12a
0119
(K12a
0119
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 10 9 4 11 7 1 6
Solving Sequence
3,8
4
5,9
2
1,11
12 7 10 6
c
3
c
8
c
2
c
1
c
11
c
7
c
10
c
6
c
4
, c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
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
u
1
= h2u
13
− u
11
+ 2u
10
+ 5u
9
+ 2u
8
+ 2u
7
− 4u
6
+ 3u
5
+ 2u
4
− 2u
3
− 12u
2
+ 4d − 8u − 8,
− u
13
+ u
11
− u
10
− 4u
9
+ u
8
+ u
7
− 4u
5
− u
4
+ 2u
3
+ 8u
2
+ 4c + 4,
− u
13
+ u
11
− u
10
− 3u
9
+ u
7
+ u
6
− 2u
5
− u
4
+ 2u
3
+ 6u
2
+ 2b + 2u + 2,
3u
13
− 2u
11
+ 3u
10
+ 9u
9
+ u
8
− u
7
− 4u
6
+ 7u
5
+ 3u
4
− 6u
3
− 18u
2
+ 4a − 8u − 12,
u
14
− u
13
− u
12
+ 2u
11
+ 2u
10
− 3u
9
− u
8
− u
7
+ 4u
6
− u
5
− 4u
4
− 4u
3
+ 4u
2
+ 4i
I
u
2
= h−3u
21
+ 9u
19
+ ··· + 4d + 4, −2u
22
+ 6u
20
+ ··· + 4c − 2,
− u
16
+ 2u
14
− 5u
12
+ 6u
10
− u
9
− 6u
8
+ u
7
+ 4u
6
− 4u
5
− u
4
+ 3u
3
− 4u
2
+ 2b − 2u,
− 2u
21
+ 4u
20
+ ··· + 4a + 6, u
23
− 2u
22
+ ··· + 2u − 2i
I
u
3
= h−3u
21
+ 9u
19
+ ··· + 4d + 4, −2u
22
+ 6u
20
+ ··· + 4c − 2, 2u
22
− 2u
21
+ ··· + 4b + 2,
− 2u
22
+ u
21
+ ··· + 4a − 6, u
23
− 2u
22
+ ··· + 2u − 2i
I
u
4
= h−2u
22
+ 3u
21
+ ··· + 4d + 10u, u
19
− 2u
17
+ ··· + 4c + 4, 2u
22
− 2u
21
+ ··· + 4b + 2,
− 2u
22
+ u
21
+ ··· + 4a − 6, u
23
− 2u
22
+ ··· + 2u − 2i
I
u
5
= h−a
2
u
2
c − u
2
ca + 2a
2
u
2
− a
2
c + 2cau + 2u
2
a + 4ca − 3cu + au − u
2
+ d − 4c − 5a + u + 3,
a
2
u
2
c − a
2
cu + 3u
2
ca − 2a
2
u
2
− a
2
c + 4cau − 2u
2
c − u
2
a + c
2
− ca − 2cu + 2a
2
− 5au + 2a + 3u − 1,
− a
2
u
2
+ b + 2a − 2, a
3
− 2a
2
u − 2a
2
+ 3au + 3a − u − 1, u
3
+ u
2
− 1i
I
v
1
= ha, d, c + 1, b − 1, v + 1i
I
v
2
= hc, d + 1, b, a − 1, v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
I
v
4
= ha, da − c + 1, dv − 1, cv −a −v, b − 1i
* 8 irreducible components of dim
C
= 0, with total 104 representations.
* 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
= h2u
13
− u
11
+ · · · + 4d − 8, −u
13
+ u
11
+ · · · + 4c + 4, −u
13
+ u
11
+
· · · + 2b + 2, 3u
13
− 2u
11
+ · · · + 4a − 12, u
14
− u
13
+ · · · + 4u
2
+ 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
−
3
4
u
13
+
1
2
u
11
+ ··· + 2u + 3
1
2
u
13
−
1
2
u
11
+ ··· − u − 1
a
9
=
u
−u
3
+ u
a
2
=
−
3
4
u
13
+
1
2
u
11
+ ··· + 2u + 3
1
2
u
13
−
1
4
u
11
+ ··· − 2u − 2
a
1
=
−
1
4
u
13
+
1
4
u
11
+ ··· +
3
2
u
2
+ 1
1
2
u
13
−
1
4
u
11
+ ··· − 2u − 2
a
11
=
1
4
u
13
−
1
4
u
11
+ ··· − 2u
2
− 1
−
1
2
u
13
+
1
4
u
11
+ ··· + 2u + 2
a
12
=
1
2
u
13
−
1
2
u
11
+ ··· − u − 2
−
1
2
u
13
−
1
2
u
10
+ ··· + 2u + 2
a
7
=
−u
3
u
5
− u
3
+ u
a
10
=
−
1
4
u
13
+
1
4
u
11
+ ··· + 2u + 1
1
4
u
11
−
1
4
u
9
+ ··· −
3
2
u
3
+ u
a
6
=
−
3
4
u
13
+
1
2
u
11
+ ··· + 2u + 3
1
2
u
13
−
1
2
u
11
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
13
−u
12
+ u
11
−2u
10
−8u
9
−5u
8
−3u
7
+ 7u
6
−2u
5
−7u
4
+ 4u
3
+ 22u
2
+ 16u + 10
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
14
+ 7u
13
+ ··· + 3u + 1
c
2
, c
4
, c
5
c
6
, c
10
, c
12
u
14
− u
13
+ ··· + u + 1
c
3
, c
8
u
14
+ u
13
+ ··· + 4u
2
+ 4
c
7
u
14
− 3u
13
+ ··· + 32u + 16
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
