12n
0064
(K12n
0064
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 11 4 8 6 11
Solving Sequence
4,9
5
6,10,11
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
= h5.37718 × 10
22
u
20
− 1.64184 × 10
23
u
19
+ ··· + 1.18107 × 10
25
d + 1.07557 × 10
24
,
− 6.27749 × 10
23
u
20
+ 1.76680 × 10
24
u
19
+ ··· + 2.36214 × 10
25
c − 1.96176 × 10
25
,
4.23740 × 10
23
u
20
− 1.22487 × 10
24
u
19
+ ··· + 1.18107 × 10
25
b + 1.27339 × 10
25
,
1.40999 × 10
24
u
20
− 3.56156 × 10
24
u
19
+ ··· + 1.18107 × 10
25
a + 8.01422 × 10
25
, u
21
− 3u
20
+ ··· − 32u + 32i
I
u
2
= h182575u
12
c − 236482u
12
+ ··· − 1091678c − 1127628,
152367u
12
c − 563814u
12
+ ··· − 1320834c + 1767620,
− 72875u
12
+ 44515u
11
+ ··· + 2792824b − 1858402,
− 112621u
12
− 236501u
11
+ ··· + 1396412a − 268784,
u
13
+ u
12
+ 8u
11
+ 7u
10
+ 22u
9
+ 18u
8
+ 20u
7
+ 21u
6
− u
5
+ 5u
4
+ 8u
3
− 9u
2
+ 4u − 4i
I
v
1
= ha, d, c − v, b − v − 1, v
2
+ v + 1i
I
v
2
= ha, d + v + 1, c + a, 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 52 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
= h5.38 × 10
22
u
20
− 1.64 × 10
23
u
19
+ · · · + 1.18 × 10
25
d + 1.08 ×
10
24
, −6.28×10
23
u
20
+1.77× 10
24
u
19
+· · ·+ 2.36 ×10
25
c −1.96 ×10
25
, 4.24×
10
23
u
20
− 1.22 × 10
24
u
19
+ · · · + 1.18 × 10
25
b + 1.27 × 10
25
, 1.41 × 10
24
u
20
−
3.56 × 10
24
u
19
+ · · · + 1.18 × 10
25
a + 8.01 × 10
25
, u
21
− 3u
20
+ · · · − 32u + 32i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
6
=
−0.119382u
20
+ 0.301554u
19
+ ··· + 2.04903u − 6.78557
−0.0358777u
20
+ 0.103709u
19
+ ··· − 0.171384u − 1.07817
a
10
=
u
u
a
11
=
0.0265755u
20
− 0.0747968u
19
+ ··· + 1.58156u + 0.830504
−0.00455281u
20
+ 0.0139013u
19
+ ··· + 0.741851u − 0.0910676
a
12
=
0.110080u
20
− 0.272643u
19
+ ··· − 1.63885u + 6.53790
0.0218260u
20
− 0.0597864u
19
+ ··· + 1.24989u + 0.673905
a
3
=
−0.135687u
20
+ 0.428519u
19
+ ··· − 9.42931u + 0.294719
−0.0249995u
20
+ 0.0790420u
19
+ ··· − 2.07117u + 0.534476
a
2
=
−0.155819u
20
+ 0.505452u
19
+ ··· − 12.3868u + 0.446924
−0.0342125u
20
+ 0.109848u
19
+ ··· − 3.24459u + 1.06368
a
1
=
−0.0835048u
20
+ 0.197846u
19
+ ··· + 2.22041u − 5.70740
−0.0132576u
20
+ 0.0335645u
19
+ ··· − 0.815372u − 0.607226
a
8
=
−0.0311283u
20
+ 0.0886981u
19
+ ··· − 0.839713u − 0.921571
−0.00455281u
20
+ 0.0139013u
19
+ ··· + 0.741851u − 0.0910676
a
7
=
−0.0442495u
20
+ 0.128821u
19
+ ··· − 1.53238u − 1.07932
−0.0176741u
20
+ 0.0540245u
19
+ ··· + 0.0491821u − 0.248813
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
203971647344418191706557
1476335887006576019057698
u
20
+
2056765698754565732069615
5905343548026304076230792
u
19
+
··· +
11041294381070090419087484
738167943503288009528849
u −
9937042912284907740395116
738167943503288009528849
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 11u
