12n
0219
(K12n
0219
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 3 10 7 5 6 11
Solving Sequence
3,7 5,8,10
11 2 1 4 9 6 12
c
7
c
10
c
2
c
1
c
4
c
9
c
6
c
12
c
3
, c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.93434 × 10
85
u
46
+ 3.71779 × 10
85
u
45
+ ··· + 2.55773 × 10
87
d − 1.93229 × 10
88
,
2.15362 × 10
85
u
46
− 4.85011 × 10
85
u
45
+ ··· + 1.02309 × 10
88
c + 2.94200 × 10
88
,
1.12139 × 10
85
u
46
− 1.67513 × 10
85
u
45
+ ··· + 4.44856 × 10
87
b + 1.22255 × 10
88
,
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
= hau + d, u
4
a + u
3
a − 2u
2
a − a
2
− au + c + a, a
2
u − u
2
a + 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 + 1, b, a − v, v
2
− v + 1i
I
v
2
= ha, d, c − 1, b + v + 1, v
2
+ v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v − 1i
I
v
4
= hc, d + 1, a
2
v
2
+ 2cav + v
2
a + c
2
+ cv + 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−2.93 × 10
85
u
46
+ 3.72 × 10
85
u
45
+ · · · + 2.56 × 10
87
d − 1.93 ×
10
88
, 2.15 × 10
85
u
46
− 4.85 × 10
85
u
45
+ · · · + 1.02 × 10
88
c + 2.94 × 10
88
, 1.12 ×
10
85
u
46
− 1.68 × 10
85
u
45
+ · · · + 4.45 × 10
87
b + 1.22 × 10
88
, 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
3
=
0
u
a
7
=
1
0
a
5
=
−0.00652403u
46
+ 0.00939975u
45
+ ··· + 0.175259u − 5.28451
−0.00252080u
46
+ 0.00376556u
45
+ ··· + 1.87177u − 2.74819
a
8
=
1
u
2
a
10
=
−0.00210501u
46
+ 0.00474064u
45
+ ··· + 0.461395u − 2.87560
0.0114724u
46
− 0.0145355u
45
+ ··· − 4.65650u + 7.55472
a
11
=
−0.00461353u
46
+ 0.00835301u
45
+ ··· + 2.10921u − 5.15564
0.0115443u
46
− 0.0142337u
45
+ ··· − 4.45469u + 6.85180
a
2
=
0.00732363u
46
− 0.0107206u
45
+ ··· − 1.65147u + 6.16477
0.00115968u
46
− 0.00136478u
45
+ ··· + 1.20500u + 1.13020
a
1
=
0.00732363u
46
− 0.0107206u
45
+ ··· − 1.65147u + 6.16477
−0.000799603u
46
+ 0.00132083u
45
+ ··· + 1.47622u − 0.880259
a
4
=
−u
−u
3
+ u
a
9
=
−0.0135774u
46
+ 0.0192761u
45
+ ··· + 5.11789u − 10.4303
0.0114724u
46
− 0.0145355u
45
+ ··· − 4.65650u + 7.55472
a
6
=
0.00753427u
46
− 0.00851325u
45
+ ··· − 2.57398u + 4.40744
−0.00963927u
46
+ 0.0132539u
45
+ ··· + 3.03538u − 7.28304
a
12
=
−0.00704613u
46
+ 0.0105560u
45
+ ··· + 5.29963u − 4.88261
−0.000358237u
46
− 0.0000756380u
45
+ ··· + 1.71290u − 0.326765
(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
+ 54u
46
+ ··· + 544u + 256
c
2
, c
4
u
47
− 8u
46
+ ··· + 56u + 16
c
3
, c
7
u
47
+ 2u
46
+ ··· + 1024u + 512
c
5
, c
11
u
47
+ 2u
46
+ ··· + 16u + 4
c
6
, c
9
u
47
+ 8u
46
+ ··· + 56u + 16
c
8
u
47
− 14u
46
+ ··· + 6688u − 256
c
10
u
47
− 2u
46
+ ··· − 21456u + 2592
c
12
u
47
+ 24u
46
+ ··· + 216u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
− 114y
46
+ ··· − 1990144y − 65536
c
2
, c
4
y
47
− 54y
46
+ ··· + 544y − 256
c
3
, c
7
y
47
− 30y
46
+ ··· + 1572864y − 262144
c
5
, c
11
y
47
+ 24y
46
+ ··· + 216y − 16
c
6
, c
9
y
47
− 14y
46
+ ··· + 6688y − 256
c
8
y
47
+ 46y
46
+ ··· + 11182592y − 65536
c
10