14
+ 5y
13
+ ··· + 9y + 1
c
2
, c
4
, c
5
c
6
, c
10
, c
12
y
14
− 7y
13
+ ··· − 3y + 1
c
3
, c
8
y
14
− 3y
13
+ ··· + 32y + 16
c
7
y
14
+ 9y
13
+ ··· − 1536y + 256
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351654 + 0.974470I
a = 0.484407 + 0.125788I
b = 0.933970 − 0.502203I
c = 0.065921 − 0.250683I
d = −0.762746 − 0.668204I
−2.00841 + 5.97343I −8.41754 − 8.60965I
u = −0.351654 − 0.974470I
a = 0.484407 − 0.125788I
b = 0.933970 + 0.502203I
c = 0.065921 + 0.250683I
d = −0.762746 + 0.668204I
−2.00841 − 5.97343I −8.41754 + 8.60965I
u = −0.915559 + 0.598258I
a = 0.664888 − 0.608266I
b = −0.181237 + 0.749038I
c = −1.159390 + 0.550105I
d = −0.936616 − 0.512222I
0.94494 − 2.29172I −1.04510 + 1.71019I
u = −0.915559 − 0.598258I
a = 0.664888 + 0.608266I
b = −0.181237 − 0.749038I
c = −1.159390 − 0.550105I
d = −0.936616 + 0.512222I
0.94494 + 2.29172I −1.04510 − 1.71019I
u = 1.120580 + 0.015323I
a = 0.577432 − 1.267280I
b = −0.702265 + 0.653431I
c = 0.530358 + 0.435838I
d = −0.072651 − 0.949218I
4.01770 + 3.65190I −0.27967 − 6.51151I
u = 1.120580 − 0.015323I
a = 0.577432 + 1.267280I
b = −0.702265 − 0.653431I
c = 0.530358 − 0.435838I
d = −0.072651 + 0.949218I
4.01770 − 3.65190I −0.27967 + 6.51151I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.145230 + 0.485598I
a = −0.08828 + 1.64061I
b = −1.032700 − 0.607770I
c = 0.834303 + 0.325183I
d = −0.546866 − 0.244514I
0.82935 − 11.25490I −6.02298 + 10.89166I
u = −1.145230 − 0.485598I
a = −0.08828 − 1.64061I
b = −1.032700 + 0.607770I
c = 0.834303 − 0.325183I
d = −0.546866 + 0.244514I
0.82935 + 11.25490I −6.02298 − 10.89166I
u = −0.065300 + 0.726861I
a = 0.634835 − 0.129477I
b = 0.512305 + 0.308441I
c = −0.117499 + 0.636011I
d = 0.171343 + 0.691065I
−0.66587 − 1.25835I −4.79341 + 6.11957I
u = −0.065300 − 0.726861I
a = 0.634835 + 0.129477I
b = 0.512305 − 0.308441I
c = −0.117499 − 0.636011I
d = 0.171343 − 0.691065I
−0.66587 + 1.25835I −4.79341 − 6.11957I
u = 0.800659 + 0.997483I
a = 0.429409 − 0.097928I
b = 1.213650 + 0.504832I
c = −0.65473 − 1.70324I
d = −2.26378 − 1.40323I
−9.38350 − 10.57210I −12.21836 + 7.10513I
u = 0.800659 − 0.997483I
a = 0.429409 + 0.097928I
b = 1.213650 − 0.504832I
c = −0.65473 + 1.70324I
d = −2.26378 + 1.40323I
−9.38350 + 10.57210I −12.21836 − 7.10513I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.056500 + 0.850786I
a = −0.70270 − 1.54576I
b = −1.243720 + 0.536134I
c = −1.99896 − 0.54543I
d = −2.08869 + 1.91409I
−8.5386 + 17.3286I −11.2229 − 10.7940I
u = 1.056500 − 0.850786I
a = −0.70270 + 1.54576I
b = −1.243720 − 0.536134I
c = −1.99896 + 0.54543I
d = −2.08869 − 1.91409I
−8.5386 − 17.3286I −11.2229 + 10.7940I
8
II. I
u
2
= h−3u
21
+ 9u
19
+ · · · + 4d + 4, −2u
22
+ 6u
20
+ · · · + 4c − 2, −u
16
+
2u
14
+ · · · + 2b − 2u, −2u
21
+ 4u
20
+ · · · + 4a + 6, u
23
− 2u
22
+ · · · + 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
1
2
u
21
− u
20
+ ··· + 5u −
3
2
1
2
u
16
− u
14
+ ··· + 2u
2
+ u
a
9
=
u
−u
3
+ u
a
2
=
1
2
u
21
− u
20
+ ··· + 5u −
3
2
−
1
4
u
18
+
1
2
u
16
+ ··· − u
3
− 1
a
1
=
1
2
u
21
− u
20
+ ··· + 5u −
5
2
−
1
4
u
18
+
1
2
u
