12n
0223
(K12n
0223
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 12 9 4 6 8 5 6 11
Solving Sequence
4,7 6,8
9
3,12
5 2 1 11 10
c
7
c
8
c
3
c
5
c
2
c
1
c
11
c
10
c
4
, c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.05608 × 10
32
u
27
+ 2.39983 × 10
32
u
26
+ ··· + 4.71199 × 10
33
d − 1.14579 × 10
30
,
− 7.16121 × 10
28
u
27
+ 2.11432 × 10
32
u
26
+ ··· + 9.42397 × 10
33
c + 9.50662 × 10
33
,
7.43837 × 10
31
u
27
− 2.05180 × 10
32
u
26
+ ··· + 4.71199 × 10
33
b − 3.81499 × 10
32
,
5.68907 × 10
31
u
27
− 1.81131 × 10
32
u
26
+ ··· + 1.88479 × 10
34
a − 1.63326 × 10
34
, u
28
− 3u
27
+ ··· − 64u + 32i
I
u
2
= h−7778149750u
19
a + 21085480149u
19
+ ··· + 37111822100a − 70739740318,
18555911050u
19
a − 33847094283u
19
+ ··· − 266919956828a + 210342367834,
4182326921u
19
a + 3076005459u
19
+ ··· − 29433713862a + 28068851486,
49133842327u
19
a − 33157787379u
19
+ ··· − 204672432210a + 75288972938,
u
20
+ u
19
+ ··· − 8u − 4i
I
v
1
= hc, d − v, b, a − 1, v
2
+ v + 1i
I
v
2
= ha, d + v, −av + c − v − 1, b + 1, v
2
+ v + 1i
I
v
3
= ha, d − 1, c + a, b + 1, v + 1i
I
v
4
= ha, d
2
a + d
2
v + dc − dv − d + v + 1, d
2
v
2
− v
2
d − dv + v
2
+ 2v + 1,
dca + dcv − da − dv + c
2
− cv − av − 2c − a + 1, v
2
dc − v
2
d − v
2
c − v
2
a − cv − 2av − a,
dav + da + dv + cv + c − v − 1, c
2
v
2
+ v
2
ca + a
2
v
2
+ cav − v
2
c + 2a
2
v + v
2
a + a
2
+ av + v
2
, b + 1i
* 5 irreducible components of dim
C
= 0, with total 73 representations.
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
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h−1.06 × 10
32
u
27
+ 2.40 × 10
32
u
26
+ · · · + 4.71 × 10
33
d − 1.15 ×
10
30
, −7.16×10
28
u
27
+2.11× 10
32
u
26
+· · ·+ 9.42 ×10
33
c +9.51 ×10
33
, 7.44×
10
31
u
27
− 2.05 × 10
32
u
26
+ · · · + 4.71 × 10
33
b − 3.81 × 10
32
, 5.69 × 10
31
u
27
−
1.81 × 10
32
u
26
+ · · · + 1.88 × 10
34
a − 1.63 × 10
34
, u
28
− 3u
27
+ · · · − 64u + 32i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
6
=
−0.00301840u
27
+ 0.00961014u
26
+ ··· − 0.512168u + 0.866547
−0.0157861u
27
+ 0.0435442u
26
+ ··· − 1.70037u + 0.0809635
a
8
=
1
−u
2
a
9
=
−0.00301840u
27
+ 0.00961014u
26
+ ··· − 0.512168u + 0.866547
0.0152750u
27
− 0.0402637u
26
+ ··· + 1.56827u − 0.0632056
a
3
=
−u
u
a
12
=
7.59893 × 10
−6
u
27
− 0.0224355u
26
+ ··· + 3.09707u − 1.00877
0.0224127u
27
− 0.0509304u
26
+ ··· + 1.00828u + 0.000243166
a
5
=
−0.00253011u
27
− 0.00819574u
26
+ ··· + 1.54524u − 1.53844
0.000554935u
27
− 0.00115373u
26
+ ··· + 0.673369u + 0.0965888
a
2
=
0.00197517u
27
+ 0.00934947u
26
+ ··· − 2.21861u + 1.44185
0.000554935u
27
− 0.00115373u
26
+ ··· + 0.673369u + 0.0965888
a
1
=
0.00578915u
27
− 0.00833409u
26
+ ··· − 1.28926u + 0.936700