y
47
− 24y
46
+ ··· + 353776896y − 6718464
c
12
y
47
+ 48y
45
+ ··· + 67872y − 256
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 = 1.79611 + 1.03730I
c = 0.514128 − 0.147532I
d = −0.797065 − 0.515679I
−0.50019 + 4.79223I −2.43501 − 7.48976I
u = 0.168857 − 0.977277I
a = −0.502467 + 0.614921I
b = 1.79611 − 1.03730I
c = 0.514128 + 0.147532I
d = −0.797065 + 0.515679I
−0.50019 − 4.79223I −2.43501 + 7.48976I
u = −0.758370 + 0.572620I
a = 0.677402 + 0.992682I
b = 0.723028 − 0.014162I
c = 0.744657 − 0.533323I
d = 0.112391 − 0.635705I
−3.62778 − 1.19000I −10.45074 + 1.01195I
u = −0.758370 − 0.572620I
a = 0.677402 − 0.992682I
b = 0.723028 + 0.014162I
c = 0.744657 + 0.533323I
d = 0.112391 + 0.635705I
−3.62778 + 1.19000I −10.45074 − 1.01195I
u = −0.798854 + 0.256222I
a = 0.588853 − 0.419968I
b = −0.414268 − 0.500295I
c = 0.87223 + 2.38627I
d = 0.864877 + 0.369674I
1.43042 + 3.68269I −0.57615 − 8.67104I
u = −0.798854 − 0.256222I
a = 0.588853 + 0.419968I
b = −0.414268 + 0.500295I
c = 0.87223 − 2.38627I
d = 0.864877 − 0.369674I
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 = −1.121890 + 0.627489I
c = 0.513089 + 0.082248I
d = −0.900154 + 0.304593I
1.71355 − 0.99880I 4.04476 + 2.43406I
u = −0.287114 − 0.709757I
a = 0.383641 + 0.556567I
b = −1.121890 − 0.627489I
c = 0.513089 − 0.082248I
d = −0.900154 − 0.304593I
1.71355 + 0.99880I 4.04476 − 2.43406I
u = 0.723521 + 0.092490I
a = −0.704709 − 0.351766I
b = 0.164985 − 0.316883I
c = 0.454839 − 0.008386I
d = −1.197840 − 0.040523I
0.84436 − 2.80891I −4.36866 + 6.45196I
u = 0.723521 − 0.092490I
a = −0.704709 + 0.351766I
b = 0.164985 + 0.316883I
c = 0.454839 + 0.008386I
d = −1.197840 + 0.040523I
0.84436 + 2.80891I −4.36866 − 6.45196I
u = −0.549584 + 0.433005I
a = 0.450542 − 0.396109I
b = −0.716682 − 0.079816I
c = 0.472953 + 0.041513I
d = −1.098210 + 0.184170I
2.18982 − 0.74670I 2.91211 − 1.96105I
u = −0.549584 − 0.433005I
a = 0.450542 + 0.396109I
b = −0.716682 + 0.079816I
c = 0.472953 − 0.041513I
d = −1.098210 − 0.184170I
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 = 0.295226 − 0.244825I
c = 2.12917 − 2.54866I
d = 0.806949 − 0.231086I
1.05099 + 1.22135I −3.11104 + 2.86511I
u = 0.659997 − 0.157577I
a = −0.620233 + 0.304010I
b = 0.295226 + 0.244825I
c = 2.12917 + 2.54866I
d = 0.806949 + 0.231086I
1.05099 − 1.22135I −3.11104 − 2.86511I
u = 0.226818 + 1.310000I
a = −0.108597 + 1.104710I
b = −0.40730 − 1.37054I
c = 0.458775 − 0.181209I
d = −0.885550 − 0.744761I
−4.12204 + 2.83071I −3.10594 − 2.47522I
u = 0.226818 − 1.310000I
a = −0.108597 − 1.104710I
b = −0.40730 + 1.37054I
c = 0.458775 + 0.181209I
d = −0.885550 + 0.744761I
−4.12204 − 2.83071I −3.10594 + 2.47522I
u = −0.024914 + 0.666306I
a = −0.311476 − 0.943178I
b = 0.79000 + 1.91440I
c = 0.640075 − 0.081018I
d = −0.537681 − 0.194634I
−0.68586 − 1.51893I −2.03699 − 0.09471I
u = −0.024914 − 0.666306I
a = −0.311476 + 0.943178I
b = 0.79000 − 1.91440I
c = 0.640075 + 0.081018I
