12n
0061
(K12n
0061
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 4 7 9 1 7
Solving Sequence
4,9 5,7 10,12
1 6 3 2 8 11
c
4
c
9
c
12
c
6
c
3
c
2
c
8
c
11
c
1
, c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.70930 × 10
96
u
46
− 9.84287 × 10
96
u
45
+ ··· + 6.09681 × 10
98
d − 6.16018 × 10
99
,
− 1.03963 × 10
97
u
46
− 1.48428 × 10
97
u
45
+ ··· + 3.04841 × 10
98
c − 8.34618 × 10
99
,
− 3.55708 × 10
84
u
46
− 5.87581 × 10
84
u
45
+ ··· + 4.44856 × 10
87
b − 3.91588 × 10
87
,
2.90225 × 10
85
u
46
+ 4.18154 × 10
85
u
45
+ ··· + 4.44856 × 10
87
a + 2.35085 × 10
88
,
u
47
+ 2u
46
+ ··· + 1024u + 512i
I
u
2
= ha
2
u + d − a, a
2
u + c, a
2
u + b − a, −u
4
a + 2u
3
a − u
4
+ a
3
+ u
2
a + u
3
− 3au + 2u
2
− u − 1,
u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
I
v
1
= hc, d − v + 1, b, a − v, v
2
− v + 1i
I
v
2
= ha, d + v + 1, c + a, b − v − 1, v
2
+ v + 1i
I
v
3
= ha, d − 1, c + a − 1, b + 1, v − 1i
I
v
4
= ha, d
2
+ 2db + b
2
+ d + b + 1, dc − dv + 2cb + ba − av + c + a − v + 2, da − cb − 1,
a
2
v
2
− cav − a
2
v + v
2
a + c
2
+ 2ca − 2cv + a
2
− 2av + v
2
, bv + 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−6.71 × 10
96
u
46
− 9.84 × 10
96
u
45
+ · · · + 6.10 × 10
98
d − 6.16 ×
10
99
, −1.04×10
97
u
46
−1.48×10
97
u
45
+· · ·+3.05×10
98
c−8.35×10
99
, −3.56×
10
84
u
46
− 5.88 × 10
84
u
45
+ · · · + 4.45 × 10
87
b − 3.92 × 10
87
, 2.90 × 10
85
u
46
+
4.18×10
85
u
45
+· · ·+4.45 × 10
87
a+2.35 × 10
88
, u
47
+2u
46
+· · ·+1024u + 512i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
7
=
−0.00652403u
46
− 0.00939975u
45
+ ··· − 0.175259u − 5.28451
0.000799603u
46
+ 0.00132083u
45
+ ··· + 1.47622u + 0.880259
a
10
=
0.00732363u
46
+ 0.0107206u
45
+ ··· + 1.65147u + 6.16477
0.000799603u
46
+ 0.00132083u
45
+ ··· + 1.47622u + 0.880259
a
12
=
0.0341039u
46
+ 0.0486904u
45
+ ··· + 14.6818u + 27.3788
0.0110046u
46
+ 0.0161443u
45
+ ··· + 4.15721u + 10.1039
a
1
=
0.0252497u
46
+ 0.0366947u
45
+ ··· + 11.3108u + 20.0129
0.00558802u
46
+ 0.00914935u
45
+ ··· + 0.890394u + 6.27203
a
6
=
−0.0265369u
46
− 0.0375470u
45
+ ··· − 11.6287u − 20.8089
−0.00128717u
46
− 0.000852284u
45
+ ··· − 0.317834u − 0.796018
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
8
=
u
u
a
11
=
0.00732363u
46
+ 0.0107206u
45
+ ··· + 1.65147u + 6.16477
0.00275888u
46
+ 0.00400645u
45
+ ··· + 1.74743u + 2.89071
(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
12
u
47
+ 8u
46
+ ··· + 56u + 16
c
7
, c
9
u
47
− 8u
46
+ ··· + 56u + 16
c
10
u
47
+ 54u
46
+ ··· + 544u + 256
c
11
u
47
− 14u
46
+ ··· + 6688u − 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
12
y
47
− 14y
46
+ ··· + 6688y − 256
c
7
, c
9
y
47
− 54y
46
+ ··· + 544y − 256
c
10
y
47
− 114y
46
+ ··· − 1990144y − 65536
c
11
y
47
+ 46y
46
+ ··· + 11182592y − 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.168857 + 0.977277I
a = −0.502467 + 0.614921I
b = −1.127600 + 0.633374I
c = −0.961290 + 0.734797I
d = −0.756569 + 0.908522I
−0.50019 − 4.79223I −2.43501 + 7.48976I
u = −0.168857 − 0.977277I
a = −0.502467 − 0.614921I
b = −1.127600 − 0.633374I
c = −0.961290 − 0.734797I
d = −0.756569 − 0.908522I
−0.50019 + 4.79223I −2.43501 − 7.48976I
u = 0.758370 + 0.572620I
a = 0.677402 − 0.992682I
b = 0.306606 + 0.328751I
