12n
0261
(K12n
0261
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 10 3 7 5 6 11
Solving Sequence
3,8 5,9,10
11 2 1 4 7 6 12
c
8
c
10
c
2
c
1
c
4
c
7
c
6
c
12
c
3
, c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.82214 × 10
22
u
20
− 3.29635 × 10
23
u
19
+ ··· + 1.18107 × 10
25
d − 1.00440 × 10
25
,
− 6.72232 × 10
22
u
20
+ 3.09213 × 10
23
u
19
+ ··· + 2.36214 × 10
25
c − 1.53724 × 10
25
,
5.37718 × 10
22
u
20
− 1.64184 × 10
23
u
19
+ ··· + 1.18107 × 10
25
b + 1.07557 × 10
24
,
− 6.27749 × 10
23
u
20
+ 1.76680 × 10
24
u
19
+ ··· + 2.36214 × 10
25
a − 1.96176 × 10
25
,
u
21
− 3u
20
+ ··· − 32u + 32i
I
u
2
= h−182575u
12
− 264525u
11
+ ··· + 1396412d − 304734,
1091678u
12
a − 2056829u
12
+ ··· + 8227316a + 8353986,
182575u
12
a − 236482u
12
+ ··· − 1091678a − 1127628,
152367u
12
a − 563814u
12
+ ··· − 1320834a + 1767620,
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 − 1, b + v + 1, v
2
+ v + 1i
I
v
2
= hc, d − 1, b, a − v, 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 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).
1
I. I
u
1
= h5.82 × 10
22
u
20
− 3.30 × 10
23
u
19
+ · · · + 1.18 × 10
25
d − 1.00 ×
10
25
, −6.72×10
22
u
20
+3.09× 10
23
u
19
+· · ·+ 2.36 ×10
25
c −1.54 ×10
25
, 5.38×
10
22
u
20
− 1.64 × 10
23
u
19
+ · · · + 1.18 × 10
25
b + 1.08 × 10
24
, −6.28 × 10
23
u
20
+
1.77 × 10
24
u
19
+ · · · + 2.36 × 10
25
a − 1.96 × 10
25
, u
21
− 3u
20
+ · · · − 32u + 32i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
5
=
0.0265755u
20
− 0.0747968u
19
+ ··· + 1.58156u + 0.830504
−0.00455281u
20
+ 0.0139013u
19
+ ··· + 0.741851u − 0.0910676
a
9
=
1
−u
2
a
10
=
0.00284586u
20
− 0.0130904u
19
+ ··· + 0.686169u + 0.650783
−0.00492955u
20
+ 0.0279099u
19
+ ··· − 1.68092u + 0.850415
a
11
=
−0.0210595u
20
+ 0.0850046u
19
+ ··· − 3.46686u + 1.92380
−0.00576337u
20
+ 0.0431394u
19
+ ··· − 2.97976u + 1.42272
a
2
=
−0.0311283u
20
+ 0.0886981u
19
+ ··· − 0.839713u − 0.921571
−0.00455281u
20
+ 0.0139013u
19
+ ··· + 0.741851u − 0.0910676
a
1
=
−0.0311283u
20
+ 0.0886981u
19
+ ··· − 0.839713u − 0.921571
−0.0204279u
20
+ 0.0622591u
19
+ ··· − 0.104280u − 0.241041
a
4
=
u
u
a
7
=
0.00284586u
20
− 0.0130904u
19
+ ··· + 0.686169u + 0.650783
0.00468667u
20
− 0.0299351u
19
+ ··· + 1.91768u − 0.996105
a
6
=
0.00777542u
20
− 0.0410003u
19
+ ··· + 2.36709u − 0.199631
0.00392727u
20
− 0.0344353u
19
+ ··· + 2.49530u − 1.41598
a
12
=
−0.00320223u
20
+ 0.0332571u
19
+ ··· − 2.57523u + 0.998926
0.0165563u
20
− 0.0374854u
19
+ ··· + 0.0371713u + 0.859283
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
203971647344418191706557
1476335887006576019057698
u
20
+
2056765698754565732069615
5905343548026304076230792
u
19
+