d = −0.537681 + 0.194634I
−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 = −0.57900 − 1.52065I
c = −0.01559 + 1.43836I
d = 1.007540 + 0.695155I
−1.49383 + 5.48046I −1.24533 − 5.03878I
u = −1.275400 − 0.425723I
a = 0.527825 + 0.529108I
b = −0.57900 + 1.52065I
c = −0.01559 − 1.43836I
d = 1.007540 − 0.695155I
−1.49383 − 5.48046I −1.24533 + 5.03878I
u = −1.351470 + 0.126259I
a = −1.098230 − 0.058069I
b = 0.731592 + 0.348244I
c = 0.263301 + 1.208440I
d = 0.827868 + 0.790009I
−5.10242 − 0.08441I −6.12902 + 0.I
u = −1.351470 − 0.126259I
a = −1.098230 + 0.058069I
b = 0.731592 − 0.348244I
c = 0.263301 − 1.208440I
d = 0.827868 − 0.790009I
−5.10242 + 0.08441I −6.12902 + 0.I
u = 0.062543 + 0.611080I
a = −0.14897 + 1.86717I
b = −0.061997 − 0.416831I
c = 0.572392 − 0.040588I
d = −0.738313 − 0.123261I
−0.53961 + 2.33649I −0.16377 − 3.97632I
u = 0.062543 − 0.611080I
a = −0.14897 − 1.86717I
b = −0.061997 + 0.416831I
c = 0.572392 + 0.040588I
d = −0.738313 + 0.123261I
−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 = −0.714948 + 0.830918I
c = 0.098591 − 1.307110I
d = 0.942622 − 0.760717I
−4.74548 − 5.93381I −5.07129 + 5.57342I
u = 1.354510 − 0.305217I
a = 1.072310 + 0.133945I
b = −0.714948 − 0.830918I
c = 0.098591 + 1.307110I
d = 0.942622 + 0.760717I
−4.74548 + 5.93381I −5.07129 − 5.57342I
u = 1.42975 + 0.19774I
a = −0.527124 − 0.570614I
b = −0.01996 − 1.72223I
c = 0.160939 − 1.189000I
d = 0.888208 − 0.825909I
−5.91128 − 1.72117I −6.79419 + 0.I
u = 1.42975 − 0.19774I
a = −0.527124 + 0.570614I
b = −0.01996 + 1.72223I
c = 0.160939 + 1.189000I
d = 0.888208 + 0.825909I
−5.91128 + 1.72117I −6.79419 + 0.I
u = 0.01170 + 1.48787I
a = −0.004491 + 1.046020I
b = −0.02316 − 1.73362I
c = 0.447414 + 0.229022I
d = −0.771023 + 0.906547I
−8.14593 + 1.35024I 0
u = 0.01170 − 1.48787I
a = −0.004491 − 1.046020I
b = −0.02316 + 1.73362I
c = 0.447414 − 0.229022I
d = −0.771023 − 0.906547I
−8.14593 − 1.35024I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509235
a = −1.62785
b = −0.143706
c = 1.39211
d = 0.281666
−1.19981 −8.75910
u = 1.38697 + 0.55724I
a = −0.508516 − 0.527555I
b = 0.83000 − 1.84270I
c = −0.174994 − 1.314570I
d = 1.099500 − 0.747460I
−4.40802 − 10.56830I 0
u = 1.38697 − 0.55724I
a = −0.508516 + 0.527555I
b = 0.83000 + 1.84270I
c = −0.174994 + 1.314570I
d = 1.099500 + 0.747460I
−4.40802 + 10.56830I 0
u = −0.40359 + 1.45989I
a = 0.149185 + 1.016750I
b = 0.78993 − 1.59477I
c = 0.426684 + 0.171312I
d = −1.018310 + 0.810344I
−7.37650 − 7.69255I 0
u = −0.40359 − 1.45989I
a = 0.149185 − 1.016750I
b = 0.78993 + 1.59477I
c = 0.426684 − 0.171312I
d = −1.018310 − 0.810344I
−7.37650 + 7.69255I 0
u = 1.43182 + 0.71566I
a = 0.954104 − 0.236457I
b = −0.54843 + 1.86272I
c = −0.319543 − 1.240410I
d = 1.194760 − 0.756016I
−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 = −0.54843 − 1.86272I
c = −0.319543 + 1.240410I
d = 1.194760 + 0.756016I
−7.91018 + 10.04820I 0
u = −1.55076 + 0.46120I