c = −0.587766 + 0.872152I
d = −0.654201 + 0.089268I
−3.62778 + 1.19000I −10.45074 − 1.01195I
u = 0.758370 − 0.572620I
a = 0.677402 + 0.992682I
b = 0.306606 − 0.328751I
c = −0.587766 − 0.872152I
d = −0.654201 − 0.089268I
−3.62778 − 1.19000I −10.45074 + 1.01195I
u = 0.798854 + 0.256222I
a = 0.588853 + 0.419968I
b = 0.579476 − 0.018798I
c = −0.544662 − 1.097250I
d = −0.20396 − 1.54472I
1.43042 − 3.68269I −0.57615 + 8.67104I
u = 0.798854 − 0.256222I
a = 0.588853 − 0.419968I
b = 0.579476 + 0.018798I
c = −0.544662 + 1.097250I
d = −0.20396 + 1.54472I
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 = 0.383641 + 0.556567I
b = 0.733419 + 0.549353I
c = 1.205770 + 0.404495I
d = 0.597302 + 0.839395I
1.71355 + 0.99880I 4.04476 − 2.43406I
u = 0.287114 − 0.709757I
a = 0.383641 − 0.556567I
b = 0.733419 − 0.549353I
c = 1.205770 − 0.404495I
d = 0.597302 − 0.839395I
1.71355 − 0.99880I 4.04476 + 2.43406I
u = −0.723521 + 0.092490I
a = −0.704709 + 0.351766I
b = −0.480781 − 0.041433I
c = −3.56166 + 1.78408I
d = −1.048200 + 0.427037I
0.84436 + 2.80891I −4.36866 − 6.45196I
u = −0.723521 − 0.092490I
a = −0.704709 − 0.351766I
b = −0.480781 + 0.041433I
c = −3.56166 − 1.78408I
d = −1.048200 − 0.427037I
0.84436 − 2.80891I −4.36866 + 6.45196I
u = 0.549584 + 0.433005I
a = 0.450542 + 0.396109I
b = 0.579765 + 0.179992I
c = 2.21899 + 0.55940I
d = 0.703512 + 0.579046I
2.18982 + 0.74670I 2.91211 + 1.96105I
u = 0.549584 − 0.433005I
a = 0.450542 − 0.396109I
b = 0.579765 − 0.179992I
c = 2.21899 − 0.55940I
d = 0.703512 − 0.579046I
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 = −0.620233 + 0.304010I
b = −0.486762 + 0.009061I
c = 0.225348 − 0.901957I
d = −0.488745 − 1.323290I
1.05099 − 1.22135I −3.11104 − 2.86511I
u = −0.659997 − 0.157577I
a = −0.620233 − 0.304010I
b = −0.486762 − 0.009061I
c = 0.225348 + 0.901957I
d = −0.488745 + 1.323290I
1.05099 + 1.22135I −3.11104 + 2.86511I
u = −0.226818 + 1.310000I
a = −0.108597 − 1.104710I
b = −0.068409 + 0.532975I
c = 0.830749 − 0.602517I
d = −1.046880 − 0.665279I
−4.12204 − 2.83071I −3.10594 + 2.47522I
u = −0.226818 − 1.310000I
a = −0.108597 + 1.104710I
b = −0.068409 − 0.532975I
c = 0.830749 + 0.602517I
d = −1.046880 + 0.665279I
−4.12204 + 2.83071I −3.10594 − 2.47522I
u = 0.024914 + 0.666306I
a = −0.311476 + 0.943178I
b = −0.68322 + 1.48591I
c = −0.472994 + 0.671049I
d = −0.54160 + 1.46349I
−0.68586 + 1.51893I −2.03699 + 0.09471I
u = 0.024914 − 0.666306I
a = −0.311476 − 0.943178I
b = −0.68322 − 1.48591I
c = −0.472994 − 0.671049I
d = −0.54160 − 1.46349I
−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 = 0.527825 + 0.529108I
b = 0.767343 − 0.182692I
c = −1.00554 − 1.01478I
d = −1.17436 − 1.26704I
−1.49383 − 5.48046I −1.24533 + 5.03878I
u = 1.275400 − 0.425723I
a = 0.527825 − 0.529108I
b = 0.767343 + 0.182692I
c = −1.00554 + 1.01478I
d = −1.17436 + 1.26704I
−1.49383 + 5.48046I −1.24533 − 5.03878I
u = 1.351470 + 0.126259I
a = −1.098230 + 0.058069I
b = −2.73978 + 0.07859I
c = 0.428611 + 0.687312I
d = 0.23689 + 2.41586I
−5.10242 + 0.08441I −6.12902 + 0.I
u = 1.351470 − 0.126259I
a = −1.098230 − 0.058069I
b = −2.73978 − 0.07859I
c = 0.428611 − 0.687312I
d = 0.23689 − 2.41586I
−5.10242 − 0.08441I −6.12902 + 0.I
u = −0.062543 + 0.611080I
a = −0.14897 − 1.86717I