−0.00325904u
27
+ 0.0165298u
26
+ ··· − 0.255976u + 0.601743
a
11
=
−0.00186302u
27
− 0.00814762u
26
+ ··· + 1.14940u − 0.178203
0.0260420u
27
− 0.0682809u
26
+ ··· + 2.68644u − 0.560928
a
10
=
−0.0188045u
27
+ 0.0531544u
26
+ ··· − 2.21254u + 0.947510
0.00903337u
27
− 0.0298398u
26
+ ··· + 1.30721u − 0.185253
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.217306u
27
+ 0.532528u
26
+ ··· − 20.8205u − 2.69421
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
28
+ 9u
27
+ ··· + u + 1
c
2
, c
4
, c
6
c
8
u
28
− 5u
27
+ ··· − 3u + 1
c
3
, c
7
u
28
− 3u
27
+ ··· − 64u + 32
c
5
, c
11
u
28
+ u
27
+ ··· + 8u + 4
c
10
u
28
− u
27
+ ··· + 1736u + 1252
c
12
u
28
+ 9u
27
+ ··· − 56u + 16
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
28
+ 31y
27
+ ··· + 39y + 1
c
2
, c
4
, c
6
c
8
y
28
− 9y
27
+ ··· − y + 1
c
3
, c
7
y
28
− 15y
27
+ ··· + 3072y + 1024
c
5
, c
11
y
28
+ 9y
27
+ ··· − 56y + 16
c
10
y
28
+ 33y
27
+ ··· − 17874936y + 1567504
c
12
y
28
+ 21y
27
+ ··· − 6432y + 256
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387721 + 0.851263I
a = 0.488405 − 0.103669I
b = −0.747142 − 0.797802I
c = −0.79488 − 1.41620I
d = −0.89737 + 1.22574I
−4.11180 − 3.97036I −11.03599 + 5.92521I
u = 0.387721 − 0.851263I
a = 0.488405 + 0.103669I
b = −0.747142 + 0.797802I
c = −0.79488 + 1.41620I
d = −0.89737 − 1.22574I
−4.11180 + 3.97036I −11.03599 − 5.92521I
u = −0.048850 + 0.802561I
a = 0.570907 + 0.125829I
b = −0.313957 + 0.493682I
c = 0.167451 + 0.444862I
d = 0.365209 − 0.112658I
−1.00554 + 1.45329I −3.70692 − 4.69342I
u = −0.048850 − 0.802561I
a = 0.570907 − 0.125829I
b = −0.313957 − 0.493682I
c = 0.167451 − 0.444862I
d = 0.365209 + 0.112658I
−1.00554 − 1.45329I −3.70692 + 4.69342I
u = 1.195800 + 0.230197I
a = 0.28063 − 1.44187I
b = −0.310268 + 1.162650I
c = 1.94455 − 0.47579I
d = −2.43482 + 0.12132I
0.294538 + 1.243650I −3.92766 − 2.52803I
u = 1.195800 − 0.230197I
a = 0.28063 + 1.44187I
b = −0.310268 − 1.162650I
c = 1.94455 + 0.47579I
d = −2.43482 − 0.12132I
0.294538 − 1.243650I −3.92766 + 2.52803I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.512543 + 0.548760I
a = 0.810755 + 0.367303I
b = 0.214405 + 0.021676I
c = 1.012830 − 0.121876I
d = −0.586000 − 0.493336I
0.77284 + 1.38296I 2.12358 − 4.20585I
u = 0.512543 − 0.548760I
a = 0.810755 − 0.367303I
b = 0.214405 − 0.021676I
c = 1.012830 + 0.121876I
d = −0.586000 + 0.493336I
0.77284 − 1.38296I 2.12358 + 4.20585I
u = 1.240340 + 0.558685I
a = −0.19285 − 1.48947I
b = −0.74229 + 1.43353I
c = −2.20653 − 0.25596I
d = 2.59385 + 1.55023I
−1.36469 + 9.34331I −7.27750 − 7.90351I
u = 1.240340 − 0.558685I
a = −0.19285 + 1.48947I
b = −0.74229 − 1.43353I
c = −2.20653 + 0.25596I
d = 2.59385 − 1.55023I