··· +
11041294381070090419087484
738167943503288009528849
u −
9937042912284907740395116
738167943503288009528849
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 31u
20
+ ··· − 4u + 1
c
2
, c
4
, c
6
c
7
, c
9
u
21
− 5u
20
+ ··· − 2u + 1
c
3
, c
8
u
21
+ 3u
20
+ ··· − 32u − 32
c
5
, c
11
u
21
+ u
20
+ ··· − 12u − 4
c
10
u
21
− u
20
+ ··· − 636u − 612
c
12
u
21
+ 11u
20
+ ··· + 40u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 71y
20
+ ··· − 144y − 1
c
2
, c
4
, c
6
c
7
, c
9
y
21
− 31y
20
+ ··· − 4y − 1
c
3
, c
8
y
21
+ 15y
20
+ ··· − 4096y − 1024
c
5
, c
11
y
21
+ 11y
20
+ ··· + 40y − 16
c
10
y
21
− 13y
20
+ ··· + 1093608y − 374544
c
12
y
21
− y
20
+ ··· + 3616y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036987 + 1.146540I
a = 0.578318 + 0.602865I
b = −0.222232 + 0.595413I
c = 0.512526 + 0.210362I
d = 0.669819 − 0.685364I
−3.32924 + 4.98790I −8.89610 − 7.00933I
u = 0.036987 − 1.146540I
a = 0.578318 − 0.602865I
b = −0.222232 − 0.595413I
c = 0.512526 − 0.210362I
d = 0.669819 + 0.685364I
−3.32924 − 4.98790I −8.89610 + 7.00933I
u = −0.154679 + 0.793727I
a = −0.412466 + 0.647829I
b = 0.050314 + 0.532414I
c = 0.634334 − 0.187007I
d = 0.450400 + 0.427591I
−0.57334 − 1.34767I −3.83291 + 5.35474I
u = −0.154679 − 0.793727I
a = −0.412466 − 0.647829I
b = 0.050314 − 0.532414I
c = 0.634334 + 0.187007I
d = 0.450400 − 0.427591I
−0.57334 + 1.34767I −3.83291 − 5.35474I
u = −0.470495 + 0.448103I
a = −0.409901 + 0.397885I
b = −0.268303 + 0.555704I
c = 0.888871 − 0.334537I
d = −0.014563 + 0.370881I
0.53740 − 1.37698I 1.82779 + 4.46485I
u = −0.470495 − 0.448103I
a = −0.409901 − 0.397885I
b = −0.268303 − 0.555704I
c = 0.888871 + 0.334537I
d = −0.014563 − 0.370881I
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 = 0.535926 + 1.193030I
b = −0.103617 + 0.330827I
c = 0.549782 + 0.053680I
d = 0.801726 − 0.175920I
−2.84340 − 1.62330I −11.63179 + 1.59969I
u = −0.128491 − 0.614288I
a = 0.535926 − 1.193030I
b = −0.103617 − 0.330827I
c = 0.549782 − 0.053680I
d = 0.801726 + 0.175920I
−2.84340 + 1.62330I −11.63179 − 1.59969I
u = 0.518224 + 0.162575I
a = 0.507737 + 0.210413I
b = 0.583653 + 0.355856I
c = 1.221470 + 0.303490I
d = −0.228914 − 0.191587I
−0.25092 − 2.48183I 1.69657 + 3.99164I
u = 0.518224 − 0.162575I
a = 0.507737 − 0.210413I
b = 0.583653 − 0.355856I
c = 1.221470 − 0.303490I
d = −0.228914 + 0.191587I
−0.25092 + 2.48183I 1.69657 − 3.99164I
u = −1.63718
a = 0.993823
b = −0.623198
c = 0.380652
d = 1.62707
−10.0156 −8.03320
u = −0.11848 + 1.68160I
a = −0.035721 − 0.977610I
b = −0.04009 − 2.59088I
c = −1.53144 + 0.13174I
d = −1.64818 − 0.05576I
−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 = −0.035721 + 0.977610I
b = −0.04009 + 2.59088I