b = −0.025679 + 0.284490I
c = 3.03261 + 4.80458I
d = −0.366383 − 1.198400I
−0.53961 − 2.33649I −0.16377 + 3.97632I
u = −0.062543 − 0.611080I
a = −0.14897 + 1.86717I
b = −0.025679 − 0.284490I
c = 3.03261 − 4.80458I
d = −0.366383 + 1.198400I
−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 = 1.072310 + 0.133945I
b = 2.69315 + 0.17757I
c = −0.777654 + 0.758804I
d = −0.87546 + 2.59578I
−4.74548 + 5.93381I −5.07129 − 5.57342I
u = −1.354510 − 0.305217I
a = 1.072310 − 0.133945I
b = 2.69315 − 0.17757I
c = −0.777654 − 0.758804I
d = −0.87546 − 2.59578I
−4.74548 − 5.93381I −5.07129 + 5.57342I
u = −1.42975 + 0.19774I
a = −0.527124 + 0.570614I
b = −0.714333 − 0.280041I
c = 0.985847 − 0.867635I
d = 1.15748 − 0.96588I
−5.91128 + 1.72117I −6.79419 + 0.I
u = −1.42975 − 0.19774I
a = −0.527124 − 0.570614I
b = −0.714333 + 0.280041I
c = 0.985847 + 0.867635I
d = 1.15748 + 0.96588I
−5.91128 − 1.72117I −6.79419 + 0.I
u = −0.01170 + 1.48787I
a = −0.004491 − 1.046020I
b = −0.003311 + 0.582025I
c = −0.374959 − 0.326873I
d = 1.076620 − 0.549413I
−8.14593 − 1.35024I 0
u = −0.01170 − 1.48787I
a = −0.004491 + 1.046020I
b = −0.003311 − 0.582025I
c = −0.374959 + 0.326873I
d = 1.076620 + 0.549413I
−8.14593 + 1.35024I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.509235
a = −1.62785
b = −0.278429
c = 1.42620
d = 0.0709079
−1.19981 −8.75910
u = −1.38697 + 0.55724I
a = −0.508516 + 0.527555I
b = −0.834857 − 0.205621I
c = 1.10528 − 1.01088I
d = 1.36984 − 1.26145I
−4.40802 + 10.56830I 0
u = −1.38697 − 0.55724I
a = −0.508516 − 0.527555I
b = −0.834857 + 0.205621I
c = 1.10528 + 1.01088I
d = 1.36984 + 1.26145I
−4.40802 − 10.56830I 0
u = 0.40359 + 1.45989I
a = 0.149185 − 1.016750I
b = 0.114536 + 0.582400I
c = −0.560529 − 0.949843I
d = 1.124480 − 0.685590I
−7.37650 + 7.69255I 0
u = 0.40359 − 1.45989I
a = 0.149185 + 1.016750I
b = 0.114536 − 0.582400I
c = −0.560529 + 0.949843I
d = 1.124480 + 0.685590I
−7.37650 − 7.69255I 0
u = −1.43182 + 0.71566I
a = 0.954104 + 0.236457I
b = 2.50037 + 0.27104I
c = −1.42231 + 0.42095I
d = −2.09633 + 2.01103I
−7.91018 + 10.04820I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43182 − 0.71566I
a = 0.954104 − 0.236457I
b = 2.50037 − 0.27104I
c = −1.42231 − 0.42095I
d = −2.09633 − 2.01103I
−7.91018 − 10.04820I 0
u = 1.55076 + 0.46120I
a = −0.979860 + 0.150029I
b = −2.56948 + 0.17354I
c = 0.0100774 + 0.0710674I
d = −0.347517 − 0.964881I
−10.01530 − 3.44751I 0
u = 1.55076 − 0.46120I
a = −0.979860 − 0.150029I
b = −2.56948 − 0.17354I
c = 0.0100774 − 0.0710674I
d = −0.347517 + 0.964881I
−10.01530 + 3.44751I 0
u = 1.43192 + 0.83141I
a = −0.924993 + 0.257013I
b = −2.45089 + 0.28141I
c = 1.54648 + 0.31162I
d = 2.32957 + 1.80759I
−10.6565 − 15.7212I 0
u = 1.43192 − 0.83141I
a = −0.924993 − 0.257013I
b = −2.45089 − 0.28141I
c = 1.54648 − 0.31162I
d = 2.32957 − 1.80759I
−10.6565 + 15.7212I 0
u = −1.59024 + 0.63743I
a = 0.938344 + 0.185530I
b = 2.50574 + 0.19991I
c = 0.028561 + 0.229108I
d = 0.361646 − 0.685663I
−13.2358 + 8.9369I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59024 − 0.63743I
a = 0.938344 − 0.185530I
b = 2.50574 − 0.19991I
c = 0.028561 − 0.229108I
d = 0.361646 + 0.685663I
−13.2358 − 8.9369I 0
u = 1.61640 + 0.61957I
a = −0.936055 + 0.176897I
b = −2.50694 + 0.18872I
