 + 0.16826I
9.06107 + 0.86504I 11.01805 − 0.17133I
u = −0.351447 − 1.312440I
a = 1.33782 + 2.18315I
b = −3.47360 − 0.63971I
c = −0.402867 − 0.835349I
d = 1.47320 − 0.16826I
9.06107 − 0.86504I 11.01805 + 0.17133I
u = −0.611782 + 1.268620I
a = −0.19716 − 2.64343I
b = −3.14566 + 0.96096I
c = −0.094088 + 1.305100I
d = 1.45334 + 0.29571I
7.09875 + 9.27148I 8.26421 − 6.23171I
u = −0.611782 − 1.268620I
a = −0.19716 + 2.64343I
b = −3.14566 − 0.96096I
c = −0.094088 − 1.305100I
d = 1.45334 − 0.29571I
7.09875 − 9.27148I 8.26421 + 6.23171I
u = −0.053785 + 0.584876I
a = 1.43770 − 0.61824I
b = 2.23372 − 1.30037I
c = −0.191785 + 0.115518I
d = −0.758918 + 0.087353I
2.76296 − 2.31801I 12.30250 + 4.19824I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.053785 − 0.584876I
a = 1.43770 + 0.61824I
b = 2.23372 + 1.30037I
c = −0.191785 − 0.115518I
d = −0.758918 − 0.087353I
2.76296 + 2.31801I 12.30250 − 4.19824I
u = 1.38673 + 0.43185I
a = −1.48910 + 0.29979I
b = −3.28939 + 0.65121I
c = −1.113710 − 0.239357I
d = −1.50951 − 0.20675I
11.58920 + 2.62797I 12.22236 − 0.42879I
u = 1.38673 − 0.43185I
a = −1.48910 − 0.29979I
b = −3.28939 − 0.65121I
c = −1.113710 + 0.239357I
d = −1.50951 + 0.20675I
11.58920 − 2.62797I 12.22236 + 0.42879I
u = 0.489796 + 0.230188I
a = 1.109100 + 0.758351I
b = −0.062609 + 0.144250I
c = 1.276410 + 0.540576I
d = 0.164799 + 0.231913I
0.15528 − 1.56621I −1.22779 + 2.98994I
u = 0.489796 − 0.230188I
a = 1.109100 − 0.758351I
b = −0.062609 − 0.144250I
c = 1.276410 − 0.540576I
d = 0.164799 − 0.231913I
0.15528 + 1.56621I −1.22779 − 2.98994I
u = −1.35730 + 0.53891I
a = −1.43837 − 0.36025I
b = −3.18755 − 0.78570I
c = −1.099800 + 0.300126I
d = −1.49615 + 0.25900I
10.79550 − 8.72073I 10.94592 + 5.35160I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35730 − 0.53891I
a = −1.43837 + 0.36025I
b = −3.18755 + 0.78570I
c = −1.099800 − 0.300126I
d = −1.49615 − 0.25900I
10.79550 + 8.72073I 10.94592 − 5.35160I
u = 0.48684 + 1.39736I
a = 0.45444 + 2.00395I
b = −3.21670 − 0.69297I
c = −0.095787 − 0.962823I
d = 1.51512 − 0.23328I
12.10590 − 5.85939I 13.7252 + 3.8290I
u = 0.48684 − 1.39736I
a = 0.45444 − 2.00395I
b = −3.21670 + 0.69297I
c = −0.095787 + 0.962823I
d = 1.51512 + 0.23328I
12.10590 + 5.85939I 13.7252 − 3.8290I
u = −0.82581 + 1.33817I
a = −0.91423 − 1.96766I
b = −2.83075 + 0.93309I
c = 0.26972 + 1.39679I
d = 1.49169 + 0.40077I
13.4411 + 16.4286I 10.77382 − 8.75984I
u = −0.82581 − 1.33817I
a = −0.91423 + 1.96766I
b = −2.83075 − 0.93309I
c = 0.26972 − 1.39679I
d = 1.49169 − 0.40077I
13.4411 − 16.4286I 10.77382 + 8.75984I
u = 0.77347 + 1.38729I
a = −0.67577 + 1.91732I
b = −2.88328 − 0.86577I
c = 0.242390 − 1.297210I
d = 1.51473 − 0.37364I
14.7439 − 10.2508I 12.57547 + 4.19472I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.77347 − 1.38729I
a = −0.67577 − 1.91732I
b = −2.88328 + 0.86577I
c = 0.242390 + 1.297210I
d = 1.51473 + 0.37364I
14.7439 + 10.2508I 12.57547 − 4.19472I
u = 0.05858 + 1.69521I
a = 0.748153 + 0.165681I
b = −3.14863 − 0.06028I
c = 0.129127 − 0.091732I
d = 1.65444 − 0.02754I
−19.6551 − 3.2714I 13.9526 + 2.4448I
u = 0.05858 − 1.69521I
a = 0.748153 − 0.165681I
b = −3.14863 + 0.06028I
c = 0.129127 + 0.091732I
d = 1.65444 + 0.02754I
−19.6551 + 3.2714I 13.9526 − 2.4448I
10
II.