16
+ ··· − u
3
− 1
a
11
=
1
2
u
22
−
3
2
u
20
+ ··· −
1
2
u +
1
2
3
4
u
21
−
9
4
u
19
+ ··· +
1
2
u − 1
a
12
=
−
1
2
u
21
+ u
20
+ ··· −
9
2
u + 2
1
a
7
=
−u
3
u
5
− u
3
+ u
a
10
=
1
4
u
18
−
3
4
u
16
+ ··· +
1
2
u +
1
2
1
4
u
18
−
1
2
u
16
+ ··· − u
3
+ u
a
6
=
−
1
2
u
22
+
3
4
u
21
+ ··· + u −
3
2
−
1
2
u
22
+
1
2
u
21
+ ··· + u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
22
− 6u
20
+ 4u
19
+ 14u
18
− 8u
17
− 20u
16
+ 22u
15
+ 20u
14
− 28u
13
− 6u
12
+ 34u
11
−
6u
10
− 28u
9
+ 36u
8
+ 10u
7
− 30u
6
+ 26u
5
+ 10u
4
− 10u
3
+ 10u
2
+ 4u − 8
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 14u
22
+ ··· + 24u + 16
c
2
, c
4
u
23
− 7u
21
+ ··· − 3u
2
+ 4
c
3
, c
8
u
23
+ 2u
22
+ ··· + 2u + 2
c
5
, c
6
, c
10
c
12
u
23
− 2u
22
+ ··· + 3u − 1
c
7
u
23
− 6u
22
+ ··· + 8u − 4
c
9
, c
11
u
23
+ 12u
22
+ ··· + 7u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 14y
22
+ ··· − 736y −256
c
2
, c
4
y
23
− 14y
22
+ ··· + 24y −16
c
3
, c
8
y
23
− 6y
22
+ ··· + 8y −4
c
5
, c
6
, c
10
c
12
y
23
− 12y
22
+ ··· + 7y −1
c
7
y
23
+ 18y
22
+ ··· − 8y −16
c
9
, c
11
y
23
+ 32y
21
+ ··· + 31y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694668 + 0.784847I
a = 0.450244 − 0.080442I
b = 1.152320 + 0.384542I
c = 0.782630 + 0.951667I
d = 1.54383 + 0.54732I
−2.86000 − 1.29238I −6.06322 + 0.45977I
u = 0.694668 − 0.784847I
a = 0.450244 + 0.080442I
b = 1.152320 − 0.384542I
c = 0.782630 − 0.951667I
d = 1.54383 − 0.54732I
−2.86000 + 1.29238I −6.06322 − 0.45977I
u = −0.892323 + 0.293165I
a = 0.438777 + 0.026420I
b = 1.270830 − 0.136735I
c = 0.009889 − 0.214450I
d = −0.224788 − 1.053390I
−3.02064 − 3.59706I −7.24355 + 7.79597I
u = −0.892323 − 0.293165I
a = 0.438777 − 0.026420I
b = 1.270830 + 0.136735I
c = 0.009889 + 0.214450I
d = −0.224788 + 1.053390I
−3.02064 + 3.59706I −7.24355 − 7.79597I
u = −1.095410 + 0.175785I
a = 0.45789 + 1.51421I
b = −0.817025 − 0.605081I
c = −0.908669 − 0.269252I
d = 0.299223 + 0.396395I
3.68412 − 1.20490I −0.197865 + 0.587959I
u = −1.095410 − 0.175785I
a = 0.45789 − 1.51421I
b = −0.817025 + 0.605081I
c = −0.908669 + 0.269252I
d = 0.299223 − 0.396395I
3.68412 + 1.20490I −0.197865 − 0.587959I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.159876 + 0.866608I
a = 0.607182 + 0.204119I
b = 0.479725 − 0.497445I
c = −0.128604 + 0.305274I
d = 0.691140 + 0.217382I
−0.79201 − 1.83570I −5.62427 + 3.60335I
u = 0.159876 − 0.866608I
a = 0.607182 − 0.204119I
b = 0.479725 + 0.497445I
c = −0.128604 − 0.305274I
d = 0.691140 − 0.217382I
−0.79201 + 1.83570I −5.62427 − 3.60335I
u = 1.115790 + 0.351606I
a = 0.621931 + 0.844762I
b = −0.434825 − 0.767671I
c = −0.374060 + 0.344406I
d = 0.457120 − 0.806395I
2.56195 + 6.12354I −2.77038 − 6.59776I
u = 1.115790 − 0.351606I
a = 0.621931 − 0.844762I
b = −0.434825 + 0.767671I
c = −0.374060 − 0.344406I
d = 0.457120 + 0.806395I
2.56195 − 6.12354I −2.77038 + 6.59776I
u = 0.810032 + 0.844947I
a = −1.09305 − 1.85522I
b = −1.235740 + 0.400126I
c = −1.17221 − 1.42613I
d = −1.79180 − 0.10501I
−10.13410 − 1.43226I −13.58922 + 0.72835I
u = 0.810032 − 0.844947I
a = −1.09305 + 1.85522I