c = 1.188010 + 0.269021I
d = 1.66723 + 1.72517I
−13.4084 − 6.2441I 0
u = 1.61640 − 0.61957I
a = −0.936055 − 0.176897I
b = −2.50694 − 0.18872I
c = 1.188010 − 0.269021I
d = 1.66723 − 1.72517I
−13.4084 + 6.2441I 0
u = −1.74703 + 0.30124I
a = 0.947443 + 0.082473I
b = 2.55085 + 0.08714I
c = −0.250062 + 0.065643I
d = −0.059801 − 1.037630I
−14.9547 − 0.9173I 0
u = −1.74703 − 0.30124I
a = 0.947443 − 0.082473I
b = 2.55085 − 0.08714I
c = −0.250062 − 0.065643I
d = −0.059801 + 1.037630I
−14.9547 + 0.9173I 0
12
II. I
u
2
= ha
2
u + d − a, a
2
u + c, a
2
u + b − a, −u
4
a − u
4
+ · · · + a
3
− 1, 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
7
=
a
−a
2
u + a
a
10
=
−a
2
u
−a
2
u + a
a
12
=
−a
2
u
−a
2
u + a
a
1
=
0
u
a
6
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
−u
4
+ u
2
+ 1
−u
4
− u
3
+ u
2
+ 2u + 1
a
8
=
u
u
a
11
=
−a
2
u
−u
3
a
2
− a
2
u + a
(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
9
c
12
u
15
− 5u
13
+ ··· + u − 1
c
10
u
15
+ 10u
14
+ ··· − 5u + 1
c
11
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
9
c
12
y
15
− 10y
14
+ ··· − 5y − 1
c
10
, c
11
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 = −0.586248 + 0.597241I
b = −0.602091 − 0.255494I
c = −0.015843 − 0.852735I
d = −0.602091 − 0.255494I
−2.40108 −3.48110
u = −1.21774
a = −0.586248 − 0.597241I
b = −0.602091 + 0.255494I
c = −0.015843 + 0.852735I
d = −0.602091 + 0.255494I
−2.40108 −3.48110
u = −1.21774
a = 1.17250
b = 2.84657
c = 1.67408
d = 2.84657
−2.40108 −3.48110
u = −0.309916 + 0.549911I
a = −0.331889 + 0.475420I
b = −0.541336 + 0.441339I
c = −0.209448 − 0.034081I
d = −0.541336 + 0.441339I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −0.309916 + 0.549911I
a = 1.02081 + 1.15644I
b = 2.22763 + 2.05055I
c = 1.20682 + 0.89411I
d = 2.22763 + 2.05055I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −0.309916 + 0.549911I
a = −0.68892 − 1.63186I
b = −0.130685 + 0.268368I
c = 0.55823 + 1.90023I
d = −0.130685 + 0.268368I
−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 = −0.331889 − 0.475420I
b = −0.541336 − 0.441339I
c = −0.209448 + 0.034081I
d = −0.541336 − 0.441339I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.309916 − 0.549911I
a = 1.02081 − 1.15644I
b = 2.22763 − 2.05055I
c = 1.20682 − 0.89411I
d = 2.22763 − 2.05055I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = −0.309916 − 0.549911I
a = −0.68892 + 1.63186I
b = −0.130685 − 0.268368I
c = 0.55823 − 1.90023I
d = −0.130685 − 0.268368I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 1.41878 + 0.21917I
a = −1.060130 + 0.090162I
b = −2.68504 + 0.11685I
c = −1.62491 + 0.02669I
d = −2.68504 + 0.11685I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 1.41878 + 0.21917I
a = 0.532546 − 0.656825I
b = 0.588938 + 0.368121I
c = 0.056392 + 1.024950I
d = 0.588938 + 0.368121I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = 1.41878 + 0.21917I
a = 0.527587 + 0.566662I
b = 0.719297 − 0.272295I
c = 0.191710 − 0.838957I
d = 0.719297 − 0.272295I
−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 = −1.060130 − 0.090162I
b = −2.68504 − 0.11685I
c = −1.62491 − 0.02669I
d = −2.68504 − 0.11685I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = 1.41878 − 0.21917I
a = 0.532546 + 0.656825I
b = 0.588938 − 0.368121I