I
u
2
= h−3.36×10
13
au
24
+5.33×10
13
u
24
+· · ·+1.96×10
14
a+1.40×10
14
, −1.07×
10
14
au
24
− 1.53 × 10
14
u
24
+ · · · − 2.80 × 10
14
a − 5.52 × 10
14
, b − 1, −1.34 ×
10
14
au
24
+1.93×10
14
u
24
+· · ·+1.96×10
15
a+2.03×10
15
, u
25
−u
24
+· · ·+4u+4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
7
=
a
1
a
10
=
1
u
2
a
12
=
0.721304au
24
+ 1.03816u
24
+ ··· + 1.89681a + 3.73603
0.454329au
24
− 0.721304u
24
+ ··· − 2.65203a − 1.89681
a
1
=
−0.266975u
24
− 0.378004u
23
+ ··· − 6.66427u − 4.54883
−0.454329u
24
+ 0.893251u
23
+ ··· + 1.84504u + 2.65203
a
3
=
u
u
3
+ u
a
6
=
0.282934u
24
− 0.934782u
23
+ ··· − 4.86150u − 4.62094
0.549909u
24
− 0.556778u
23
+ ··· + 1.80277u − 0.0721112
a
5
=
−0.458322u
24
+ 1.29881u
23
+ ··· + 3.35855u + 5.36998
0.447032u
24
− 0.0235195u
23
+ ··· + 4.94194u + 1.21733
a
2
=
−0.688545u
24
+ 0.415749u
23
+ ··· − 5.18862u − 1.94144
−0.450261u
24
+ 1.04887u
23
+ ··· + 3.51825u + 3.77069
a
11
=
0.266975au
24
+ 1.75947u
24
+ ··· + 4.54883a + 5.63284
0.454329au
24
− 0.721304u
24
+ ··· − 2.65203a − 1.89681
a
8
=
0.266975au
24
+ 1.75947u
24
+ ··· + 4.54883a + 5.63284
−0.549909au
24
− 0.266975u
24
+ ··· + 0.0721112a − 2.54883
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
6062761600965
9238337702138
u
24
−
3225176474347
9238337702138
u
23
+ ··· −
61042729884201
9238337702138
u +
27155343409896
4619168851069
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
25
+ 8u
24
+ ··· + 11u − 1)
2
c
2
, c
5
(u
25
+ 2u
24
+ ··· + 3u + 1)
2
c
3
, c
9
(u
25
+ u
24
+ ··· + 4u − 4)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
50
+ 3u
49
+ ··· + 24u − 16
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
25
+ 20y
24
+ ··· + 251y − 1)
2
c
2
, c
5
(y
25
+ 8y
24
+ ··· + 11y − 1)
2
c
3
, c
9
(y
25
+ 15y
24
+ ··· − 88y − 16)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
50
− 39y
49
+ ··· − 3872y + 256
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111975 + 0.962557I
a = 0.887355 + 0.433567I
b = 1.00000
c = 0.010055 + 0.767731I
d = −0.557801 + 0.562636I
3.08820 − 2.66172I 9.28523 + 3.57661I
u = 0.111975 + 0.962557I
a = 0.774124 − 0.392043I
b = 1.00000
c = −0.222055 − 0.664059I
d = −0.748963 − 0.510317I
3.08820 − 2.66172I 9.28523 + 3.57661I
u = 0.111975 − 0.962557I
a = 0.887355 − 0.433567I
b = 1.00000
c = 0.010055 − 0.767731I
d = −0.557801 − 0.562636I
3.08820 + 2.66172I 9.28523 − 3.57661I
u = 0.111975 − 0.962557I
a = 0.774124 + 0.392043I
b = 1.00000
c = −0.222055 + 0.664059I
d = −0.748963 + 0.510317I
3.08820 + 2.66172I 9.28523 − 3.57661I
u = −1.061780 + 0.135314I
a = 0.243332 + 0.435875I
b = 1.00000
c = −0.928818 + 0.075525I
d = −1.353420 + 0.063981I
4.81480 + 0.43356I 8.91196 + 0.04506I
u = −1.061780 + 0.135314I
a = 1.38189 − 1.33044I
b = 1.00000
c = 1.27869 − 1.72252I
d = 0.571600 − 0.649877I