c = −1.53144 − 0.13174I
d = −1.64818 + 0.05576I
−10.91870 + 3.26339I −9.90010 − 2.49959I
u = 1.80226 + 0.29000I
a = −0.934416 + 0.075142I
b = 0.669749 + 0.073622I
c = 0.368644 − 0.018467I
d = 1.70586 + 0.13555I
−14.0445 − 5.1370I −11.02836 + 2.94498I
u = 1.80226 − 0.29000I
a = −0.934416 − 0.075142I
b = 0.669749 − 0.073622I
c = 0.368644 + 0.018467I
d = 1.70586 − 0.13555I
−14.0445 + 5.1370I −11.02836 − 2.94498I
u = −0.77417 + 1.65700I
a = −0.199071 − 0.900171I
b = −0.19629 − 2.45464I
c = −1.170520 + 0.665347I
d = −1.64570 − 0.36703I
−15.0920 − 8.4883I −8.50111 + 3.29621I
u = −0.77417 − 1.65700I
a = −0.199071 + 0.900171I
b = −0.19629 + 2.45464I
c = −1.170520 − 0.665347I
d = −1.64570 + 0.36703I
−15.0920 + 8.4883I −8.50111 − 3.29621I
u = 0.94230 + 1.60086I
a = 0.234926 − 0.876218I
b = 0.22253 − 2.40487I
c = −1.054920 − 0.759955I
d = −1.62407 + 0.44958I
−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 = 0.234926 + 0.876218I
b = 0.22253 + 2.40487I
c = −1.054920 + 0.759955I
d = −1.62407 − 0.44958I
−18.0417 − 14.4957I −10.41632 + 6.77876I
u = 0.66513 + 1.94791I
a = 0.137757 − 0.866713I
b = 0.11588 − 2.45183I
c = −1.109070 − 0.438193I
d = −1.77991 + 0.30814I
18.5711 + 4.0668I −12.30105 − 1.16982I
u = 0.66513 − 1.94791I
a = 0.137757 + 0.866713I
b = 0.11588 + 2.45183I
c = −1.109070 + 0.438193I
d = −1.77991 − 0.30814I
18.5711 − 4.0668I −12.30105 + 1.16982I
8
II. I
u
2
= h−1.83 × 10
5
u
12
− 2.65 × 10
5
u
11
+ · · · + 1.40 × 10
6
d − 3.05 ×
10
5
, 1.09 × 10
6
au
12
− 2.06 × 10
6
u
12
+ · · · + 8.23 × 10
6
a + 8.35 × 10
6
, 1.83 ×
10
5
au
12
− 2.36 × 10
5
u
12
+ · · · − 1.09 × 10
6
a − 1.13 × 10
6
, 1.52 × 10
5
au
12
−
5.64 × 10
5
u
12
+ · · · − 1.32 × 10
6
a + 1.77 × 10
6
, u
13
+ u
12
+ · · · + 4u − 4i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
5
=
a
−0.130746au
12
+ 0.169350u
12
+ ··· + 0.781774a + 0.807518
a
9
=
1
−u
2
a
10
=
−0.195443au
12
+ 0.368235u
12
+ ··· − 1.47294a − 1.49562
0.130746u
12
+ 0.189432u
11
+ ··· − 0.691165u + 0.218226
a
11
=
−0.169350au
12
+ 0.368235u
12
+ ··· − 0.807518a − 1.49562
0.0521873au
12
+ 0.261492u
12
+ ··· + 1.33084a − 0.563547
a
2
=
−0.130746au
12
+ 0.169350u
12
+ ··· − 0.218226a + 0.807518
−0.130746au
12
+ 0.169350u
12
+ ··· + 0.781774a + 0.807518
a
1
=
−0.130746au
12
+ 0.169350u
12
+ ··· − 0.218226a + 0.807518
−0.112072au
12
+ 0.214783u
12
+ ··· + 1.01652a + 1.16237
a
4
=
u
u
a
7
=
−0.195443au
12
+ 0.368235u
12
+ ··· − 1.47294a − 1.49562
−0.0586861au
12
− 0.0773597au
11
+ ··· − 0.522983a − 1
a
6
=
−0.195443au
12
+ 0.237489u
12
+ ··· − 1.47294a − 1.71384
−0.0586861au
12
+ 0.0186736u
12
+ ··· − 0.522983a − 0.765256
a
12
=
−0.280165au
12
+ 0.0140927u
12
+ ··· + 0.328803a − 1.76474