−1.36469 − 9.34331I −7.27750 + 7.90351I
u = −0.306891 + 1.332240I
a = 0.448937 + 0.172706I
b = −0.32703 + 1.40380I
c = −0.489703 − 0.253197I
d = −0.487603 + 0.574696I
2.80790 + 2.77377I −2.82329 − 2.35775I
u = −0.306891 − 1.332240I
a = 0.448937 − 0.172706I
b = −0.32703 − 1.40380I
c = −0.489703 + 0.253197I
d = −0.487603 − 0.574696I
2.80790 − 2.77377I −2.82329 + 2.35775I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599185 + 0.160658I
a = 1.279080 − 0.454824I
b = −0.032693 + 0.151013I
c = 0.283924 − 1.075350I
d = −0.002639 − 0.689945I
−0.29820 + 2.58448I 1.60498 − 4.48843I
u = −0.599185 − 0.160658I
a = 1.279080 + 0.454824I
b = −0.032693 − 0.151013I
c = 0.283924 + 1.075350I
d = −0.002639 + 0.689945I
−0.29820 − 2.58448I 1.60498 + 4.48843I
u = 0.449039 + 1.329150I
a = 0.437109 − 0.156367I
b = −0.53079 − 1.49203I
c = 0.884456 + 0.900024I
d = 0.79911 − 1.57972I
2.18074 − 8.77807I −4.21049 + 7.13120I
u = 0.449039 − 1.329150I
a = 0.437109 + 0.156367I
b = −0.53079 + 1.49203I
c = 0.884456 − 0.900024I
d = 0.79911 + 1.57972I
2.18074 + 8.77807I −4.21049 − 7.13120I
u = −1.36520 + 0.37405I
a = 0.022772 + 1.320010I
b = −0.40047 − 1.49490I
c = −0.019011 + 0.257960I
d = 0.070537 + 0.359277I
3.38586 − 5.92225I −1.05943 + 5.53498I
u = −1.36520 − 0.37405I
a = 0.022772 − 1.320010I
b = −0.40047 + 1.49490I
c = −0.019011 − 0.257960I
d = 0.070537 − 0.359277I
3.38586 + 5.92225I −1.05943 − 5.53498I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.128781 + 0.527754I
a = 0.536628 − 0.033094I
b = −0.720363 − 0.196098I
c = 0.53943 + 1.55105I
d = 0.749102 − 0.484434I
−2.91457 + 1.71407I −11.28016 − 2.34859I
u = 0.128781 − 0.527754I
a = 0.536628 + 0.033094I
b = −0.720363 + 0.196098I
c = 0.53943 − 1.55105I
d = 0.749102 + 0.484434I
−2.91457 − 1.71407I −11.28016 + 2.34859I
u = 1.36013 + 0.80195I
a = −0.423558 − 1.271240I
b = −1.02615 + 1.75013I
c = 1.77646 + 0.86372I
d = −1.72355 − 2.59940I
5.1047 + 16.3284I −4.49305 − 9.50798I
u = 1.36013 − 0.80195I
a = −0.423558 + 1.271240I
b = −1.02615 − 1.75013I
c = 1.77646 − 0.86372I
d = −1.72355 + 2.59940I
5.1047 − 16.3284I −4.49305 + 9.50798I
u = −1.41454 + 0.73498I
a = −0.342095 + 1.249650I
b = −0.89493 − 1.79229I
c = 0.231981 − 0.161062I
d = 0.209770 − 0.398331I
6.34910 − 10.12380I −2.60535 + 5.05088I
u = −1.41454 − 0.73498I
a = −0.342095 − 1.249650I
b = −0.89493 + 1.79229I
c = 0.231981 + 0.161062I
d = 0.209770 + 0.398331I
6.34910 + 10.12380I −2.60535 − 5.05088I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57578 + 0.34473I
a = 0.317772 + 0.829753I
b = 0.74767 − 1.25595I
c = −1.012250 − 0.840874I
d = 1.30521 + 1.67398I
9.40632 + 3.24641I 0.187126 − 1.202849I
u = 1.57578 − 0.34473I
a = 0.317772 − 0.829753I