4.81480 + 0.43356I 8.91196 + 0.04506I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.061780 − 0.135314I
a = 0.243332 − 0.435875I
b = 1.00000
c = −0.928818 − 0.075525I
d = −1.353420 − 0.063981I
4.81480 − 0.43356I 8.91196 − 0.04506I
u = −1.061780 − 0.135314I
a = 1.38189 + 1.33044I
b = 1.00000
c = 1.27869 + 1.72252I
d = 0.571600 + 0.649877I
4.81480 − 0.43356I 8.91196 − 0.04506I
u = 0.465035 + 1.033020I
a = −0.665026 − 0.733516I
b = 1.00000
c = −0.72869 − 1.59218I
d = 1.336380 − 0.223022I
1.37392 − 5.41987I 4.64303 + 6.54919I
u = 0.465035 + 1.033020I
a = 0.21222 − 2.16973I
b = 1.00000
c = 0.244469 + 1.086540I
d = −0.323623 + 0.760243I
1.37392 − 5.41987I 4.64303 + 6.54919I
u = 0.465035 − 1.033020I
a = −0.665026 + 0.733516I
b = 1.00000
c = −0.72869 + 1.59218I
d = 1.336380 + 0.223022I
1.37392 + 5.41987I 4.64303 − 6.54919I
u = 0.465035 − 1.033020I
a = 0.21222 + 2.16973I
b = 1.00000
c = 0.244469 − 1.086540I
d = −0.323623 − 0.760243I
1.37392 + 5.41987I 4.64303 − 6.54919I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.096160 + 0.296196I
a = 0.306675 − 0.445331I
b = 1.00000
c = −0.948099 − 0.166211I
d = −1.368770 − 0.141145I
4.43073 + 5.11531I 7.81745 − 5.48464I
u = 1.096160 + 0.296196I
a = 1.28492 + 1.16223I
b = 1.00000
c = 1.11556 + 1.62331I
d = 0.465476 + 0.732479I
4.43073 + 5.11531I 7.81745 − 5.48464I
u = 1.096160 − 0.296196I
a = 0.306675 + 0.445331I
b = 1.00000
c = −0.948099 + 0.166211I
d = −1.368770 + 0.141145I
4.43073 − 5.11531I 7.81745 + 5.48464I
u = 1.096160 − 0.296196I
a = 1.28492 − 1.16223I
b = 1.00000
c = 1.11556 − 1.62331I
d = 0.465476 − 0.732479I
4.43073 − 5.11531I 7.81745 + 5.48464I
u = −0.202658 + 1.122680I
a = −1.166770 + 0.081144I
b = 1.00000
c = −1.078630 + 0.717142I
d = 1.382070 + 0.096385I
5.39169 + 2.44039I 11.83401 − 3.61173I
u = −0.202658 + 1.122680I
a = −0.14908 + 1.80180I
b = 1.00000
c = −0.008599 − 0.965558I
d = −0.541755 − 0.717454I
5.39169 + 2.44039I 11.83401 − 3.61173I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.202658 − 1.122680I
a = −1.166770 − 0.081144I
b = 1.00000
c = −1.078630 − 0.717142I
d = 1.382070 − 0.096385I
5.39169 − 2.44039I 11.83401 + 3.61173I
u = −0.202658 − 1.122680I
a = −0.14908 − 1.80180I
b = 1.00000
c = −0.008599 + 0.965558I
d = −0.541755 + 0.717454I
5.39169 − 2.44039I 11.83401 + 3.61173I
u = 0.641188 + 0.544744I
a = 0.469914 − 0.315102I
b = 1.00000
c = −0.672537 − 0.303472I
d = −1.134680 − 0.249465I
−0.175498 + 1.059220I 0.606046 − 0.370576I
u = 0.641188 + 0.544744I
a = 1.31697 + 0.65566I
b = 1.00000
c = 0.858117 + 1.005430I
d = 0.060728 + 0.543785I
−0.175498 + 1.059220I 0.606046 − 0.370576I
u = 0.641188 − 0.544744I
a = 0.469914 + 0.315102I
b = 1.00000
c = −0.672537 + 0.303472I
d = −1.134680 + 0.249465I
−0.175498 − 1.059220I 0.606046 + 0.370576I
u = 0.641188 − 0.544744I
a = 1.31697 − 0.65566I
b = 1.00000
c = 0.858117 − 1.005430I
