12n
0060
(K12n
0060
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 4 11 8 6 11
Solving Sequence
4,9 5,11 6,10
12 3 2 1 8 7
c
4
c
9
c
11
c
3
c
2
c
1
c
8
c
7
c
5
, c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.71438 × 10
84
u
46
− 3.94862 × 10
84
u
45
+ ··· + 5.11546 × 10
87
d + 5.51326 × 10
87
,
1.81915 × 10
85
u
46
− 2.40556 × 10
85
u
45
+ ··· + 1.27887 × 10
87
c + 1.47462 × 10
88
,
− 7.84763 × 10
95
u
46
+ 5.19621 × 10
95
u
45
+ ··· + 6.09681 × 10
98
b − 4.85317 × 10
98
,
− 1.61790 × 10
97
u
46
+ 2.28917 × 10
97
u
45
+ ··· + 6.09681 × 10
98
a − 1.26868 × 10
100
,
u
47
− 2u
46
+ ··· + 1024u − 512i
I
u
2
= hu
4
c
2
+ u
3
c
2
− u
4
c − 2c
2
u
2
− 2u
3
c − c
2
u + u
2
c + c
2
+ 3cu + d − c,
− 2u
4
c
2
− 2u
3
c
2
+ u
4
c + 4c
2
u
2
+ 2u
3
c + c
3
+ 2c
2
u − u
2
c − 2c
2
− 3cu − u, b − u, a − u,
u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
v
1
= ha, d − v + 1, c + a, b + v − 1, v
2
− v + 1i
I
v
2
= ha, d, c − v, b − v − 1, v
2
+ v + 1i
I
v
3
= hc, d + 1, b, a − 1, v − 1i
I
v
4
= ha, da − cb + 1, dv + 1, cv − ba + bv + a − v, b
2
− b + 1i
* 5 irreducible components of dim
C
= 0, with total 67 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−2.71×10
84
u
46
−3.95×10
84
u
45
+· · ·+5.12×10
87
d+5.51×10
87
, 1.82×
10
85
u
46
− 2.41 × 10
85
u
45
+ · · · + 1.28 × 10
87
c + 1.47 × 10
88
, −7.85 × 10
95
u
46
+
5.20 × 10
95
u
45
+ · · · + 6.10 × 10
98
b − 4.85 × 10
98
, −1.62 × 10
97
u
46
+ 2.29 ×
10
97
u
45
+ · · · + 6.10 × 10
98
a − 1.27 × 10
100
, u
47
− 2u
46
+ · · · + 1024u − 512i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
11
=
−0.0142247u
46
+ 0.0188101u
45
+ ··· + 6.02241u − 11.5307
0.000530623u
46
+ 0.000771899u
45
+ ··· − 0.720071u − 1.07776
a
6
=
0.0265369u
46
− 0.0375470u
45
+ ··· − 11.6287u + 20.8089
0.00128717u
46
− 0.000852284u
45
+ ··· − 0.317834u + 0.796018
a
10
=
−0.0226340u
46
+ 0.0298604u
45
+ ··· + 10.2154u − 17.4046
−0.00787872u
46
+ 0.0118222u
45
+ ··· + 3.47297u − 6.95164
a
12
=
−0.0239734u
46
+ 0.0351954u
45
+ ··· + 10.0932u − 19.6370
−0.000874062u
46
+ 0.00264928u
45
+ ··· − 0.431382u − 2.36213
a
3
=
0.00513208u
46
− 0.00817440u
45
+ ··· + 0.763266u + 5.03316
0.00862965u
46
− 0.0123123u
45
+ ··· − 4.96716u + 7.59297
a
2
=
−0.00521744u
46
+ 0.00448641u
45
+ ··· + 6.21813u − 1.48986
0.00291266u
46
− 0.00502319u
45
+ ··· − 2.03496u + 3.47740
a
1
=
0.0252497u
46
− 0.0366947u
45
+ ··· − 11.3108u + 20.0129
0.00558802u
46
− 0.00914935u
45
+ ··· − 0.890394u + 6.27203
a
8
=
u
u
a
7
=
0.0207800u
46
− 0.0264941u
45
+ ··· − 9.33005u + 15.3882
0.00655528u
46
− 0.00768405u
45
+ ··· − 3.30765u + 3.85754
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0132573u
46
− 0.0100723u
45
+ ··· − 23.2337u − 1.69873
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 24u
46
+ ··· + 216u − 16
c
2
, c
5
u
47
+ 2u
46
+ ··· + 16u + 4
c
3
u
47
− 2u
46
+ ··· − 21456u + 2592
c
4
, c
8
u
47
+ 2u
46
+ ··· + 1024u + 512
c
6
, c
11
u
47
− 8u
46
+ ··· + 56u + 16
c
7
, c
10
u
47
+ 8u
46
+ ··· + 56u + 16
c
9
u
47
− 14u
46
+ ··· + 6688u − 256
c
12
u
47
+ 54u
46
+ ··· + 544u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 48y
45
+ ··· + 67872y − 256
c
2
, c