20
+ ··· + 40u − 16
c
2
, c
5
u
21
+ u
20
+ ··· − 12u − 4
c
3
u
21
− u
20
+ ··· − 636u − 612
c
4
, c
9
u
21
+ 3u
20
+ ··· − 32u − 32
c
6
, c
7
, c
8
c
10
, c
11
u
21
− 5u
20
+ ··· − 2u + 1
c
12
u
21
+ 31u
20
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− y
20
+ ··· + 3616y − 256
c
2
, c
5
y
21
+ 11y
20
+ ··· + 40y − 16
c
3
y
21
− 13y
20
+ ··· + 1093608y − 374544
c
4
, c
9
y
21
+ 15y
20
+ ··· − 4096y − 1024
c
6
, c
7
, c
8
c
10
, c
11
y
21
− 31y
20
+ ··· − 4y − 1
c
12
y
21
− 71y
20
+ ··· − 144y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036987 + 1.146540I
a = −1.67484 + 0.76411I
b = −1.039700 + 0.250963I
c = 0.578318 + 0.602865I
d = −0.222232 + 0.595413I
−3.32924 + 4.98790I −8.89610 − 7.00933I
u = 0.036987 − 1.146540I
a = −1.67484 − 0.76411I
b = −1.039700 − 0.250963I
c = 0.578318 − 0.602865I
d = −0.222232 − 0.595413I
−3.32924 − 4.98790I −8.89610 + 7.00933I
u = −0.154679 + 0.793727I
a = 1.361070 + 0.002102I
b = 0.594261 + 0.212903I
c = −0.412466 + 0.647829I
d = 0.050314 + 0.532414I
−0.57334 − 1.34767I −3.83291 + 5.35474I
u = −0.154679 − 0.793727I
a = 1.361070 − 0.002102I
b = 0.594261 − 0.212903I
c = −0.412466 − 0.647829I
d = 0.050314 − 0.532414I
−0.57334 + 1.34767I −3.83291 − 5.35474I
u = −0.470495 + 0.448103I
a = 0.393211 + 0.432952I
b = 0.089016 + 0.741526I
c = −0.409901 + 0.397885I
d = −0.268303 + 0.555704I
0.53740 − 1.37698I 1.82779 + 4.46485I
u = −0.470495 − 0.448103I
a = 0.393211 − 0.432952I
b = 0.089016 − 0.741526I
c = −0.409901 − 0.397885I
d = −0.268303 − 0.555704I
0.53740 + 1.37698I 1.82779 − 4.46485I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.128491 + 0.614288I
a = −4.90846 − 2.20239I
b = −0.714269 − 0.685882I
c = 0.535926 + 1.193030I
d = −0.103617 + 0.330827I
−2.84340 − 1.62330I −11.63179 + 1.59969I
u = −0.128491 − 0.614288I
a = −4.90846 + 2.20239I
b = −0.714269 + 0.685882I
c = 0.535926 − 1.193030I
d = −0.103617 − 0.330827I
−2.84340 + 1.62330I −11.63179 − 1.59969I
u = 0.518224 + 0.162575I
a = 0.202826 + 0.452275I
b = 0.680830 + 0.757240I
c = 0.507737 + 0.210413I
d = 0.583653 + 0.355856I
−0.25092 − 2.48183I 1.69657 + 3.99164I
u = 0.518224 − 0.162575I
a = 0.202826 − 0.452275I
b = 0.680830 − 0.757240I
c = 0.507737 − 0.210413I
d = 0.583653 − 0.355856I
−0.25092 + 2.48183I 1.69657 − 3.99164I
u = −1.63718
a = 0.346145
b = −1.85424
c = 0.993823
d = −0.623198
−10.0156 −8.03320
u = −0.11848 + 1.68160I
a = 0.200381 + 0.247887I
b = 0.39834 + 2.34923I
c = −0.035721 − 0.977610I
d = −0.04009 − 2.59088I
−10.91870 − 3.26339I −9.90010 + 2.49959I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11848 − 1.68160I
a = 0.200381 − 0.247887I
b = 0.39834 − 2.34923I
c = −0.035721 + 0.977610I
d = −0.04009 + 2.59088I
−10.91870 + 3.26339I −9.90010 − 2.49959I
u = 1.80226 + 0.29000I
a = 0.004080 + 0.391285I