a = −0.979860 − 0.150029I
b = 0.206872 + 1.246280I
c = 0.345065 − 0.777884I
d = 0.523505 − 1.074170I
−10.01530 + 3.44751I 0
u = −1.55076 − 0.46120I
a = −0.979860 + 0.150029I
b = 0.206872 − 1.246280I
c = 0.345065 + 0.777884I
d = 0.523505 + 1.074170I
−10.01530 − 3.44751I 0
u = −1.43192 + 0.83141I
a = −0.924993 − 0.257013I
b = 0.58171 + 2.13451I
c = −0.416016 + 1.198340I
d = 1.25854 + 0.74473I
−10.6565 + 15.7212I 0
u = −1.43192 − 0.83141I
a = −0.924993 + 0.257013I
b = 0.58171 − 2.13451I
c = −0.416016 − 1.198340I
d = 1.25854 − 0.74473I
−10.6565 − 15.7212I 0
u = 1.59024 + 0.63743I
a = 0.938344 − 0.185530I
b = −0.13792 + 1.70847I
c = 0.339068 + 0.700979I
d = 0.440794 + 1.156090I
−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 = −0.13792 − 1.70847I
c = 0.339068 − 0.700979I
d = 0.440794 − 1.156090I
−13.2358 + 8.9369I 0
u = −1.61640 + 0.61957I
a = −0.936055 − 0.176897I
b = 0.06628 + 1.66930I
c = −0.208465 + 1.110670I
d = 1.16324 + 0.86972I
−13.4084 + 6.2441I 0
u = −1.61640 − 0.61957I
a = −0.936055 + 0.176897I
b = 0.06628 − 1.66930I
c = −0.208465 − 1.110670I
d = 1.16324 − 0.86972I
−13.4084 − 6.2441I 0
u = 1.74703 + 0.30124I
a = 0.947443 − 0.082473I
b = 0.341668 + 0.840130I
c = 0.235184 + 0.814143I
d = 0.672509 + 1.133680I
−14.9547 + 0.9173I 0
u = 1.74703 − 0.30124I
a = 0.947443 + 0.082473I
b = 0.341668 − 0.840130I
c = 0.235184 − 0.814143I
d = 0.672509 − 1.133680I
−14.9547 − 0.9173I 0
12
II. I
u
2
= hau + d, u
4
a + u
3
a + · · · − a
2
+ a, a
2
u − u
2
a + b + a, −u
4
a − u
4
+
· · · + a
3
− 1, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
5
=
a
−a
2
u + u
2
a − a
a
8
=
1
u
2
a
10
=
−u
4
a − u
3
a + 2u
2
a + a
2
+ au − a
−au
a
11
=
−u
4
a − u
3
a + 2u
2
a + a
2
+ 2au − a
−a
2
u
2
+ u
3
a − 2au
a
2
=
a
2
u
u
3
a
2
− a
2
u − a
a
1
=
a
2
u
−a
2
u − a
a
4
=
−u
−u
3
+ u
a
9
=
−u
4
a − u
3
a + 2u
2
a + a
2
+ 2au − a
−au
a
6
=
−u
4
a − a
2
u
2
− u
3
a + 2u
2
a + a
2
+ au − a
a
2
u
2
a
12
=
−u
3
a
2
− u
4
a + 2a
2
u + 2u
2
a − a
−u
4
a
2
+ u
3
a
2
+ a
2
u
2
+ u
3
a − 2a
2
u + a
2
− 2au
(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
15
+ 10u
14
+ ··· − 5u + 1
c
2
, c
4
, c
6
c
9
u
15
− 5u
13
+ ··· + u − 1
c
3
, c
7
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
c
5
, c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
c
8
u
15
− 10u
14
+ ··· − 5u − 1
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
15
− 10y
14
+ ··· − 25y − 1
c
2
, c
4
, c
6
c
9
y
15
− 10y
14
+ ··· − 5y − 1
c
3
, c
7
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
c
5
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
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 = −0.267245 + 1.141130I
c = 0.468414 − 1.190710I
d = 0.713895 − 0.727282I
−2.40108 −3.48110
u = 1.21774
a = −0.586248 − 0.597241I
b = −0.267245 − 1.141130I
c = 0.468414 + 1.190710I
d = 0.713895 + 0.727282I
−2.40108 −3.48110
u = 1.21774
a = 1.17250
b = −1.10790
c = 0.411897
d = −1.42779
−2.40108 −3.48110
u = 0.309916 + 0.549911I