5
y
47
+ 24y
46
+ ··· + 216y − 16
c
3
y
47
− 24y
46
+ ··· + 353776896y − 6718464
c
4
, c
8
y
47
− 30y
46
+ ··· + 1572864y − 262144
c
6
, c
11
y
47
− 54y
46
+ ··· + 544y − 256
c
7
, c
10
y
47
− 14y
46
+ ··· + 6688y − 256
c
9
y
47
+ 46y
46
+ ··· + 11182592y − 65536
c
12
y
47
− 114y
46
+ ··· − 1990144y − 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.168857 + 0.977277I
a = 0.115176 − 0.466477I
b = 0.993069 − 0.480924I
c = 0.880204 − 0.225891I
d = 0.230994 + 0.477533I
−0.50019 + 4.79223I −2.43501 − 7.48976I
u = 0.168857 − 0.977277I
a = 0.115176 + 0.466477I
b = 0.993069 + 0.480924I
c = 0.880204 + 0.225891I
d = 0.230994 − 0.477533I
−0.50019 − 4.79223I −2.43501 + 7.48976I
u = −0.758370 + 0.572620I
a = −0.056911 − 1.268310I
b = −0.176331 − 0.077095I
c = 0.238166 + 0.368256I
d = −0.259334 + 0.830862I
−3.62778 − 1.19000I −10.45074 + 1.01195I
u = −0.758370 − 0.572620I
a = −0.056911 + 1.268310I
b = −0.176331 + 0.077095I
c = 0.238166 − 0.368256I
d = −0.259334 − 0.830862I
−3.62778 + 1.19000I −10.45074 − 1.01195I
u = −0.798854 + 0.256222I
a = 0.287839 − 0.327673I
b = 0.167965 − 1.279390I
c = −0.461116 − 0.948349I
d = −1.30820 − 1.68280I
1.43042 + 3.68269I −0.57615 − 8.67104I
u = −0.798854 − 0.256222I
a = 0.287839 + 0.327673I
b = 0.167965 + 1.279390I
c = −0.461116 + 0.948349I
d = −1.30820 + 1.68280I
1.43042 − 3.68269I −0.57615 + 8.67104I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.287114 + 0.709757I
a = 0.578531 − 0.174810I
b = −0.451429 − 0.388165I
c = −1.015380 − 0.600162I
d = −0.205691 + 0.340554I
1.71355 − 0.99880I 4.04476 + 2.43406I
u = −0.287114 − 0.709757I
a = 0.578531 + 0.174810I
b = −0.451429 + 0.388165I
c = −1.015380 + 0.600162I
d = −0.205691 − 0.340554I
1.71355 + 0.99880I 4.04476 − 2.43406I
u = 0.723521 + 0.092490I
a = −3.48927 − 1.92959I
b = −0.757487 − 0.595429I
c = 1.96585 − 0.11713I
d = 0.329861 + 0.036001I
0.84436 − 2.80891I −4.36866 + 6.45196I
u = 0.723521 − 0.092490I
a = −3.48927 + 1.92959I
b = −0.757487 + 0.595429I
c = 1.96585 + 0.11713I
d = 0.329861 − 0.036001I
0.84436 + 2.80891I −4.36866 − 6.45196I
u = −0.549584 + 0.433005I
a = 1.88335 − 0.62690I
b = 0.086194 − 0.585488I
c = −1.67372 − 0.58265I
d = −0.277903 + 0.181976I
2.18982 − 0.74670I 2.91211 − 1.96105I
u = −0.549584 − 0.433005I
a = 1.88335 + 0.62690I
b = 0.086194 + 0.585488I
c = −1.67372 + 0.58265I
d = −0.277903 − 0.181976I
2.18982 + 0.74670I 2.91211 + 1.96105I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.659997 + 0.157577I
a = 0.229959 − 0.371748I
b = 0.575360 − 1.171710I
c = 0.729227 − 0.739183I
d = 1.80686 − 1.34660I
1.05099 + 1.22135I −3.11104 + 2.86511I
u = 0.659997 − 0.157577I
a = 0.229959 + 0.371748I
b = 0.575360 + 1.171710I
c = 0.729227 + 0.739183I
d = 1.80686 + 1.34660I
1.05099 − 1.22135I −3.11104 − 2.86511I
u = 0.226818 + 1.310000I
a = 0.395536 + 0.047557I
b = −1.354130 + 0.342438I
c = 1.007050 − 0.000849I
d = 0.341442 + 0.559896I
−4.12204 + 2.83071I −3.10594 − 2.47522I
u = 0.226818 − 1.310000I
a = 0.395536 − 0.047557I
b = −1.354130 − 0.342438I
c = 1.007050 + 0.000849I
d = 0.341442 − 0.559896I
−4.12204 − 2.83071I −3.10594 + 2.47522I
u = −0.024914 + 0.666306I
a = 0.187765 + 0.490307I