b = 1.85242 + 0.01325I
c = −0.934416 + 0.075142I
d = 0.669749 + 0.073622I
−14.0445 − 5.1370I −11.02836 + 2.94498I
u = 1.80226 − 0.29000I
a = 0.004080 − 0.391285I
b = 1.85242 − 0.01325I
c = −0.934416 − 0.075142I
d = 0.669749 − 0.073622I
−14.0445 + 5.1370I −11.02836 − 2.94498I
u = −0.77417 + 1.65700I
a = 0.954850 − 0.309679I
b = 1.86573 + 1.18814I
c = −0.199071 − 0.900171I
d = −0.19629 − 2.45464I
−15.0920 − 8.4883I −8.50111 + 3.29621I
u = −0.77417 − 1.65700I
a = 0.954850 + 0.309679I
b = 1.86573 − 1.18814I
c = −0.199071 + 0.900171I
d = −0.19629 + 2.45464I
−15.0920 + 8.4883I −8.50111 − 3.29621I
u = 0.94230 + 1.60086I
a = −1.068660 − 0.473361I
b = −2.07474 + 0.83917I
c = 0.234926 − 0.876218I
d = 0.22253 − 2.40487I
−18.0417 + 14.4957I −10.41632 − 6.77876I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.94230 − 1.60086I
a = −1.068660 + 0.473361I
b = −2.07474 − 0.83917I
c = 0.234926 + 0.876218I
d = 0.22253 + 2.40487I
−18.0417 − 14.4957I −10.41632 + 6.77876I
u = 0.66513 + 1.94791I
a = −0.637538 − 0.381670I
b = −1.22477 + 1.08336I
c = 0.137757 − 0.866713I
d = 0.11588 − 2.45183I
18.5711 + 4.0668I −12.30105 − 1.16982I
u = 0.66513 − 1.94791I
a = −0.637538 + 0.381670I
b = −1.22477 − 1.08336I
c = 0.137757 + 0.866713I
d = 0.11588 + 2.45183I
18.5711 − 4.0668I −12.30105 + 1.16982I
8
II. I
u
2
= h1.83 × 10
5
cu
12
− 2.36 × 10
5
u
12
+ · · · − 1.09 × 10
6
c − 1.13 ×
10
6
, 1.52 × 10
5
cu
12
− 5.64 × 10
5
u
12
+ · · · − 1.32 × 10
6
c + 1.77 × 10
6
, −7.29 ×
10
4
u
12
+ 4.45 × 10
4
u
11
+ · · · + 2.79 × 10
6
b − 1.86 × 10
6
, −1.13 × 10
5
u
12
−
2.37 × 10
5
u
11
+ · · · + 1.40 × 10
6
a − 2.69 × 10
5
, u
13
+ u
12
+ · · · + 4u − 4i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
6
=
0.0806503u
12
+ 0.169363u
11
+ ··· − 0.809567u + 0.192482
0.0260937u
12
− 0.0159391u
11
+ ··· − 1.52812u + 0.665420
a
10
=
u
u
a
11
=
c
−0.130746cu
12
+ 0.169350u
12
+ ··· + 0.781774c + 0.807518
a
12
=
−0.0887131cu
12
− 0.0545566u
12
+ ··· + 0.677399c + 0.472939
−0.0887131cu
12
+ 0.195443u
12
+ ··· + 0.677399c + 1.47294
a
3
=
−0.0356093u
12
− 0.00301684u
11
+ ··· + 0.564974u + 1.08093
−0.201964u
12
− 0.195466u
11
+ ··· + 1.82111u − 0.0563709
a
2
=
0.105649u
12
+ 0.155843u
11
+ ··· − 0.983332u + 1.00693
−0.158242u
12
− 0.179223u
11
+ ··· + 1.32649u − 0.126777
a
1
=
0.0545566u
12
+ 0.185302u
11
+ ··· + 0.718555u − 0.472939
−0.0847798u
12
− 0.0614206u
11
+ ··· + 1.83288u − 1.18840
a
8
=
−0.130746cu
12
+ 0.169350u
12
+ ··· − 0.218226c + 0.807518
−0.130746cu
12
+ 0.169350u
12
+ ··· + 0.781774c + 0.807518
a
7
=
−0.130746cu
12
+ 0.169350u
12
+ ··· − 0.218226c + 0.807518
−0.130746cu
12
+ 0.169350u
12
+ ··· + 0.781774c + 0.807518
(ii) Obstruction class = −1
(iii) Cusp Shapes =
498055
698206
u
12
+
527627
698206
u
11
+ ··· −
3711195
698206
u −
2197714
349103