a = −0.331889 − 0.475420I
b = 0.771871 + 0.426319I
c = 0.798410 + 0.227308I
d = −0.158581 + 0.329849I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.309916 + 0.549911I
a = 1.02081 − 1.15644I
b = −2.04410 + 2.63713I
c = 0.506739 − 0.052679I
d = −0.952303 − 0.202954I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.309916 + 0.549911I
a = −0.68892 + 1.63186I
b = −0.283376 − 0.303192I
c = −3.90469 − 4.46850I
d = 1.110880 − 0.126895I
−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 = 0.771871 − 0.426319I
c = 0.798410 − 0.227308I
d = −0.158581 − 0.329849I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.309916 − 0.549911I
a = 1.02081 + 1.15644I
b = −2.04410 − 2.63713I
c = 0.506739 + 0.052679I
d = −0.952303 + 0.202954I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = 0.309916 − 0.549911I
a = −0.68892 − 1.63186I
b = −0.283376 + 0.303192I
c = −3.90469 + 4.46850I
d = 1.110880 + 0.126895I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −1.41878 + 0.21917I
a = −1.060130 − 0.090162I
b = 0.545899 + 0.598986I
c = 0.395542 + 0.016365I
d = −1.52386 + 0.10442I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.41878 + 0.21917I
a = 0.532546 + 0.656825I
b = 0.86595 + 1.32754I
c = 0.148945 + 1.208370I
d = 0.899520 + 0.815176I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.41878 + 0.21917I
a = 0.527587 − 0.566662I
b = −0.03504 − 1.71384I
c = 0.380692 − 0.931915I
d = 0.624338 − 0.919600I
−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 = 0.545899 − 0.598986I
c = 0.395542 − 0.016365I
d = −1.52386 − 0.10442I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −1.41878 − 0.21917I
a = 0.532546 − 0.656825I
b = 0.86595 − 1.32754I
c = 0.148945 − 1.208370I
d = 0.899520 − 0.815176I
−5.87256 − 4.40083I −6.74431 + 3.49859I
u = −1.41878 − 0.21917I
a = 0.527587 + 0.566662I
b = −0.03504 + 1.71384I
c = 0.380692 + 0.931915I
d = 0.624338 + 0.919600I
−5.87256 − 4.40083I −6.74431 + 3.49859I
18
III. I
v
1
= hc, d + 1, b, a − v, v
2
− v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
5
=
v
0
a
8
=
1
0
a
10
=
0
−1
a
11
=
v − 1
−1
a
2
=
v
0
a
1
=
v
0
a
4
=
v
0
a
9
=
1
−1
a
6
=
0
1
a
12
=
v − 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 1
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
2
c
5
, c
10
u
2
− u + 1
c
6
, c
8
(u + 1)
2
c
9
(u − 1)
2
c
11
, c
12
u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
8
, c
9
(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 = −1.00000
1.64493 − 2.02988I 3.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0
c = 0
d = −1.00000
1.64493 + 2.02988I 3.00000 − 3.46410I
22
IV. I
v
2
= ha, d, c − 1, b + v + 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
5
=
0
−v − 1
a
8
=
1
0
a
10
=
1
0
a
11
=
1
v
a
2
=
v
v + 1
a
1
=
0
v + 1
a
4
=
v
0
a
9
=
1
0
a
6
=
1
0
a
12
=
v + 1
v
(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
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
10
, c
12
u
2
+ u + 1
c
11