b = 0.676859 + 0.593604I
c = 0.299606 − 0.388234I
d = 0.038036 + 0.428504I
−0.68586 − 1.51893I −2.03699 − 0.09471I
u = −0.024914 − 0.666306I
a = 0.187765 − 0.490307I
b = 0.676859 − 0.593604I
c = 0.299606 + 0.388234I
d = 0.038036 − 0.428504I
−0.68586 + 1.51893I −2.03699 + 0.09471I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.275400 + 0.425723I
a = 1.190730 + 0.205684I
b = 1.29665 − 0.64292I
c = −0.045370 − 1.113460I
d = −0.59246 − 1.84112I
−1.49383 + 5.48046I −1.24533 − 5.03878I
u = −1.275400 − 0.425723I
a = 1.190730 − 0.205684I
b = 1.29665 + 0.64292I
c = −0.045370 + 1.113460I
d = −0.59246 + 1.84112I
−1.49383 − 5.48046I −1.24533 + 5.03878I
u = −1.351470 + 0.126259I
a = 0.200409 + 0.288465I
b = 0.63511 + 1.89146I
c = 0.044710 − 0.963693I
d = −0.50842 − 1.59992I
−5.10242 − 0.08441I −6.12902 + 0.I
u = −1.351470 − 0.126259I
a = 0.200409 − 0.288465I
b = 0.63511 − 1.89146I
c = 0.044710 + 0.963693I
d = −0.50842 + 1.59992I
−5.10242 + 0.08441I −6.12902 + 0.I
u = 0.062543 + 0.611080I
a = 2.98020 − 5.04065I
b = −0.392543 + 1.124120I
c = 0.382597 − 0.828016I
d = 0.060601 + 0.347239I
−0.53961 + 2.33649I −0.16377 − 3.97632I
u = 0.062543 − 0.611080I
a = 2.98020 + 5.04065I
b = −0.392543 − 1.124120I
c = 0.382597 + 0.828016I
d = 0.060601 − 0.347239I
−0.53961 − 2.33649I −0.16377 + 3.97632I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.354510 + 0.305217I
a = 0.237962 + 0.257635I
b = 0.10673 + 1.95842I
c = −0.009355 − 1.056680I
d = 0.53250 − 1.74040I
−4.74548 − 5.93381I −5.07129 + 5.57342I
u = 1.354510 − 0.305217I
a = 0.237962 − 0.257635I
b = 0.10673 − 1.95842I
c = −0.009355 + 1.056680I
d = 0.53250 + 1.74040I
−4.74548 + 5.93381I −5.07129 − 5.57342I
u = 1.42975 + 0.19774I
a = −1.065100 + 0.614192I
b = −1.111480 − 0.181975I
c = −0.065967 − 1.017040I
d = 0.46521 − 1.66816I
−5.91128 − 1.72117I −6.79419 + 0.I
u = 1.42975 − 0.19774I
a = −1.065100 − 0.614192I
b = −1.111480 + 0.181975I
c = −0.065967 + 1.017040I
d = 0.46521 + 1.66816I
−5.91128 + 1.72117I −6.79419 + 0.I
u = 0.01170 + 1.48787I
a = 0.011715 − 0.454077I
b = 1.331480 + 0.029628I
c = −0.940701 + 0.145408I
d = −0.335520 + 0.668373I
−8.14593 + 1.35024I 0
u = 0.01170 − 1.48787I
a = 0.011715 + 0.454077I
b = 1.331480 − 0.029628I
c = −0.940701 − 0.145408I
d = −0.335520 − 0.668373I
−8.14593 − 1.35024I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509235
a = 1.22614
b = 0.258456
c = 0.155794
d = 0.708911
−1.19981 −8.75910
u = 1.38697 + 0.55724I
a = −1.46233 + 0.24224I
b = −1.61416 − 0.56868I
c = −0.006312 − 1.182540I
d = 0.48982 − 1.92078I
−4.40802 − 10.56830I 0
u = 1.38697 − 0.55724I
a = −1.46233 − 0.24224I
b = −1.61416 + 0.56868I
c = −0.006312 + 1.182540I
d = 0.48982 + 1.92078I
−4.40802 + 10.56830I 0
u = −0.40359 + 1.45989I
a = 0.049725 + 0.404703I
b = 1.58609 + 0.36933I
c = −1.117100 + 0.048331I
d = −0.422301 + 0.553774I
−7.37650 − 7.69255I 0
u = −0.40359 − 1.45989I
a = 0.049725 − 0.404703I
b = 1.58609 − 0.36933I
c = −1.117100 − 0.048331I
d = −0.422301 − 0.553774I
−7.37650 + 7.69255I 0
u = 1.43182 + 0.71566I
a = 1.063460 − 0.335902I
b = 1.52462 + 1.08887I
c = −0.026296 − 1.248550I
d = 0.43018 − 2.00472I