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
13
+ 8u
12
+ ··· + 5u − 1)
2
c
2
, c
5
(u
13
+ 2u
12
+ ··· + u − 1)
2
c
3
(u
13
− 2u
12
+ ··· + 3u − 1)
2
c
4
, c
9
(u
13
− u
12
+ ··· + 4u + 4)
2
c
6
, c
7
, c
8
c
10
, c
11
u
26
− 3u
25
+ ··· − 24u − 16
c
12
u
26
+ 23u
25
+ ··· + 1824u + 256
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
13
− 4y
12
+ ··· + 85y − 1)
2
c
2
, c
5
(y
13
+ 8y
12
+ ··· + 5y − 1)
2
c
3
(y
13
− 16y
12
+ ··· + 5y − 1)
2
c
4
, c
9
(y
13
+ 15y
12
+ ··· − 56y − 16)
2
c
6
, c
7
, c
8
c
10
, c
11
y
26
− 23y
25
+ ··· − 1824y + 256
c
12
y
26
− 43y
25
+ ··· − 2728448y + 65536
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997974 + 0.288600I
a = 0.076708 + 0.591760I
b = 0.651902 + 0.098264I
c = −0.683330 − 0.720692I
d = −0.91523 − 1.71878I
−4.89799 − 2.52293I −10.35428 + 4.38707I
u = −0.997974 + 0.288600I
a = 0.076708 + 0.591760I
b = 0.651902 + 0.098264I
c = 1.258530 + 0.227197I
d = −0.435677 + 0.098702I
−4.89799 − 2.52293I −10.35428 + 4.38707I
u = −0.997974 − 0.288600I
a = 0.076708 − 0.591760I
b = 0.651902 − 0.098264I
c = −0.683330 + 0.720692I
d = −0.91523 + 1.71878I
−4.89799 + 2.52293I −10.35428 − 4.38707I
u = −0.997974 − 0.288600I
a = 0.076708 − 0.591760I
b = 0.651902 − 0.098264I
c = 1.258530 − 0.227197I
d = −0.435677 − 0.098702I
−4.89799 + 2.52293I −10.35428 − 4.38707I
u = 0.452299 + 0.637242I
a = 0.45190 − 1.65380I
b = −0.181675 − 0.314949I
c = −1.050080 + 0.855900I
d = 0.262779 + 0.278726I
−2.32452 − 0.99909I −8.45638 − 0.58191I
u = 0.452299 + 0.637242I
a = 0.45190 − 1.65380I
b = −0.181675 − 0.314949I
c = 0.416509 + 0.482947I
d = 0.133116 + 0.626828I
−2.32452 − 0.99909I −8.45638 − 0.58191I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452299 − 0.637242I
a = 0.45190 + 1.65380I
b = −0.181675 + 0.314949I
c = −1.050080 − 0.855900I
d = 0.262779 − 0.278726I
−2.32452 + 0.99909I −8.45638 + 0.58191I
u = 0.452299 − 0.637242I
a = 0.45190 + 1.65380I
b = −0.181675 + 0.314949I
c = 0.416509 − 0.482947I
d = 0.133116 − 0.626828I
−2.32452 + 0.99909I −8.45638 + 0.58191I
u = −0.032142 + 0.650070I
a = 0.248194 − 0.369192I
b = 0.469692 − 1.165710I
c = 0.289254 + 0.995266I
d = −0.055887 + 0.387220I
−2.68970 + 2.36301I −10.56487 − 4.19898I
u = −0.032142 + 0.650070I
a = 0.248194 − 0.369192I
b = 0.469692 − 1.165710I
c = −0.06776 − 1.79178I
d = −0.12255 − 3.88363I
−2.68970 + 2.36301I −10.56487 − 4.19898I
u = −0.032142 − 0.650070I
a = 0.248194 + 0.369192I
b = 0.469692 + 1.165710I
c = 0.289254 − 0.995266I
d = −0.055887 − 0.387220I
−2.68970 − 2.36301I −10.56487 + 4.19898I
u = −0.032142 − 0.650070I
a = 0.248194 + 0.369192I
b = 0.469692 + 1.165710I
c = −0.06776 + 1.79178I
d = −0.12255 + 3.88363I
−2.68970 − 2.36301I −10.56487 + 4.19898I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612460
a = 0.691952
b = −0.370964
c = 0.817082