c = 0.056392 − 1.024950I
d = 0.588938 − 0.368121I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = 1.41878 − 0.21917I
a = 0.527587 − 0.566662I
b = 0.719297 + 0.272295I
c = 0.191710 + 0.838957I
d = 0.719297 + 0.272295I
−5.87256 + 4.40083I −6.74431 − 3.49859I
18
III. I
v
1
= hc, d − v + 1, b, a − v, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
7
=
v
0
a
10
=
v
0
a
12
=
0
v − 1
a
1
=
−v
v − 1
a
6
=
v
−v + 1
a
3
=
0
v
a
2
=
−v
v
a
8
=
v
0
a
11
=
v
0
(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
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u + 1)
2
c
12
(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
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(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 = 0.500000 + 0.866025I
b = 0
c = 0
d = −0.500000 + 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0
c = 0
d = −0.500000 − 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
22
IV. I
v
2
= 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
7
=
0
v + 1
a
10
=
v
−v − 1
a
12
=
0
−v − 1
a
1
=
0
−v − 1
a
6
=
0
v + 1
a
3
=
1
−v
a
2
=
v + 1
−v
a
8
=
v
0
a
11
=
0
−v − 1
(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
6
, c
8
c
11
, c
12
u
2
c
7
(u − 1)
2
c
9
, c
10
(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
6
, c
8
c
11
, c
12
y
2
c
7
, c
9
, c
10
(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
d = −0.500000 − 0.866025I
−1.64493 − 2.02988I −9.00000 + 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 −9.00000 − 3.46410I
26
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
5
=
1
0
a
7
=
0
−1
a
10
=
1
1
a
12
=
1
1
a
1
=
1
0
a
6
=
1
0
a
3
=
1
0
a
2
=
1
0
a
8
=
1
0
a
11
=
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
u − 1
c
9
, c
10
, c
11
c
12
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 = 0
b = −1.00000
c = 1.00000
d = 1.00000
0 0
30
VI. I
v
4
= ha, d
2
+ 2db + · · · + b + 1, −dv − av + · · · + a + 2, da − cb −
1, a
2
v
2
+ v
2
a + · · · + 2ca + a
2
, bv + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
7
=
0
b
a
10
=
v
−b
a
12
=
v
d
a
1
=
v
d + b
a
6
=
v
d + b
a
3
=
−dv + 2
d + b + 1
a
2
=
−dv − d − b + 1
d + b + 1
a
8
=
v
0
a
11
=
0
−b
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
2
+ v
2
− 4d − 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 −1.30108 + 3.68445I
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)(u + 1)
2
(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
− 5u
13
+ ··· + u − 1)(u
47
− 8u
46
+ ··· + 56u + 16)
c
10
u
2
(u + 1)
3
(u
15
+ 10u
14
+ ··· − 5u + 1)
· (u
47
+ 54u
46
+ ··· + 544u + 256)
c
11
u
2
(u + 1)
3
(u
15
− 10u
14
+ ··· − 5u − 1)
· (u
47
− 14u
46
+ ··· + 6688u − 256)
c
12
u
2
(u − 1)
2
(u + 1)(u
15
− 5u
13
+ ··· + u − 1)(u
47
+ 8u
46
+ ··· + 56u + 16)
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
12
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 5y − 1)
· (y
47
− 14y
46
+ ··· + 6688y − 256)
c
7
, c
9
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 5y − 1)
· (y
47
− 54y
46
+ ··· + 544y − 256)
c
10
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 25y − 1)
· (y
47
− 114y
46
+ ··· − 1990144y − 65536)
c
11
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 25y − 1)
· (y
47
+ 46y
46
+ ··· + 11182592y − 65536)
34