d = 0.060728 − 0.543785I
−0.175498 − 1.059220I 0.606046 + 0.370576I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.082989 + 0.805818I
a = −1.08067 − 1.83898I
b = 1.00000
c = 0.083284 + 0.569058I
d = −0.527939 + 0.406461I
2.66645 + 1.39976I 8.95722 − 0.06062I
u = 0.082989 + 0.805818I
a = −2.78270 − 0.32226I
b = 1.00000
c = −2.91998 − 0.70018I
d = 1.234720 − 0.037441I
2.66645 + 1.39976I 8.95722 − 0.06062I
u = 0.082989 − 0.805818I
a = −1.08067 + 1.83898I
b = 1.00000
c = 0.083284 − 0.569058I
d = −0.527939 − 0.406461I
2.66645 − 1.39976I 8.95722 + 0.06062I
u = 0.082989 − 0.805818I
a = −2.78270 + 0.32226I
b = 1.00000
c = −2.91998 + 0.70018I
d = 1.234720 + 0.037441I
2.66645 − 1.39976I 8.95722 + 0.06062I
u = −0.340493 + 0.559321I
a = −0.545776 − 0.548289I
b = 1.00000
c = −0.465623 + 0.271176I
d = −0.967761 + 0.216045I
2.95409 + 1.50728I 9.02072 − 4.31266I
u = −0.340493 + 0.559321I
a = −2.38737 + 4.52460I
b = 1.00000
c = −2.32796 + 4.47861I
d = 1.112260 + 0.141525I
2.95409 + 1.50728I 9.02072 − 4.31266I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340493 − 0.559321I
a = −0.545776 + 0.548289I
b = 1.00000
c = −0.465623 − 0.271176I
d = −0.967761 − 0.216045I
2.95409 − 1.50728I 9.02072 + 4.31266I
u = −0.340493 − 0.559321I
a = −2.38737 − 4.52460I
b = 1.00000
c = −2.32796 − 4.47861I
d = 1.112260 − 0.141525I
2.95409 − 1.50728I 9.02072 + 4.31266I
u = 0.291960 + 1.368920I
a = −0.071208 + 1.221280I
b = 1.00000
c = −0.490940 − 0.949387I
d = −0.936546 − 0.771795I
10.21860 + 0.59688I 12.46758 − 1.80507I
u = 0.291960 + 1.368920I
a = −0.765668 − 1.023270I
b = 1.00000
c = −0.354801 − 0.656555I
d = 1.50021 − 0.13944I
10.21860 + 0.59688I 12.46758 − 1.80507I
u = 0.291960 − 1.368920I
a = −0.071208 − 1.221280I
b = 1.00000
c = −0.490940 + 0.949387I
d = −0.936546 + 0.771795I
10.21860 − 0.59688I 12.46758 + 1.80507I
u = 0.291960 − 1.368920I
a = −0.765668 + 1.023270I
b = 1.00000
c = −0.354801 + 0.656555I
d = 1.50021 + 0.13944I
10.21860 − 0.59688I 12.46758 + 1.80507I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.414621 + 1.342760I
a = −0.073917 − 1.142440I
b = 1.00000
c = −0.570268 + 0.899298I
d = −1.008850 + 0.738143I
9.63785 + 5.44271I 11.50171 − 3.51350I
u = −0.414621 + 1.342760I
a = −0.698244 + 1.203490I
b = 1.00000
c = −0.269346 + 0.914070I
d = 1.48812 + 0.19869I
9.63785 + 5.44271I 11.50171 − 3.51350I
u = −0.414621 − 1.342760I
a = −0.073917 + 1.142440I
b = 1.00000
c = −0.570268 − 0.899298I
d = −1.008850 − 0.738143I
9.63785 − 5.44271I 11.50171 + 3.51350I
u = −0.414621 − 1.342760I
a = −0.698244 − 1.203490I
b = 1.00000
c = −0.269346 − 0.914070I
d = 1.48812 − 0.19869I
9.63785 − 5.44271I 11.50171 + 3.51350I
u = −0.55118 + 1.32473I
a = −0.311266 + 0.170366I
b = 1.00000
c = −0.114785 + 1.146410I
d = 1.48035 + 0.26533I
8.61369 + 5.36637I 10.46678 − 3.05337I
u = −0.55118 + 1.32473I