b = 0.74767 + 1.25595I
c = −1.012250 + 0.840874I
d = 1.30521 − 1.67398I
9.40632 − 3.24641I 0.187126 + 1.202849I
u = −1.61547 + 0.19947I
a = 0.265518 − 0.890486I
b = 0.58401 + 1.42833I
c = −0.318722 + 0.271187I
d = −0.460792 + 0.501668I
9.82407 + 3.16258I 0.50415 − 3.81889I
u = −1.61547 − 0.19947I
a = 0.265518 + 0.890486I
b = 0.58401 − 1.42833I
c = −0.318722 − 0.271187I
d = −0.460792 − 0.501668I
9.82407 − 3.16258I 0.50415 + 3.81889I
10
II. I
u
2
= h−7.78 × 10
9
au
19
+ 2.11 × 10
10
u
19
+ · · · + 3.71 × 10
10
a − 7.07 ×
10
10
, 1.86× 10
10
au
19
−3.38 × 10
10
u
19
+· · · −2.67 × 10
11
a + 2.10 ×10
11
, 4.18×
10
9
au
19
+ 3.08 × 10
9
u
19
+ · · · − 2.94 × 10
10
a + 2.81 × 10
10
, 4.91 × 10
10
au
19
−
3.32 × 10
10
u
19
+ · · · − 2.05 × 10
11
a + 7.53 × 10
10
, u
20
+ u
19
+ · · · − 8u − 4i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
6
=
a
−0.154609au
19
− 0.113711u
19
+ ··· + 1.08808a − 1.03762
a
8
=
1
−u
2
a
9
=
a
0.154609au
19
+ 0.113711u
19
+ ··· − 1.08808a + 1.03762
a
3
=
−u
u
a
12
=
−0.171490au
19
+ 0.312807u
19
+ ··· + 2.46682a − 1.94394
0.143768au
19
− 0.389735u
19
+ ··· − 0.685959a + 1.30752
a
5
=
−0.272020au
19
+ 0.0220200u
19
+ ··· + 2.18366a − 0.183663
0.227980u
19
+ 0.382589u
18
+ ··· − 1.74114u − 1.81634
a
2
=
0.272020au
19
− 0.250000u
19
+ ··· − 2.18366a + 2
0.227980u
19
+ 0.382589u
18
+ ··· − 1.74114u − 1.81634
a
1
=
0.392720au
19
− 0.370700u
19
+ ··· − 2.80210a + 2.61843
−0.120700au
19
+ 0.348680u
19
+ ··· + 0.618434a − 2.43477
a
11
=
−0.486024au
19
+ 0.312807u
19
+ ··· + 3.53102a − 1.94394
0.345654au
19
− 0.0895665u
19
+ ··· − 1.54407a + 0.431179
a
10
=
−0.154609au
19
− 0.113711u
19
+ ··· + 2.08808a − 1.03762
0.409919au
19
+ 0.367791u
19
+ ··· − 1.57088a + 0.0883006
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4263121051
13525530286
u
19
−
7308875275
13525530286
u
18
+ ···+
12379392387
13525530286
u −
17100277556
6762765143
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
40
+ 19u
39
+ ··· + 288u + 256
c
2
, c
4
, c
6
c
8
u
40
− 3u
39
+ ··· + 40u − 16
c
3
, c
7
(u
20
+ u
19
+ ··· − 8u − 4)
2
c
5
, c
11
(u
20
+ 2u
19
+ ··· − 2u + 1)
2
c
10
(u
20
− 2u
19
+ ··· + 36u + 17)
2
c
12
(u
20
+ 6u
19
+ ··· − 2u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
40
+ y
39
+ ··· − 4022784y + 65536
c
2
, c
4
, c
6
c
8
y
40
− 19y
39
+ ··· − 288y + 256
c
3
, c
7
(y
20
− 15y
19
+ ··· − 24y + 16)
2
c
5
, c
11
(y
20
+ 6y
19
+ ··· − 2y + 1)
2
c
10
(y
20
+ 30y
19
+ ··· + 1254y + 289)
2
c
12
(y
20
+ 18y
19
+ ··· − 86y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.685016 + 0.443026I
a = 0.458140 − 0.042470I
b = −1.314980 − 0.467098I
c = −1.19123 − 1.35374I
d = 1.34492 + 3.28525I
−4.73160 + 1.82256I −11.12541 − 5.12436I