−0.00702658au
12
+ 0.208441u
12
+ ··· + 1.44074a − 0.142777
(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
26
+ 23u
25
+ ··· + 1824u + 256
c
2
, c
4
, c
6
c
7
, c
9
u
26
− 3u
25
+ ··· − 24u − 16
c
3
, c
8
(u
13
− u
12
+ ··· + 4u + 4)
2
c
5
, c
11
(u
13
+ 2u
12
+ ··· + u − 1)
2
c
10
(u
13
− 2u
12
+ ··· + 3u − 1)
2
c
12
(u
13
+ 8u
12
+ ··· + 5u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− 43y
25
+ ··· − 2728448y + 65536
c
2
, c
4
, c
6
c
7
, c
9
y
26
− 23y
25
+ ··· − 1824y + 256
c
3
, c
8
(y
13
+ 15y
12
+ ··· − 56y − 16)
2
c
5
, c
11
(y
13
+ 8y
12
+ ··· + 5y − 1)
2
c
10
(y
13
− 16y
12
+ ··· + 5y − 1)
2
c
12
(y
13
− 4y
12
+ ··· + 85y − 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997974 + 0.288600I
a = −0.683330 − 0.720692I
b = −0.91523 − 1.71878I
c = 0.429264 + 0.025235I
d = 1.321540 − 0.136474I
−4.89799 − 2.52293I −10.35428 + 4.38707I
u = −0.997974 + 0.288600I
a = 1.258530 + 0.227197I
b = −0.435677 + 0.098702I
c = 0.38670 + 1.83409I
d = −0.889938 − 0.522023I
−4.89799 − 2.52293I −10.35428 + 4.38707I
u = −0.997974 − 0.288600I
a = −0.683330 + 0.720692I
b = −0.91523 + 1.71878I
c = 0.429264 − 0.025235I
d = 1.321540 + 0.136474I
−4.89799 + 2.52293I −10.35428 − 4.38707I
u = −0.997974 − 0.288600I
a = 1.258530 − 0.227197I
b = −0.435677 − 0.098702I
c = 0.38670 − 1.83409I
d = −0.889938 + 0.522023I
−4.89799 + 2.52293I −10.35428 − 4.38707I
u = 0.452299 + 0.637242I
a = −1.050080 + 0.855900I
b = 0.262779 + 0.278726I
c = 0.752720 + 0.325368I
d = 0.119367 − 0.483853I
−2.32452 − 0.99909I −8.45638 − 0.58191I
u = 0.452299 + 0.637242I
a = 0.416509 + 0.482947I
b = 0.133116 + 0.626828I
c = 0.485499 − 0.067773I
d = 1.020370 + 0.282033I
−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 = −1.050080 − 0.855900I
b = 0.262779 − 0.278726I
c = 0.752720 − 0.325368I
d = 0.119367 + 0.483853I
−2.32452 + 0.99909I −8.45638 + 0.58191I
u = 0.452299 − 0.637242I
a = 0.416509 − 0.482947I
b = 0.133116 − 0.626828I
c = 0.485499 + 0.067773I
d = 1.020370 − 0.282033I
−2.32452 + 0.99909I −8.45638 + 0.58191I
u = −0.032142 + 0.650070I
a = 0.289254 + 0.995266I
b = −0.055887 + 0.387220I
c = −5.95031 + 0.48273I
d = −1.166960 − 0.013545I
−2.68970 + 2.36301I −10.56487 − 4.19898I
u = −0.032142 + 0.650070I
a = −0.06776 − 1.79178I
b = −0.12255 − 3.88363I
c = 0.598447 + 0.056382I
d = 0.656289 − 0.156046I
−2.68970 + 2.36301I −10.56487 − 4.19898I
u = −0.032142 − 0.650070I
a = 0.289254 − 0.995266I
b = −0.055887 − 0.387220I
c = −5.95031 − 0.48273I
d = −1.166960 + 0.013545I
−2.68970 − 2.36301I −10.56487 + 4.19898I
u = −0.032142 − 0.650070I
a = −0.06776 + 1.79178I
b = −0.12255 + 3.88363I
c = 0.598447 − 0.056382I
d = 0.656289 + 0.156046I