a = 0.37098 + 1.75649I
b = 1.00000
c = 0.090254 − 1.314840I
d = −0.391201 − 0.976798I
8.61369 + 5.36637I 10.46678 − 3.05337I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55118 − 1.32473I
a = −0.311266 − 0.170366I
b = 1.00000
c = −0.114785 − 1.146410I
d = 1.48035 − 0.26533I
8.61369 − 5.36637I 10.46678 + 3.05337I
u = −0.55118 − 1.32473I
a = 0.37098 − 1.75649I
b = 1.00000
c = 0.090254 + 1.314840I
d = −0.391201 + 0.976798I
8.61369 − 5.36637I 10.46678 + 3.05337I
u = 0.64072 + 1.29917I
a = −0.185163 − 0.238710I
b = 1.00000
c = −0.016343 − 1.290710I
d = 1.46878 − 0.30967I
7.62261 − 11.39030I 8.71017 + 7.76664I
u = 0.64072 + 1.29917I
a = 0.46408 − 1.77801I
b = 1.00000
c = 0.151729 + 1.358490I
d = −0.329543 + 0.997435I
7.62261 − 11.39030I 8.71017 + 7.76664I
u = 0.64072 − 1.29917I
a = −0.185163 + 0.238710I
b = 1.00000
c = −0.016343 + 1.290710I
d = 1.46878 + 0.30967I
7.62261 + 11.39030I 8.71017 − 7.76664I
u = 0.64072 − 1.29917I
a = 0.46408 + 1.77801I
b = 1.00000
c = 0.151729 − 1.358490I
d = −0.329543 − 0.997435I
7.62261 + 11.39030I 8.71017 − 7.76664I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518583
a = 0.311182
b = 1.00000
c = −0.641169
d = −1.11417
2.09579 3.55620
u = −0.518583
a = 2.02963
b = 1.00000
c = 1.71181
d = 0.294460
2.09579 3.55620
22
III. I
v
1
= ha, d, c − 1, b − 1, v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
7
=
0
1
a
10
=
1
0
a
12
=
1
0
a
1
=
1
−1
a
3
=
v
0
a
6
=
−1
1
a
5
=
0
v
a
2
=
v
−1
a
11
=
1
0
a
8
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
8
, c
9
c
10
, c
11
u
2
c
6
, c
7
(u + 1)
2
c
12
(u − 1)
2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
8
, c
9
c
10
, c
11
y
2
c
6
, c
7
, c
12
(y − 1)
2
25
(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
26
IV. I
v
2
= ha, d + 1, c + a, b − 1, v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
7
=
0
1
a
10
=
1
0
a
12
=
0
−1
a
1
=
0
−1
a
3
=
v
0
a
6
=
0
1
a
5
=
v
v
a
2
=
v − 1
−1
a
11
=
1
−1
a
8
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
3
, c
6
, c
7
c
9
, c
12
u
2
c
8
(u + 1)
2
c
10
, c
11
(u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
y
2
+ y + 1
c
3
, c
6
, c
7
c
9
, c
12
y
2
c
8
, c
10
, c
11
(y − 1)
2
29
(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 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
30
V. I
v
3
= ha, d + 1, c + a + 1, b − 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
9
=
1
0
a
7
=
0
1
a
10
=
1
0
a
12
=
−1
−1
a
1
=
−1
0
a
3
=
−1
0
a
6
=
−1
0
a
5
=
−1
0
a
2
=
−1
0
a
11
=
0
−1
a
8
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
u
c
6
, c
7
, c
10
c
11
u − 1
c
8
, c
12
u + 1
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
y
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y − 1
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = −1.00000
d = −1.00000
3.28987 12.0000
34
VI.