u = 0.685016 + 0.443026I
a = −0.09245 − 3.22238I
b = −0.921725 + 0.625666I
c = −3.57126 − 2.48620I
d = 0.21627 + 1.45508I
−4.73160 + 1.82256I −11.12541 − 5.12436I
u = 0.685016 − 0.443026I
a = 0.458140 + 0.042470I
b = −1.314980 + 0.467098I
c = −1.19123 + 1.35374I
d = 1.34492 − 3.28525I
−4.73160 − 1.82256I −11.12541 + 5.12436I
u = 0.685016 − 0.443026I
a = −0.09245 + 3.22238I
b = −0.921725 − 0.625666I
c = −3.57126 + 2.48620I
d = 0.21627 − 1.45508I
−4.73160 − 1.82256I −11.12541 + 5.12436I
u = −1.176520 + 0.244065I
a = 0.577483 − 0.947538I
b = 0.310218 + 0.817249I
c = 1.70100 − 0.02090I
d = −1.82568 + 1.36744I
0.28251 − 3.88098I −3.93502 + 4.02252I
u = −1.176520 + 0.244065I
a = 0.27911 + 1.47852I
b = −0.342116 − 1.145120I
c = −1.71890 + 0.80569I
d = 1.99616 − 0.43974I
0.28251 − 3.88098I −3.93502 + 4.02252I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.176520 − 0.244065I
a = 0.577483 + 0.947538I
b = 0.310218 − 0.817249I
c = 1.70100 + 0.02090I
d = −1.82568 − 1.36744I
0.28251 + 3.88098I −3.93502 − 4.02252I
u = −1.176520 − 0.244065I
a = 0.27911 − 1.47852I
b = −0.342116 + 1.145120I
c = −1.71890 − 0.80569I
d = 1.99616 + 0.43974I
0.28251 + 3.88098I −3.93502 − 4.02252I
u = −1.256010 + 0.124886I
a = 0.339080 + 1.286040I
b = −0.124777 − 1.175340I
c = 0.00787 − 1.59574I
d = 0.528809 + 0.982333I
1.249910 + 0.191668I −2.26430 + 0.22109I
u = −1.256010 + 0.124886I
a = 0.408592 + 0.009946I
b = −2.08731 + 0.17219I
c = 0.339897 + 0.815901I
d = −0.18941 − 2.00525I
1.249910 + 0.191668I −2.26430 + 0.22109I
u = −1.256010 − 0.124886I
a = 0.339080 − 1.286040I
b = −0.124777 + 1.175340I
c = 0.00787 + 1.59574I
d = 0.528809 − 0.982333I
1.249910 − 0.191668I −2.26430 − 0.22109I
u = −1.256010 − 0.124886I
a = 0.408592 − 0.009946I
b = −2.08731 − 0.17219I
c = 0.339897 − 0.815901I
d = −0.18941 + 2.00525I
1.249910 − 0.191668I −2.26430 − 0.22109I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.268400 + 0.295253I
a = 0.150939 − 1.397650I
b = −0.352887 + 1.306450I
c = 0.00100 + 1.90027I
d = −0.322075 − 1.194470I
0.89345 + 5.67427I −3.40403 − 5.66395I
u = 1.268400 + 0.295253I
a = 0.406505 − 0.023413I
b = −2.08796 − 0.41006I
c = 0.448812 + 0.837239I
d = 0.55980 − 2.41060I
0.89345 + 5.67427I −3.40403 − 5.66395I
u = 1.268400 − 0.295253I
a = 0.150939 + 1.397650I
b = −0.352887 − 1.306450I
c = 0.00100 − 1.90027I
d = −0.322075 + 1.194470I
0.89345 − 5.67427I −3.40403 + 5.66395I
u = 1.268400 − 0.295253I
a = 0.406505 + 0.023413I
b = −2.08796 + 0.41006I
c = 0.448812 − 0.837239I
d = 0.55980 + 2.41060I
0.89345 − 5.67427I −3.40403 + 5.66395I
u = −0.439566 + 0.534727I
a = 0.820860 − 0.314763I
b = 0.162005 − 0.050556I
c = 1.70038 − 0.48109I
d = 0.255350 + 0.690923I
−2.07115 + 0.86143I −6.44675 + 0.99952I