−2.68970 − 2.36301I −10.56487 + 4.19898I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612460
a = 0.817082
b = 1.22597
c = 0.464808
d = 1.15142
−2.28684 −1.88180
u = 0.612460
a = −1.88000
b = 0.284677
c = 2.00172
d = −0.500430
−2.28684 −1.88180
u = 0.25689 + 1.55234I
a = 0.088362 − 1.008150I
b = 0.10585 − 2.61952I
c = 0.441695 + 0.272101I
d = 0.641176 − 1.011030I
−7.65433 + 3.30324I −7.16390 − 2.39821I
u = 0.25689 + 1.55234I
a = 0.567403 + 0.506935I
b = −0.308927 + 0.755560I
c = −1.63150 − 0.33817I
d = −1.58768 + 0.12181I
−7.65433 + 3.30324I −7.16390 − 2.39821I
u = 0.25689 − 1.55234I
a = 0.088362 + 1.008150I
b = 0.10585 + 2.61952I
c = 0.441695 − 0.272101I
d = 0.641176 + 1.011030I
−7.65433 − 3.30324I −7.16390 + 2.39821I
u = 0.25689 − 1.55234I
a = 0.567403 − 0.506935I
b = −0.308927 − 0.755560I
c = −1.63150 + 0.33817I
d = −1.58768 − 0.12181I
−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 = −0.143355 − 0.943399I
b = −0.15313 − 2.52888I
c = 0.416555 − 0.312499I
d = 0.536120 + 1.152390I
−11.16570 − 8.60203I −9.58542 + 5.32797I
u = −0.50699 + 1.66583I
a = −0.543494 + 0.487244I
b = 0.309381 + 0.852342I
c = −1.36379 + 0.50699I
d = −1.64422 − 0.23949I
−11.16570 − 8.60203I −9.58542 + 5.32797I
u = −0.50699 − 1.66583I
a = −0.143355 + 0.943399I
b = −0.15313 + 2.52888I
c = 0.416555 + 0.312499I
d = 0.536120 − 1.152390I
−11.16570 + 8.60203I −9.58542 − 5.32797I
u = −0.50699 − 1.66583I
a = −0.543494 − 0.487244I
b = 0.309381 − 0.852342I
c = −1.36379 − 0.50699I
d = −1.64422 + 0.23949I
−11.16570 + 8.60203I −9.58542 − 5.32797I
u = 0.02169 + 1.76519I
a = 0.005990 − 0.955765I
b = 0.00639 − 2.56843I
c = 0.406243 − 0.232132I
d = 0.855680 + 1.060360I
−12.07010 + 1.38297I −10.93425 − 0.71622I
u = 0.02169 + 1.76519I
a = −0.606568 + 0.477299I
b = 0.418568 + 0.712063I
c = −1.45478 − 0.02149I
d = −1.68724 + 0.01015I
−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 = 0.005990 + 0.955765I
b = 0.00639 + 2.56843I
c = 0.406243 + 0.232132I
d = 0.855680 − 1.060360I
−12.07010 − 1.38297I −10.93425 + 0.71622I
u = 0.02169 − 1.76519I
a = −0.606568 − 0.477299I
b = 0.418568 − 0.712063I
c = −1.45478 + 0.02149I
d = −1.68724 − 0.01015I
−12.07010 − 1.38297I −10.93425 + 0.71622I
16
III. I
v
1
= ha, d, c − 1, b + v + 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
5
=
0
−v − 1
a
9
=
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
7
=
1
0
a
6
=
1
0
a
12
=
v + 1
v
(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
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
18
(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
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 = 1.00000
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = 1.00000
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