u
2
− u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
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 = 1.00000
d = 0
−1.64493 − 2.02988I −9.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = 1.00000
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
26
V. I
v
3
= ha, d + 1, c + a, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
5
=
0
1
a
8
=
1
0
a
10
=
0
−1
a
11
=
0
−1
a
2
=
1
−1
a
1
=
0
−1
a
4
=
1
0
a
9
=
1
−1
a
6
=
0
1
a
12
=
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
9
u − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
u
c
4
, c
6
, c
8
u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
y
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 = 0
d = −1.00000
0 0
30
VI. I
v
4
= hc, d + 1, a
2
v
2
+ 2cav + v
2
a + c
2
+ cv + v
2
, bv − 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
5
=
a
b
a
8
=
1
0
a
10
=
0
−1
a
11
=
−a − 1
ba − 1
a
2
=
−a + v
−b
a
1
=
−a
−b
a
4
=
v
0
a
9
=
1
−1
a
6
=
0
1
a
12
=
−a − 1
ba + a
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
2
+ v
2
− 4a − 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 −2.23950 − 4.57670I
32
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
15
+ 10u
14
+ ··· − 5u + 1)
· (u
47
+ 54u
46
+ ··· + 544u + 256)
c
2
u
2
(u − 1)
3
(u
15
− 5u
13
+ ··· + u − 1)(u
47
− 8u
46
+ ··· + 56u + 16)
c
3
, c
7
u
5
(u
5
− u
4
+ ··· + u + 1)
3
(u
47
+ 2u
46
+ ··· + 1024u + 512)
c
4
u
2
(u + 1)
3
(u
15
− 5u
13
+ ··· + u − 1)(u
47
− 8u
46
+ ··· + 56u + 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
3
· (u
47
+ 2u
46
+ ··· + 16u + 4)
c
6
u
2
(u + 1)
3
(u
15
− 5u
13
+ ··· + u − 1)(u
47
+ 8u
46
+ ··· + 56u + 16)
c
8
u
2
(u + 1)
3
(u
15
− 10u
14
+ ··· − 5u − 1)
· (u
47
− 14u
46
+ ··· + 6688u − 256)
c
9
u
2
(u − 1)
3
(u
15
− 5u
13
+ ··· + u − 1)(u
47
+ 8u
46
+ ··· + 56u + 16)
c
10
u(u
2
− u + 1)(u
2
+ u + 1)(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
3
· (u
47
− 2u
46
+ ··· − 21456u + 2592)
c
12
u(u
2
+ u + 1)
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
3
· (u
47
+ 24u
46
+ ··· + 216u − 16)
33
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 25y − 1)
· (y
47
− 114y
46
+ ··· − 1990144y − 65536)
c
2
, c
4
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 5y − 1)
· (y
47
− 54y
46
+ ··· + 544y − 256)
c
3
, c
7
y
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
47
− 30y
46
+ ··· + 1572864y − 262144)
c
5
, c
11
y(y
2
+ y + 1)
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
3
· (y
47
+ 24y
46
+ ··· + 216y − 16)
c
6
, c
9
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 5y − 1)
· (y
47
− 14y
46
+ ··· + 6688y − 256)
c
8
y
2
(y − 1)
3
(y
15
− 10y
14
+ ··· − 25y − 1)
· (y
47
+ 46y
46
+ ··· + 11182592y − 65536)
c
10
y(y
2
+ y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
3
· (y
47
− 24y
46
+ ··· + 353776896y − 6718464)
c
12
y(y
2
+ y + 1)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
3
· (y
47
+ 48y
45
+ ··· + 67872y − 256)
34