u = −0.439566 + 0.534727I
a = 0.487252 + 0.053221I
b = −1.007970 + 0.455517I
c = −0.536806 + 0.918810I
d = 0.490181 − 1.120710I
−2.07115 + 0.86143I −6.44675 + 0.99952I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.439566 − 0.534727I
a = 0.820860 + 0.314763I
b = 0.162005 + 0.050556I
c = 1.70038 + 0.48109I
d = 0.255350 − 0.690923I
−2.07115 − 0.86143I −6.44675 − 0.99952I
u = −0.439566 − 0.534727I
a = 0.487252 − 0.053221I
b = −1.007970 − 0.455517I
c = −0.536806 − 0.918810I
d = 0.490181 + 1.120710I
−2.07115 − 0.86143I −6.44675 − 0.99952I
u = −0.089922 + 1.317200I
a = 0.481544 − 0.234697I
b = 0.209138 − 1.109080I
c = −0.377586 + 0.174434I
d = −0.78245 − 1.28050I
3.24441 + 2.97363I −2.07664 − 2.68538I
u = −0.089922 + 1.317200I
a = 0.469189 + 0.202331I
b = −0.034817 + 1.235550I
c = 0.927267 − 0.657327I
d = 0.195810 + 0.513040I
3.24441 + 2.97363I −2.07664 − 2.68538I
u = −0.089922 − 1.317200I
a = 0.481544 + 0.234697I
b = 0.209138 + 1.109080I
c = −0.377586 − 0.174434I
d = −0.78245 + 1.28050I
3.24441 − 2.97363I −2.07664 + 2.68538I
u = −0.089922 − 1.317200I
a = 0.469189 − 0.202331I
b = −0.034817 − 1.235550I
c = 0.927267 + 0.657327I
d = 0.195810 − 0.513040I
3.24441 − 2.97363I −2.07664 + 2.68538I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36144
a = 0.339214 + 1.109820I
b = 0.119387 − 1.233010I
c = 0.299266 + 0.242908I
d = −0.407433 + 0.330704I
4.11381 0.668270
u = 1.36144
a = 0.339214 − 1.109820I
b = 0.119387 + 1.233010I
c = 0.299266 − 0.242908I
d = −0.407433 − 0.330704I
4.11381 0.668270
u = −0.610309
a = 0.465000
b = −1.32374
c = −0.750025
d = 1.42139
−2.43031 −0.135410
u = −0.610309
a = 2.94194
b = −0.435716
c = 2.32897
d = −0.457747
−2.43031 −0.135410
u = 0.078647 + 0.574169I
a = 0.556867 − 0.032704I
b = −0.612405 − 0.165972I
c = 2.18886 − 0.63265I
d = −3.72549 + 1.36694I
−2.82359 − 2.30782I −10.11267 + 3.58910I
u = 0.078647 + 0.574169I
a = −7.02820 − 1.64334I
b = −1.287020 + 0.071600I
c = −1.46449 − 6.68908I
d = −0.535397 − 1.207020I
−2.82359 − 2.30782I −10.11267 + 3.58910I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.078647 − 0.574169I
a = 0.556867 + 0.032704I
b = −0.612405 + 0.165972I
c = 2.18886 + 0.63265I
d = −3.72549 − 1.36694I
−2.82359 + 2.30782I −10.11267 − 3.58910I
u = 0.078647 − 0.574169I
a = −7.02820 + 1.64334I
b = −1.287020 − 0.071600I
c = −1.46449 + 6.68908I
d = −0.535397 + 1.207020I
−2.82359 + 2.30782I −10.11267 − 3.58910I
u = −1.47182 + 0.62184I
a = 0.387142 − 0.708904I
b = 1.015300 + 0.883621I
c = −1.36735 + 0.63910I
d = 1.04280 − 2.20163I
7.69158 − 9.88458I −1.61748 + 5.77638I
u = −1.47182 + 0.62184I
a = −0.227488 + 1.225540I
b = −0.69209 − 1.80855I
c = 1.13747 − 1.01527I
d = −1.61508 + 1.79092I