d = 1.22597
−2.28684 −1.88180
u = 0.612460
a = 0.691952
b = −0.370964
c = −1.88000
d = 0.284677
−2.28684 −1.88180
u = 0.25689 + 1.55234I
a = 1.066370 + 0.108716I
b = 1.72213 − 0.39249I
c = 0.088362 − 1.008150I
d = 0.10585 − 2.61952I
−7.65433 + 3.30324I −7.16390 − 2.39821I
u = 0.25689 + 1.55234I
a = 1.066370 + 0.108716I
b = 1.72213 − 0.39249I
c = 0.567403 + 0.506935I
d = −0.308927 + 0.755560I
−7.65433 + 3.30324I −7.16390 − 2.39821I
u = 0.25689 − 1.55234I
a = 1.066370 − 0.108716I
b = 1.72213 + 0.39249I
c = 0.088362 + 1.008150I
d = 0.10585 + 2.61952I
−7.65433 − 3.30324I −7.16390 + 2.39821I
u = 0.25689 − 1.55234I
a = 1.066370 − 0.108716I
b = 1.72213 + 0.39249I
c = 0.567403 − 0.506935I
d = −0.308927 − 0.755560I
−7.65433 − 3.30324I −7.16390 + 2.39821I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.50699 + 1.66583I
a = −1.177520 + 0.121564I
b = −1.86437 − 0.33459I
c = −0.143355 − 0.943399I
d = −0.15313 − 2.52888I
−11.16570 − 8.60203I −9.58542 + 5.32797I
u = −0.50699 + 1.66583I
a = −1.177520 + 0.121564I
b = −1.86437 − 0.33459I
c = −0.543494 + 0.487244I
d = 0.309381 + 0.852342I
−11.16570 − 8.60203I −9.58542 + 5.32797I
u = −0.50699 − 1.66583I
a = −1.177520 − 0.121564I
b = −1.86437 + 0.33459I
c = −0.143355 + 0.943399I
d = −0.15313 + 2.52888I
−11.16570 + 8.60203I −9.58542 − 5.32797I
u = −0.50699 − 1.66583I
a = −1.177520 − 0.121564I
b = −1.86437 + 0.33459I
c = −0.543494 − 0.487244I
d = 0.309381 − 0.852342I
−11.16570 + 8.60203I −9.58542 − 5.32797I
u = 0.02169 + 1.76519I
a = −1.011620 + 0.245053I
b = −1.61220 − 0.23341I
c = 0.005990 − 0.955765I
d = 0.00639 − 2.56843I
−12.07010 + 1.38297I −10.93425 − 0.71622I
u = 0.02169 + 1.76519I
a = −1.011620 + 0.245053I
b = −1.61220 − 0.23341I
c = −0.606568 + 0.477299I
d = 0.418568 + 0.712063I
−12.07010 + 1.38297I −10.93425 − 0.71622I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02169 − 1.76519I
a = −1.011620 − 0.245053I
b = −1.61220 + 0.23341I
c = 0.005990 + 0.955765I
d = 0.00639 + 2.56843I
−12.07010 − 1.38297I −10.93425 + 0.71622I
u = 0.02169 − 1.76519I
a = −1.011620 − 0.245053I
b = −1.61220 + 0.23341I
c = −0.606568 − 0.477299I
d = 0.418568 − 0.712063I
−12.07010 − 1.38297I −10.93425 + 0.71622I
16
III. I
v
1
= 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
6
=
0
v + 1
a
10
=
v
0
a
11
=
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 − 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
7
, c
8
c
9
, c
10
u
2
c
6
(u − 1)
2
c
11
, c
12
(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
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(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 = 0.500000 + 0.866025I
c = −0.500000 + 0.866025I
d = 0
−1.64493 − 2.02988I −3.00000 + 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 −3.00000 − 3.46410I
20
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