b = −1.235740 − 0.400126I
c = −1.17221 + 1.42613I
d = −1.79180 + 0.10501I
−10.13410 + 1.43226I −13.58922 − 0.72835I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746640 + 0.934392I
a = 0.575739 − 0.436897I
b = 0.102199 + 0.836400I
c = 0.76290 − 1.40128I
d = 1.61980 − 0.96664I
−6.07831 + 5.69706I −9.37968 − 4.06061I
u = −0.746640 − 0.934392I
a = 0.575739 + 0.436897I
b = 0.102199 − 0.836400I
c = 0.76290 + 1.40128I
d = 1.61980 + 0.96664I
−6.07831 − 5.69706I −9.37968 + 4.06061I
u = 1.001420 + 0.725291I
a = −0.59194 − 1.76529I
b = −1.170750 + 0.509221I
c = 1.41858 + 0.76507I
d = 1.50027 − 1.14883I
−1.95175 + 7.00485I −4.95661 − 5.13787I
u = 1.001420 − 0.725291I
a = −0.59194 + 1.76529I
b = −1.170750 − 0.509221I
c = 1.41858 − 0.76507I
d = 1.50027 + 1.14883I
−1.95175 − 7.00485I −4.95661 + 5.13787I
u = 0.966403 + 0.788262I
a = 0.422604 − 0.071283I
b = 1.300820 + 0.388090I
c = −1.60031 − 0.73645I
d = −2.06235 + 0.58473I
−9.64490 + 7.52364I −12.34364 − 6.02284I
u = 0.966403 − 0.788262I
a = 0.422604 + 0.071283I
b = 1.300820 − 0.388090I
c = −1.60031 + 0.73645I
d = −2.06235 − 0.58473I
−9.64490 − 7.52364I −12.34364 + 6.02284I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.040150 + 0.798969I
a = 0.541562 − 0.570958I
b = −0.125501 + 0.921967I
c = 1.77993 − 0.50191I
d = 1.69909 + 1.34789I
−5.14546 − 12.07470I −8.17479 + 8.06520I
u = −1.040150 − 0.798969I
a = 0.541562 + 0.570958I
b = −0.125501 − 0.921967I
c = 1.77993 + 0.50191I
d = 1.69909 − 1.34789I
−5.14546 + 12.07470I −8.17479 − 8.06520I
u = 0.598117
a = 0.466081
b = 1.14555
c = 0.628003
d = 0.737621
−2.27356 −1.62820
u = −0.272723 + 0.504579I
a = −4.66398 + 5.23784I
b = −1.094820 − 0.106487I
c = 1.115910 + 0.788549I
d = −0.100347 + 0.172505I
−4.96054 + 0.60932I −15.8427 − 0.8440I
u = −0.272723 − 0.504579I
a = −4.66398 − 5.23784I
b = −1.094820 + 0.106487I
c = 1.115910 − 0.788549I
d = −0.100347 − 0.172505I
−4.96054 − 0.60932I −15.8427 + 0.8440I
15
III. I
u
3
= h−3u
21
+ 9u
19
+ · · · + 4d + 4, −2u
22
+ 6u
20
+ · · · + 4c − 2, 2u
22
−
2u
21
+ · · · + 4b + 2, −2u
22
+ u
21
+ · · · + 4a − 6, u
23
− 2u
22
+ · · · + 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
1
2
u
22
−
1
4
u
21
+ ··· +
1
4
u
2
+
3
2
−
1
2
u
22
+
1
2
u
21
+ ··· −
1
4
u
2
−
1
2
a
9
=
u
−u
3
+ u
a
2
=
1
2
u
22
−
1
4
u
21
+ ··· +
1
4
u
2
+
3
2
1
4
u
21
−
3
4
u
19
+ ··· +
1
2
u − 1
a
1
=
1
2
u
22
−
3
2
u
20
+ ··· +
1
2
u +
1
2
1
4
u
21
−
3
4
u
19
+ ··· +
1
2
u − 1
a
11
=
1
2
u
22
−
3
2
u
20
+ ··· −
1
2
u +
1
2
3
4
u
21
−
9
4
u
19
+ ··· +
1
2
u − 1
a
12
=
−
1
2
u
22
+
3
2
u
20
+ ··· −
5
2
u
2
−
1
2
u
1
a
7
=
−u
3
u
5
− u
3
+ u
a
10
=
1
4
u
18
−
3
4
u
16
+ ··· +
1
2
u +
1
2
1
4
u
18
−
1
2
u
16
+ ··· − u
3
+ u
a
6
=
−
1
2
u
22
+
3
4
u
21
+ ··· + u −
3
2
−
1
2
u
22
+
1
2
u
21
+ ··· + u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
22
− 6u
20
+ 4u
19
+ 14u
18
− 8u
17
− 20u
16
+ 22u
15
+ 20u
14
− 28u
13
− 6u
12
+ 34u
11
−
6u
10
− 28u
9
+ 36u
8
+ 10u
7
− 30u
6
+ 26u
5
+ 10u
4
− 10u
3
+ 10u
2
+ 4u − 8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
23
+ 12u
22
+ ··· + 7u + 1
c
2
, c
4
, c
6
c
10
u
23
− 2u
22