7.69158 − 9.88458I −1.61748 + 5.77638I
u = −1.47182 − 0.62184I
a = 0.387142 + 0.708904I
b = 1.015300 − 0.883621I
c = −1.36735 − 0.63910I
d = 1.04280 + 2.20163I
7.69158 + 9.88458I −1.61748 − 5.77638I
u = −1.47182 − 0.62184I
a = −0.227488 − 1.225540I
b = −0.69209 + 1.80855I
c = 1.13747 + 1.01527I
d = −1.61508 − 1.79092I
7.69158 + 9.88458I −1.61748 − 5.77638I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52621 + 0.50989I
a = 0.360132 + 0.757386I
b = 0.921521 − 1.050930I
c = −0.411289 + 0.112437I
d = 0.106033 − 0.813106I
8.58220 + 3.56941I −0.284129 − 1.007355I
u = 1.52621 + 0.50989I
a = −0.127382 − 1.185430I
b = −0.49179 + 1.81736I
c = 0.097619 + 0.500148I
d = 0.685044 + 0.038109I
8.58220 + 3.56941I −0.284129 − 1.007355I
u = 1.52621 − 0.50989I
a = 0.360132 − 0.757386I
b = 0.921521 + 1.050930I
c = −0.411289 − 0.112437I
d = 0.106033 + 0.813106I
8.58220 − 3.56941I −0.284129 + 1.007355I
u = 1.52621 − 0.50989I
a = −0.127382 + 1.185430I
b = −0.49179 − 1.81736I
c = 0.097619 − 0.500148I
d = 0.685044 − 0.038109I
8.58220 − 3.56941I −0.284129 + 1.007355I
20
III. I
v
1
= hc, d − v, b, a − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
6
=
1
0
a
8
=
1
0
a
9
=
1
0
a
3
=
v
0
a
12
=
0
v
a
5
=
1
−v − 1
a
2
=
v − 1
v + 1
a
1
=
−1
v + 1
a
11
=
−v
v
a
10
=
1
0
(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
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
22
(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
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = −0.500000 + 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = −0.500000 − 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
24
IV. I
v
2
= ha, d + v, −av + c − v − 1, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
6
=
0
−1
a
8
=
1
0
a
9
=
1
1
a
3
=
v
0
a
12
=
v + 1
−v
a
5
=
v
0
a
2
=
v
0
a
1
=
v
0
a
11
=
v + 1
1
a
10
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 5
25
(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
(u − 1)
2
c
8
, c
9
(u + 1)
2
c
11
, c
12
u
2
+ u + 1
26
(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
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
c = 0.500000 + 0.866025I
d = 0.500000 − 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = 0.500000 − 0.866025I
d = 0.500000 + 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
28
V. I
v
3
= ha, d − 1, c + a, b + 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
7
=
1
0
a
6
=
0
−1
a
8
=
1
0
a
9
=
1
1
a
3
=
−1
0
a
12
=
0
1
a
5
=
0
−1
a
2
=
−1
1
a
1
=
0
1
a
11
=
0
1
a
10
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
u
c
4
, c
8
, c
9
u + 1
30
(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
31
(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
32
VI.