6
=
0
v + 1
a
10
=
v
0
a
11
=
0
−v − 1
a
12
=
0
−v − 1
a
3
=
1
−v
a
2
=
v + 1
−v
a
1
=
0
−v − 1
a
8
=
v
v + 1
a
7
=
0
v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 1
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
6
, c
9
c
11
, c
12
u
2
c
7
, c
8
(u − 1)
2
c
10
(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
6
, c
9
c
11
, c
12
y
2
c
7
, c
8
, c
10
(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 = 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
24
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
6
=
1
0
a
10
=
−1
0
a
11
=
0
−1
a
12
=
1
−1
a
3
=
1
0
a
2
=
1
0
a
1
=
1
0
a
8
=
−1
1
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
25
(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
10
, c
12
u + 1
c
7
, c
8
, 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
9
y
c
6
, c
7
, c
8
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
−3.28987 −12.0000
28
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
6
=
0
b
a
10
=
v
0
a
11
=
−b + 1
d
a
12
=
−b + 1
d + b
a
3
=
1
−b + 1
a
2
=
b
−b + 1
a
1
=
0
−b
a
8
=
b + v − 1
−d
a
7
=
b − 1
−d
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
+ 4b − 12
(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 = ···
−3.28987 + 2.02988I −9.43145 − 3.98230I
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
13
+ 8u
12
+ ··· + 5u − 1)
2
· (u
21
+ 11u
20
+ ··· + 40u − 16)
c
2
u(u
2
+ u + 1)
2
(u
13
+ 2u
12
+ ··· + u − 1)
2
(u
21
+ u
20
+ ··· − 12u − 4)
c
3
u(u
2
− u + 1)
2
(u
13
− 2u
12
+ ··· + 3u − 1)
2
· (u
21
− u
20
+ ··· − 636u − 612)
c
4
, c
9
u
5
(u
13
− u
12
+ ··· + 4u + 4)
2
(u
21
+ 3u
20
+ ··· − 32u − 32)
c
5
u(u
2
− u + 1)
2
(u
13
+ 2u
12
+ ··· + u − 1)
2
(u
21
+ u
20
+ ··· − 12u − 4)
c
6
u
2
(u − 1)
2
(u + 1)(u
21
− 5u
20
+ ··· − 2u + 1)
· (u
26
− 3u
25
+ ··· − 24u − 16)
c
7
, c
8
u
2
(u − 1)
3
(u
21
− 5u
20
+ ··· − 2u + 1)(u
26
− 3u
25
+ ··· − 24u − 16)
c
10
u
2
(u + 1)
3
(u
21
− 5u
20
+ ··· − 2u + 1)(u
26
− 3u
25
+ ··· − 24u − 16)
c
11
u
2
(u − 1)(u + 1)
2
(u
21
− 5u
20
+ ··· − 2u + 1)
· (u
26
− 3u
25
+ ··· − 24u − 16)
c
12
u
2
(u + 1)
3
(u
21
+ 31u
20
+ ··· − 4u + 1)
· (u
26
+ 23u
25
+ ··· + 1824u + 256)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
13
− 4y
12
+ ··· + 85y − 1)
2
· (y
21
− y
20
+ ··· + 3616y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
13
+ 8y
12
+ ··· + 5y − 1)
2
· (y
21
+ 11y
20
+ ··· + 40y − 16)
c
3
y(y
2
+ y + 1)
2
(y
13
− 16y
12
+ ··· + 5y − 1)
2
· (y
21
− 13y
20
+ ··· + 1093608y − 374544)
c
4
, c
9
y
5
(y
13
+ 15y
12
+ ··· − 56y − 16)
2
· (y
21
+ 15y
20
+ ··· − 4096y − 1024)
c
6
, c
7
, c
8
c
10
, c
11
y
2
(y − 1)
3
(y
21
− 31y
20
+ ··· − 4y − 1)
· (y
26
− 23y
25
+ ··· − 1824y + 256)
c
12
y
2
(y − 1)
3
(y
21
− 71y
20
+ ··· − 144y − 1)
· (y
26
− 43y
25
+ ··· − 2728448y + 65536)
32