−7.91018 − 10.04820I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43182 − 0.71566I
a = 1.063460 + 0.335902I
b = 1.52462 − 1.08887I
c = −0.026296 + 1.248550I
d = 0.43018 + 2.00472I
−7.91018 + 10.04820I 0
u = −1.55076 + 0.46120I
a = 1.050920 + 0.198058I
b = 1.71496 − 0.70487I
c = 0.323059 + 0.821313I
d = −0.176351 + 1.365460I
−10.01530 + 3.44751I 0
u = −1.55076 − 0.46120I
a = 1.050920 − 0.198058I
b = 1.71496 + 0.70487I
c = 0.323059 − 0.821313I
d = −0.176351 − 1.365460I
−10.01530 − 3.44751I 0
u = −1.43192 + 0.83141I
a = −1.253390 − 0.502519I
b = −1.82714 + 0.82143I
c = 0.030872 − 1.291190I
d = −0.40061 − 2.06181I
−10.6565 + 15.7212I 0
u = −1.43192 − 0.83141I
a = −1.253390 + 0.502519I
b = −1.82714 − 0.82143I
c = 0.030872 + 1.291190I
d = −0.40061 + 2.06181I
−10.6565 − 15.7212I 0
u = 1.59024 + 0.63743I
a = −1.215800 + 0.253500I
b = −1.87247 − 0.52042I
c = −0.397507 + 0.800239I
d = 0.092374 + 1.330860I
−13.2358 − 8.9369I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59024 − 0.63743I
a = −1.215800 − 0.253500I
b = −1.87247 + 0.52042I
c = −0.397507 − 0.800239I
d = 0.092374 − 1.330860I
−13.2358 + 8.9369I 0
u = −1.61640 + 0.61957I
a = −0.679853 − 0.543396I
b = −0.932855 + 0.745500I
c = 0.096470 − 1.214810I
d = −0.35117 − 1.92445I
−13.4084 + 6.2441I 0
u = −1.61640 − 0.61957I
a = −0.679853 + 0.543396I
b = −0.932855 − 0.745500I
c = 0.096470 + 1.214810I
d = −0.35117 + 1.92445I
−13.4084 − 6.2441I 0
u = 1.74703 + 0.30124I
a = −0.853693 + 0.410109I
b = −1.33429 − 0.54288I
c = −0.316872 + 0.927449I
d = 0.16562 + 1.49317I
−14.9547 + 0.9173I 0
u = 1.74703 − 0.30124I
a = −0.853693 − 0.410109I
b = −1.33429 + 0.54288I
c = −0.316872 − 0.927449I
d = 0.16562 − 1.49317I
−14.9547 − 0.9173I 0
12
II. I
u
2
= hu
4
c
2
− u
4
c + · · · + c
2
− c, −2u
4
c
2
+ u
4
c + · · · + c
3
− 2c
2
, b − u, a −
u, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
11
=
c
−u
4
c
2
− u
3
c
2
+ u
4
c + 2c
2
u
2
+ 2u
3
c + c
2
u − u
2
c − c
2
− 3cu + c
a
6
=
u
u
a
10
=
c
2
u
−u
4
c
2
− u
3
c
2
+ u
4
c + 2c
2
u
2
+ 2u
3
c + 2c
2
u − u
2
c − c
2
− 3cu
a
12
=
c
2
u
−u
4
c
2
− u
3
c
2
+ u
4
c + 2c
2
u
2
+ 2u
3
c + 2c
2
u − u
2
c − c
2
− 3cu
a
3
=
−u
2
+ 1
−u
2
a
2
=
−u
4
+ u
2
+ 1
−u
4
+ u
3
+ u
2
− 2u + 1
a
1
=
0
−u
a
8
=
u
u
a
7
=
−u
4
c
2
− u
3
c
2
+ u
4
c + 2c
2
u
2
+ 2u
3
c + c
2
u − 2u
2
c − c
2
− 3cu
−u
4
c
2
− u
3
c
2
+ u
4
c + 2c
2
u
2
+ 2u
3
c + c
2
u − 2u
2
c − c
2
− 3cu + c
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 8u − 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
c
2
, c
5
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
c
3
, c
4
, c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
c
6
, c
7
, c
10
c
11
u
15
− 5u
13
+ ··· + u − 1
c
9
u
15
− 10u
14
+ ··· − 5u − 1
c
12
u
15
+ 10u
14
+ ··· − 5u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
c
2
, c
5
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
c
3
, c
4
, c
8
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
c
6
, c
7
, c
10
c
11
y
15
− 10y
14
+ ··· − 5y − 1
c
9
, c
12
y
15
− 10y
14
+ ··· − 25y − 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 1.21774
b = 1.21774
c = −0.015843 + 0.852735I
d = 0.57040 + 1.44998I
−2.40108 −3.48110