I
v
4
= ha, d
2
v − dv + · · · − d + 1, d
2
v
2
− dv
2
+ · · · + 2v + 1, cdv − dv + · · · − a +
1, cdv
2
−dv
2
+· · ·−2av−a, adv+dv+· · ·+ c −1 , c
2
v
2
+acv
2
+· · ·+av+a
2
, b+1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
6
=
0
−1
a
8
=
1
0
a
9
=
1
1
a
3
=
v
0
a
12
=
c
d
a
5
=
c − 1
dc − 1
a
2
=
−c + v + 1
−dc + 1
a
1
=
−c + 1
−dc + 1
a
11
=
c
d + c
a
10
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
c + d
2
+ 2dc − v
2
− 4c − 9
(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.
33
(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 −8.38377 − 3.11850I
34
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
28
+ 9u
27
+ ··· + u + 1)(u
40
+ 19u
39
+ ··· + 288u + 256)
c
2
, c
6
u
2
(u − 1)
3
(u
28
− 5u
27
+ ··· − 3u + 1)(u
40
− 3u
39
+ ··· + 40u − 16)
c
3
, c
7
u
5
(u
20
+ u
19
+ ··· − 8u − 4)
2
(u
28
− 3u
27
+ ··· − 64u + 32)
c
4
, c
8
u
2
(u + 1)
3
(u
28
− 5u
27
+ ··· − 3u + 1)(u
40
− 3u
39
+ ··· + 40u − 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)(u
20
+ 2u
19
+ ··· − 2u + 1)
2
· (u
28
+ u
27
+ ··· + 8u + 4)
c
9
u
2
(u + 1)
3
(u
28
+ 9u
27
+ ··· + u + 1)(u
40
+ 19u
39
+ ··· + 288u + 256)
c
10
u(u
2
− u + 1)(u
2
+ u + 1)(u
20
− 2u
19
+ ··· + 36u + 17)
2
· (u
28
− u
27
+ ··· + 1736u + 1252)
c
12
u(u
2
+ u + 1)
2
(u
20
+ 6u
19
+ ··· − 2u + 1)
2
· (u
28
+ 9u
27
+ ··· − 56u + 16)
35
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
2
(y − 1)
3
(y
28
+ 31y
27
+ ··· + 39y + 1)
· (y
40
+ y
39
+ ··· − 4022784y + 65536)
c
2
, c
4
, c
6
c
8
y
2
(y − 1)
3
(y
28
− 9y
27
+ ··· − y + 1)(y
40
− 19y
39
+ ··· − 288y + 256)
c
3
, c
7
y
5
(y
20
− 15y
19
+ ··· − 24y + 16)
2
· (y
28
− 15y
27
+ ··· + 3072y + 1024)
c
5
, c
11
y(y
2
+ y + 1)
2
(y
20
+ 6y
19
+ ··· − 2y + 1)
2
· (y
28
+ 9y
27
+ ··· − 56y + 16)
c
10
y(y
2
+ y + 1)
2
(y
20
+ 30y
19
+ ··· + 1254y + 289)
2
· (y
28
+ 33y
27
+ ··· − 17874936y + 1567504)
c
12
y(y
2
+ y + 1)
2
(y
20
+ 18y
19
+ ··· − 86y + 1)
2
· (y
28
+ 21y
27
+ ··· − 6432y + 256)
36