+ ··· + 3u − 1
c
3
, c
8
u
23
+ 2u
22
+ ··· + 2u + 2
c
5
, c
12
u
23
− 7u
21
+ ··· − 3u
2
+ 4
c
7
u
23
− 6u
22
+ ··· + 8u − 4
c
11
u
23
+ 14u
22
+ ··· + 24u + 16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
23
+ 32y
21
+ ··· + 31y −1
c
2
, c
4
, c
6
c
10
y
23
− 12y
22
+ ··· + 7y −1
c
3
, c
8
y
23
− 6y
22
+ ··· + 8y −4
c
5
, c
12
y
23
− 14y
22
+ ··· + 24y −16
c
7
y
23
+ 18y
22
+ ··· − 8y −16
c
11
y
23
− 14y
22
+ ··· − 736y −256
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694668 + 0.784847I
a = 0.646621 + 0.443219I
b = 0.052166 − 0.721195I
c = 0.782630 + 0.951667I
d = 1.54383 + 0.54732I
−2.86000 − 1.29238I −6.06322 + 0.45977I
u = 0.694668 − 0.784847I
a = 0.646621 − 0.443219I
b = 0.052166 + 0.721195I
c = 0.782630 − 0.951667I
d = 1.54383 − 0.54732I
−2.86000 + 1.29238I −6.06322 − 0.45977I
u = −0.892323 + 0.293165I
a = 0.52674 + 2.12395I
b = −0.890003 − 0.443541I
c = 0.009889 − 0.214450I
d = −0.224788 − 1.053390I
−3.02064 − 3.59706I −7.24355 + 7.79597I
u = −0.892323 − 0.293165I
a = 0.52674 − 2.12395I
b = −0.890003 + 0.443541I
c = 0.009889 + 0.214450I
d = −0.224788 + 1.053390I
−3.02064 + 3.59706I −7.24355 − 7.79597I
u = −1.095410 + 0.175785I
a = 0.663876 − 1.020630I
b = −0.552165 + 0.688491I
c = −0.908669 − 0.269252I
d = 0.299223 + 0.396395I
3.68412 − 1.20490I −0.197865 + 0.587959I
u = −1.095410 − 0.175785I
a = 0.663876 + 1.020630I
b = −0.552165 − 0.688491I
c = −0.908669 + 0.269252I
d = 0.299223 − 0.396395I
3.68412 + 1.20490I −0.197865 − 0.587959I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.159876 + 0.866608I
a = 0.531180 − 0.126379I
b = 0.781744 + 0.423915I
c = −0.128604 + 0.305274I
d = 0.691140 + 0.217382I
−0.79201 − 1.83570I −5.62427 + 3.60335I
u = 0.159876 − 0.866608I
a = 0.531180 + 0.126379I
b = 0.781744 − 0.423915I
c = −0.128604 − 0.305274I
d = 0.691140 − 0.217382I
−0.79201 + 1.83570I −5.62427 − 3.60335I
u = 1.115790 + 0.351606I
a = 0.15695 − 1.65297I
b = −0.943072 + 0.599566I
c = −0.374060 + 0.344406I
d = 0.457120 − 0.806395I
2.56195 + 6.12354I −2.77038 − 6.59776I
u = 1.115790 − 0.351606I
a = 0.15695 + 1.65297I
b = −0.943072 − 0.599566I
c = −0.374060 − 0.344406I
d = 0.457120 + 0.806395I
2.56195 − 6.12354I −2.77038 + 6.59776I
u = 0.810032 + 0.844947I
a = 0.435558 − 0.082401I
b = 1.216570 + 0.419344I
c = −1.17221 − 1.42613I
d = −1.79180 − 0.10501I
−10.13410 − 1.43226I −13.58922 + 0.72835I
u = 0.810032 − 0.844947I
a = 0.435558 + 0.082401I
b = 1.216570 − 0.419344I
c = −1.17221 + 1.42613I
d = −1.79180 + 0.10501I
−10.13410 + 1.43226I −13.58922 − 0.72835I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746640 + 0.934392I
a = 0.438031 + 0.094410I
b = 1.181600 − 0.470208I
c = 0.76290 − 1.40128I
d = 1.61980 − 0.96664I
−6.07831 + 5.69706I −9.37968 − 4.06061I
u = −0.746640 − 0.934392I
a = 0.438031 − 0.094410I
b = 1.181600 + 0.470208I
c = 0.76290 + 1.40128I
d = 1.61980 + 0.96664I
−6.07831 − 5.69706I −9.37968 + 4.06061I
u = 1.001420 + 0.725291I
a = 0.578527 + 0.586894I
b = −0.148145 − 0.864175I
c = 1.41858 + 0.76507I
d = 1.50027 − 1.14883I
−1.95175 + 7.00485I −4.95661 − 5.13787I
u = 1.001420 − 0.725291I