u = 1.21774
a = 1.21774
b = 1.21774
c = −0.015843 − 0.852735I
d = 0.57040 − 1.44998I
−2.40108 −3.48110
u = 1.21774
a = 1.21774
b = 1.21774
c = 1.67408
d = 0.501582
−2.40108 −3.48110
u = 0.309916 + 0.549911I
a = 0.309916 + 0.549911I
b = 0.309916 + 0.549911I
c = 1.20682 − 0.89411I
d = 0.186015 + 0.262335I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.309916 + 0.549911I
a = 0.309916 + 0.549911I
b = 0.309916 + 0.549911I
c = −0.209448 + 0.034081I
d = 0.122441 + 0.509500I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.309916 + 0.549911I
a = 0.309916 + 0.549911I
b = 0.309916 + 0.549911I
c = 0.55823 − 1.90023I
d = 1.24715 − 3.53209I
−0.32910 − 1.53058I −2.51511 + 4.43065I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309916 − 0.549911I
a = 0.309916 − 0.549911I
b = 0.309916 − 0.549911I
c = 1.20682 + 0.89411I
d = 0.186015 − 0.262335I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.309916 − 0.549911I
a = 0.309916 − 0.549911I
b = 0.309916 − 0.549911I
c = −0.209448 − 0.034081I
d = 0.122441 − 0.509500I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.309916 − 0.549911I
a = 0.309916 − 0.549911I
b = 0.309916 − 0.549911I
c = 0.55823 + 1.90023I
d = 1.24715 + 3.53209I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −1.41878 + 0.21917I
a = −1.41878 + 0.21917I
b = −1.41878 + 0.21917I
c = 0.056392 − 1.024950I
d = −0.47615 − 1.68177I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.41878 + 0.21917I
a = −1.41878 + 0.21917I
b = −1.41878 + 0.21917I
c = 0.191710 + 0.838957I
d = −0.33588 + 1.40562I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.41878 + 0.21917I
a = −1.41878 + 0.21917I
b = −1.41878 + 0.21917I
c = −1.62491 − 0.02669I
d = −0.564775 + 0.063470I
−5.87256 + 4.40083I −6.74431 − 3.49859I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41878 − 0.21917I
a = −1.41878 − 0.21917I
b = −1.41878 − 0.21917I
c = 0.056392 + 1.024950I
d = −0.47615 + 1.68177I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −1.41878 − 0.21917I
a = −1.41878 − 0.21917I
b = −1.41878 − 0.21917I
c = 0.191710 − 0.838957I
d = −0.33588 − 1.40562I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −1.41878 − 0.21917I
a = −1.41878 − 0.21917I
b = −1.41878 − 0.21917I
c = −1.62491 + 0.02669I
d = −0.564775 − 0.063470I
−5.87256 − 4.40083I −6.74431 + 3.49859I
18
III. I
v
1
= ha, d − v + 1, c + a, b + v − 1, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
11
=
0
v − 1
a
6
=
0
−v + 1
a
10
=
v
v − 1
a
12
=
0
v − 1
a
3
=
1
v
a
2
=
−v + 1
v
a
1
=
0
v − 1
a
8
=
v
0
a
7
=
0
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 5
19
(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
20
(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
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = 0
d = −0.500000 + 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
c = 0
d = −0.500000 − 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
22
IV. I
v
2
= ha, d, c − v, b − v − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
11
=
v
0
a
6
=
0
v + 1
a
10
=
v
0
a
12
=
v
−v − 1
a
3
=
1
−v
a
2
=
v + 1
−v
a
1
=
0
−v − 1
a
8
=
v
0
a
7
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 7
23