I
v
4
= hc, d + 1, cb + a + 1, −v
2
ba + v
2
c + · · · + c − v, b
2
v
2
− 2v
2
b + · · · − v + 1i
(i) Arc colorings
a
4
=
v
0
a
9
=
1
0
a
7
=
−1
b
a
10
=
1
0
a
12
=
0
−1
a
1
=
−1
b − 1
a
3
=
v
0
a
6
=
−1
b − 1
a
5
=
−bv + 2v
b
2
v − 2bv + v
a
2
=
−v
2
b + v
2
− 1
b − 1
a
11
=
1
−1
a
8
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
3
v − 3b
2
v − bv + v
2
+ 3v + 8
(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.
35
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
3.28987 − 2.02988I 8.46981 − 3.56831I
36
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u(u
2
− u + 1)
2
(u
25
+ 8u
24
+ ··· + 11u − 1)
2
· (u
33
+ 11u
32
+ ··· + 8u − 16)
c
2
u(u
2
+ u + 1)
2
(u
25
+ 2u
24
+ ··· + 3u + 1)
2
(u
33
+ u
32
+ ··· − 12u + 4)
c
3
, c
9
u
5
(u
25
+ u
24
+ ··· + 4u − 4)
2
(u
33
− 3u
32
+ ··· − 32u + 32)
c
5
u(u
2
− u + 1)
2
(u
25
+ 2u
24
+ ··· + 3u + 1)
2
(u
33
+ u
32
+ ··· − 12u + 4)
c
6
, c
7
u
2
(u − 1)(u + 1)
2
(u
33
+ 5u
32
+ ··· − 7u
2
− 1)
· (u
50
+ 3u
49
+ ··· + 24u − 16)
c
8
u
2
(u + 1)
3
(u
33
+ 5u
32
+ ··· − 7u
2
− 1)(u
50
+ 3u
49
+ ··· + 24u − 16)
c
10
, c
11
u
2
(u − 1)
3
(u
33
+ 5u
32
+ ··· − 7u
2
− 1)(u
50
+ 3u
49
+ ··· + 24u − 16)
c
12
u
2
(u − 1)
2
(u + 1)(u
33
+ 5u
32
+ ··· − 7u
2
− 1)
· (u
50
+ 3u
49
+ ··· + 24u − 16)
37
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y(y
2
+ y + 1)
2
(y
25
+ 20y
24
+ ··· + 251y − 1)
2
· (y
33
+ 23y
32
+ ··· − 14304y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
25
+ 8y
24
+ ··· + 11y − 1)
2
· (y
33
+ 11y
32
+ ··· + 8y − 16)
c
3
, c
9
y
5
(y
25
+ 15y
24
+ ··· − 88y − 16)
2
· (y
33
+ 15y
32
+ ··· − 6144y − 1024)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
2
(y − 1)
3
(y
33
− 39y
32
+ ··· − 14y − 1)
· (y
50
− 39y
49
+ ··· − 3872y + 256)
38