a = 0.578527 − 0.586894I
b = −0.148145 + 0.864175I
c = 1.41858 − 0.76507I
d = 1.50027 + 1.14883I
−1.95175 − 7.00485I −4.95661 + 5.13787I
u = 0.966403 + 0.788262I
a = −0.73482 − 1.74058I
b = −1.205860 + 0.487616I
c = −1.60031 − 0.73645I
d = −2.06235 + 0.58473I
−9.64490 + 7.52364I −12.34364 − 6.02284I
u = 0.966403 − 0.788262I
a = −0.73482 + 1.74058I
b = −1.205860 − 0.487616I
c = −1.60031 + 0.73645I
d = −2.06235 − 0.58473I
−9.64490 − 7.52364I −12.34364 + 6.02284I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.040150 + 0.798969I
a = −0.65748 + 1.62443I
b = −1.214090 − 0.528949I
c = 1.77993 − 0.50191I
d = 1.69909 + 1.34789I
−5.14546 − 12.07470I −8.17479 + 8.06520I
u = −1.040150 − 0.798969I
a = −0.65748 − 1.62443I
b = −1.214090 + 0.528949I
c = 1.77993 + 0.50191I
d = 1.69909 − 1.34789I
−5.14546 + 12.07470I −8.17479 − 8.06520I
u = 0.598117
a = 1.80880
b = −0.447146
c = 0.628003
d = 0.737621
−2.27356 −1.62820
u = −0.272723 + 0.504579I
a = 0.510432 + 0.043771I
b = 0.944825 − 0.166773I
c = 1.115910 + 0.788549I
d = −0.100347 + 0.172505I
−4.96054 + 0.60932I −15.8427 − 0.8440I
u = −0.272723 − 0.504579I
a = 0.510432 − 0.043771I
b = 0.944825 + 0.166773I
c = 1.115910 − 0.788549I
d = −0.100347 − 0.172505I
−4.96054 − 0.60932I −15.8427 + 0.8440I
22
IV. I
u
4
= h−2u
22
+ 3u
21
+ · · · + 4d + 10u, u
19
− 2u
17
+ · · · + 4c + 4, 2u
22
−
2u
21
+ · · · + 4b + 2, −2u
22
+ u
21
+ · · · + 4a − 6, u
23
− 2u
22
+ · · · + 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
1
2
u
22
−
1
4
u
21
+ ··· +
1
4
u
2
+
3
2
−
1
2
u
22
+
1
2
u
21
+ ··· −
1
4
u
2
−
1
2
a
9
=
u
−u
3
+ u
a
2
=
1
2
u
22
−
1
4
u
21
+ ··· +
1
4
u
2
+
3
2
1
4
u
21
−
3
4
u
19
+ ··· +
1
2
u − 1
a
1
=
1
2
u
22
−
3
2
u
20
+ ··· +
1
2
u +
1
2
1
4
u
21
−
3
4
u
19
+ ··· +
1
2
u − 1
a
11
=
−
1
4
u
19
+
1
2
u
17
+ ··· − 3u − 1
1
2
u
22
−
3
4
u
21
+ ··· + 6u
2
−
5
2
u
a
12
=
−
1
2
u
19
+ u
17
+ ··· −
7
2
u − 1
1
2
u
22
−
1
2
u
21
+ ··· +
13
2
u
2
− 3u
a
7
=
−u
3
u
5
− u
3
+ u
a
10
=
−
3
4
u
19
+
3
2
u
17
+ ··· − 3u − 1
1
2
u
22
−
1
4
u
21
+ ··· + 7u
2
−
5
2
u
a
6
=
1
2
u
22
−
3
4
u
21
+ ··· +
1
2
u + 1
−
1
2
u
21
+ u
20
+ ··· − 3u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 2u
22
− 6u
20
+ 4u
19
+ 14u
18
− 8u
17
− 20u
16
+ 22u
15
+ 20u
14
− 28u
13
− 6u
12
+ 34u
11
−
6u
10
− 28u
9
+ 36u
8
+ 10u
7
− 30u
6
+ 26u
5
+ 10u
4
− 10u
3
+ 10u
2
+ 4u − 8
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
23
+ 12u
22
+ ··· + 7u + 1
c
2
, c
4
, c
5
c
12
u
23
− 2u
22
+ ··· + 3u − 1
c
3
, c
8
u
23
+ 2u
22
+ ··· + 2u + 2
c
6
, c
10
u
23
− 7u
21
+ ··· − 3u
2
+ 4
c
7
u
23
− 6u
22
+ ··· + 8u − 4
c
9
u
23
+ 14u
22
+ ··· + 24u + 16
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
23
+ 32y
21
+ ··· + 31y −1
c
2
, c
4
, c
5
c
12
y
23
− 12y
22
+ ··· + 7y −1
c
3
, c
8
y
23
− 6y
22
+ ··· + 8y −4
c
6
, c
10
y
23
− 14y
22
+ ··· + 24y −16
c
7
y
23
+ 18y
22
+ ··· − 8y −16
c
9
y
23
− 14y
22
+ ··· − 736y −256
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694668 + 0.784847I
a = 0.646621 + 0.443219I
b = 0.052166 − 0.721195I
c = −1.12753 − 0.96163I
d = −0.947232 − 0.143060I
−2.86000 − 1.29238I −6.06322 + 0.45977I