(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
24
(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
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
c = −0.500000 + 0.866025I
d = 0
−1.64493 − 2.02988I −9.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = −0.500000 − 0.866025I
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
26
V. I
v
3
= hc, d + 1, b, a − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
5
=
1
0
a
11
=
0
−1
a
6
=
1
0
a
10
=
1
−1
a
12
=
1
−1
a
3
=
1
0
a
2
=
1
0
a
1
=
1
0
a
8
=
1
0
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
27
(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
c
12
u + 1
c
10
, c
11
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
8
y
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y − 1
29
(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
30
VI. I
v
4
= ha, da − cb + 1, dv + 1, cv − ba + bv + a − v, b
2
− b + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
11
=
−b + 1
d
a
6
=
0
b
a
10
=
−b + v + 1
d
a
12
=
−b + 1
d + b
a
3
=
1
−b + 1
a
2
=
b
−b + 1
a
1
=
0
−b
a
8
=
v
0
a
7
=
b − 1
−d
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
+ 4b − 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.
31
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
2.02988I −1.23207 − 3.46710I
32
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
· (u
47
+ 24u
46
+ ··· + 216u − 16)
c
2
u(u
2
+ u + 1)
2
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
· (u
47
+ 2u
46
+ ··· + 16u + 4)
c
3
u(u
2
− u + 1)
2
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
· (u
47
− 2u
46
+ ··· − 21456u + 2592)
c
4
, c
8
u
5
(u
5
− u
4
+ ··· + u + 1)
3
(u
47
+ 2u
46
+ ··· + 1024u + 512)
c
5
u(u
2
− u + 1)
2
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
· (u
47
+ 2u
46
+ ··· + 16u + 4)
c
6
u
2
(u − 1)
2
(u + 1)(u
15
− 5u
13
+ ··· + u − 1)(u
47
− 8u
46
+ ··· + 56u + 16)
c
7
u
2
(u + 1)
3
(u
15
− 5u
13
+ ··· + u − 1)(u
47
+ 8u
46
+ ··· + 56u + 16)
c
9
u
2
(u + 1)
3
(u
15
− 10u
14
+ ··· − 5u − 1)
· (u
47
− 14u
46
+ ··· + 6688u − 256)
c
10
u
2
(u − 1)
3
(u
15
− 5u
13
+ ··· + u − 1)(u
47
+ 8u
46
+ ··· + 56u + 16)
c
11
u
2
(u − 1)(u + 1)
2
(u
15
− 5u
13
+ ··· + u − 1)(u
47
− 8u
46
+ ··· + 56u + 16)
c
12
u
2
(u + 1)
3
(u
15
+ 10u
14
+ ··· − 5u + 1)
· (u
47
+ 54u
46
+ ··· + 544u + 256)
33
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
· (y
47
+ 48y
45
+ ··· + 67872y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
· (y
47
+ 24y
46
+ ··· + 216y − 16)
c
3
y(y
2
+ y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
47
− 24y
46
+ ··· + 353776896y − 6718464)
c
4
, c
8
y
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
47
− 30y
46
+ ··· + 1572864y − 262144)
c
6
, c
11
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 5y − 1)
· (y
47
− 54y
46
+ ··· + 544y − 256)
c
7
, c
10
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 5y − 1)
· (y
47
− 14y
46
+ ··· + 6688y − 256)
c
9
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 25y − 1)
· (y
47
+ 46y
46
+ ··· + 11182592y − 65536)
c
12
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 25y − 1)
· (y
47
− 114y
46
+ ··· − 1990144y − 65536)
34