20
IV. I
v
2
= hc, d − 1, b, a − v, v
2
+ v + 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
5
=
v
0
a
9
=
1
0
a
10
=
0
1
a
11
=
v + 1
1
a
2
=
v
0
a
1
=
v
0
a
4
=
v
0
a
7
=
1
−1
a
6
=
0
−1
a
12
=
v + 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 5
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
2
c
5
, c
10
u
2
− u + 1
c
6
, c
7
(u − 1)
2
c
9
(u + 1)
2
c
11
, c
12
u
2
+ u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
7
, c
9
(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 = −0.500000 + 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
24
V. I
v
3
= ha, d − 1, c + a, b + 1, v + 1i
(i) Arc colorings
a
3
=
−1
0
a
8
=
1
0
a
5
=
0
−1
a
9
=
1
0
a
10
=
0
1
a
11
=
0
1
a
2
=
−1
1
a
1
=
0
1
a
4
=
−1
0
a
7
=
1
−1
a
6
=
0
−1
a
12
=
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
6
c
7
u − 1
c
3
, c
5
, c
8
c
10
, c
11
, c
12
u
c
4
, c
9
u + 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
9
y − 1
c
3
, c
5
, c
8
c
10
, c
11
, c
12
y
27
(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
−3.28987 −12.0000
28
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
8
=
1
0
a
5
=
a
b
a
9
=
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
7
=
1
−1
a
6
=
0
−1
a
12
=
−a + 1
−ba + a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −b
2
− v
2
+ 4a − 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 −11.65094 + 3.33332I
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
21
+ 31u
20
+ ··· − 4u + 1)
· (u
26
+ 23u
25
+ ··· + 1824u + 256)
c
2
, c
6
, c
7
u
2
(u − 1)
3
(u
21
− 5u
20
+ ··· − 2u + 1)(u
26
− 3u
25
+ ··· − 24u − 16)
c
3
, c
8
u
5
(u
13
− u
12
+ ··· + 4u + 4)
2
(u
21
+ 3u
20
+ ··· − 32u − 32)
c
4
, c
9
u
2
(u + 1)
3
(u
21
− 5u
20
+ ··· − 2u + 1)(u
26
− 3u
25
+ ··· − 24u − 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)(u
13
+ 2u
12
+ ··· + u − 1)
2
· (u
21
+ u
20
+ ··· − 12u − 4)
c
10
u(u
2
− u + 1)(u
2
+ u + 1)(u
13
− 2u
12
+ ··· + 3u − 1)
2
· (u
21
− u
20
+ ··· − 636u − 612)
c
12
u(u
2
+ u + 1)
2
(u
13
+ 8u
12
+ ··· + 5u − 1)
2
· (u
21
+ 11u
20
+ ··· + 40u − 16)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
21
− 71y
20
+ ··· − 144y − 1)
· (y
26
− 43y
25
+ ··· − 2728448y + 65536)
c
2
, c
4
, c
6
c
7
, c
9
y
2
(y − 1)
3
(y
21
− 31y
20
+ ··· − 4y − 1)
· (y
26
− 23y
25
+ ··· − 1824y + 256)
c
3
, c
8
y
5
(y
13
+ 15y
12
+ ··· − 56y − 16)
2
· (y
21
+ 15y
20
+ ··· − 4096y − 1024)
c
5
, c
11
y(y
2
+ y + 1)
2
(y
13
+ 8y
12
+ ··· + 5y − 1)
2
· (y
21
+ 11y
20
+ ··· + 40y − 16)
c
10
y(y
2
+ y + 1)
2
(y
13
− 16y
12
+ ··· + 5y − 1)
2
· (y
21
− 13y
20
+ ··· + 1093608y − 374544)
c
12
y(y
2
+ y + 1)
2
(y
13
− 4y
12
+ ··· + 85y − 1)
2
· (y
21
− y
20
+ ··· + 3616y − 256)
32