u = 0.694668 − 0.784847I
a = 0.646621 − 0.443219I
b = 0.052166 + 0.721195I
c = −1.12753 + 0.96163I
d = −0.947232 + 0.143060I
−2.86000 + 1.29238I −6.06322 − 0.45977I
u = −0.892323 + 0.293165I
a = 0.52674 + 2.12395I
b = −0.890003 − 0.443541I
c = 2.65342 − 0.49408I
d = −0.702937 + 1.066160I
−3.02064 − 3.59706I −7.24355 + 7.79597I
u = −0.892323 − 0.293165I
a = 0.52674 − 2.12395I
b = −0.890003 + 0.443541I
c = 2.65342 + 0.49408I
d = −0.702937 − 1.066160I
−3.02064 + 3.59706I −7.24355 − 7.79597I
u = −1.095410 + 0.175785I
a = 0.663876 − 1.020630I
b = −0.552165 + 0.688491I
c = −0.136748 + 0.374893I
d = −0.248300 − 1.039030I
3.68412 − 1.20490I −0.197865 + 0.587959I
u = −1.095410 − 0.175785I
a = 0.663876 + 1.020630I
b = −0.552165 − 0.688491I
c = −0.136748 − 0.374893I
d = −0.248300 + 1.039030I
3.68412 + 1.20490I −0.197865 − 0.587959I
26
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.159876 + 0.866608I
a = 0.531180 − 0.126379I
b = 0.781744 + 0.423915I
c = 0.045517 + 0.729067I
d = −0.255613 + 1.166420I
−0.79201 − 1.83570I −5.62427 + 3.60335I
u = 0.159876 − 0.866608I
a = 0.531180 + 0.126379I
b = 0.781744 − 0.423915I
c = 0.045517 − 0.729067I
d = −0.255613 − 1.166420I
−0.79201 + 1.83570I −5.62427 − 3.60335I
u = 1.115790 + 0.351606I
a = 0.15695 − 1.65297I
b = −0.943072 + 0.599566I
c = 1.233050 − 0.090029I
d = −0.375083 − 0.309465I
2.56195 + 6.12354I −2.77038 − 6.59776I
u = 1.115790 − 0.351606I
a = 0.15695 + 1.65297I
b = −0.943072 − 0.599566I
c = 1.233050 + 0.090029I
d = −0.375083 + 0.309465I
2.56195 − 6.12354I −2.77038 + 6.59776I
u = 0.810032 + 0.844947I
a = 0.435558 − 0.082401I
b = 1.216570 + 0.419344I
c = −1.45901 − 1.35263I
d = −3.19657 − 0.86128I
−10.13410 − 1.43226I −13.58922 + 0.72835I
u = 0.810032 − 0.844947I
a = 0.435558 + 0.082401I
b = 1.216570 − 0.419344I
c = −1.45901 + 1.35263I
d = −3.19657 + 0.86128I
−10.13410 + 1.43226I −13.58922 − 0.72835I
27
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.746640 + 0.934392I
a = 0.438031 + 0.094410I
b = 1.181600 − 0.470208I
c = −0.84775 + 1.27484I
d = −2.42278 + 0.85521I
−6.07831 + 5.69706I −9.37968 − 4.06061I
u = −0.746640 − 0.934392I
a = 0.438031 − 0.094410I
b = 1.181600 + 0.470208I
c = −0.84775 − 1.27484I
d = −2.42278 − 0.85521I
−6.07831 − 5.69706I −9.37968 + 4.06061I
u = 1.001420 + 0.725291I
a = 0.578527 + 0.586894I
b = −0.148145 − 0.864175I
c = −1.45246 − 0.50095I
d = −1.32533 + 0.53961I
−1.95175 + 7.00485I −4.95661 − 5.13787I
u = 1.001420 − 0.725291I
a = 0.578527 − 0.586894I
b = −0.148145 + 0.864175I
c = −1.45246 + 0.50095I
d = −1.32533 − 0.53961I
−1.95175 − 7.00485I −4.95661 + 5.13787I
u = 0.966403 + 0.788262I
a = −0.73482 − 1.74058I
b = −1.205860 + 0.487616I
c = −1.69882 − 1.77273I
d = −2.39909 + 1.21573I
−9.64490 + 7.52364I −12.34364 − 6.02284I
u = 0.966403 − 0.788262I
a = −0.73482 + 1.74058I
b = −1.205860 − 0.487616I
c = −1.69882 + 1.77273I
d = −2.39909 − 1.21573I
−9.64490 − 7.52364I −12.34364 + 6.02284I
28
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.040150 + 0.798969I
a = −0.65748 + 1.62443I
b = −1.214090 − 0.528949I
c = −1.55675 + 0.92503I
d = −2.00676 − 1.54535I
−5.14546 − 12.07470I −8.17479 + 8.06520I
u = −1.040150 − 0.798969I
a = −0.65748 − 1.62443I
b = −1.214090 + 0.528949I
c = −1.55675 − 0.92503I
d = −2.00676 + 1.54535I
−5.14546 + 12.07470I −8.17479 − 8.06520I
u = 0.598117
a = 1.80880
b = −0.447146
c = −2.70017
d = 0.459836
−2.27356 −1.62820
u = −0.272723 + 0.504579I
a = 0.510432 + 0.043771I
b = 0.944825 − 0.166773I
c = −0.30283 − 2.30298I
d = −0.35022 − 4.81571I
−4.96054 + 0.60932I −15.8427 − 0.8440I
u = −0.272723 − 0.504579I
a = 0.510432 − 0.043771I
b = 0.944825 + 0.166773I
c = −0.30283 + 2.30298I
d = −0.35022 + 4.81571I
−4.96054 − 0.60932I −15.8427 + 0.8440I
29
V. I
u
5
= h−a
2
u
2
c − u
2
ca + · · · − 5a + 3, a
2
u
2
c + 3u
2
ca + · · · + 2a −
1, −a
2
u
2
+ b + 2a − 2, −2a
2
u + 3au + · · · + 3a − 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
5
=
a
a
2
u
2
− 2a + 2
a
9
=
u
u
2
+ u − 1
a
2
=
a
−a
2
u
2
− u
2
a + 2a − 2
a
1
=
−a
2
u
2
− u
2
a + 3a − 2
−a
2
u
2
− u
2
a + 2a − 2
a
11
=
c
a
2
u
2
c + u
2
ca + ··· + 5a − 3
a
12
=
−2a
2
u
2
c − 2u
2
ca + ··· − 7a + 5
1
a
7
=
u
2
− 1
u
2
a
10
=
−3a
2
u
2
c − 2u
2
ca + ··· − 3a + 3
−a
2
u
2
c − 3u
2
ca + ··· − 2a + 1
a
6
=
a
2
u
2
c + u
2
ca + ··· + 5a − 3
−a
2
u
2
c + 2u
2
ca + ··· + 4a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
(u
9
+ 6u
8
+ 15u
7
+ 17u
6
+ 3u
5
− 12u
4
− 9u
3
+ u
2
+ 2u + 1)
2
c
2
, c
4
, c
5
c
6
, c
10
, c
12
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
2
c
3
, c
8
(u
3
− u
2
+ 1)
6
c
7
(u
3
− u
2
+ 2u − 1)
6
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
(y
9
− 6y
8
+ 27y
7
− 73y
6
+ 139y
5
− 184y
4
+ 83y
3
− 13y
2
+ 2y −1)
2
c
2
, c
4
, c
5
c
6
, c
10
, c
12
(y
9
− 6y
8
+ 15y
7
− 17y
6
+ 3y
5
+ 12y
4
− 9y
3
− y
2
+ 2y −1)
2
c
3
, c
8
(y
3
− y
2
+ 2y −1)
6
c
7
(y
3
+ 3y
2
+ 2y −1)
6
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.616488 − 0.534141I
b = −0.073457 + 0.802780I
c = 1.28781 − 0.94152I
d = 2.02696 − 0.41525I
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = −0.877439 + 0.744862I
a = 0.616488 − 0.534141I
b = −0.073457 + 0.802780I
c = 1.61569 − 1.41115I
d = 1.64564 + 0.80187I
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = −0.877439 + 0.744862I
a = 0.432401 + 0.070043I
b = 1.253530 − 0.365043I
c = −1.14863 + 0.86295I
d = −1.67261 − 0.38662I
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = −0.877439 + 0.744862I
a = 0.432401 + 0.070043I
b = 1.253530 − 0.365043I
c = 1.28781 − 0.94152I
d = 2.02696 − 0.41525I
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = −0.877439 + 0.744862I
a = −0.80377 + 1.95382I
b = −1.180080 − 0.437737I
c = −1.14863 + 0.86295I
d = −1.67261 − 0.38662I
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = −0.877439 + 0.744862I
a = −0.80377 + 1.95382I
b = −1.180080 − 0.437737I
c = 1.61569 − 1.41115I
d = 1.64564 + 0.80187I
−6.31400 − 2.82812I −9.50976 + 2.97945I
33
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 − 0.744862I
a = 0.616488 + 0.534141I
b = −0.073457 − 0.802780I
c = 1.28781 + 0.94152I
d = 2.02696 + 0.41525I
−6.31400 + 2.82812I −9.50976 − 2.97945I
u = −0.877439 − 0.744862I
a = 0.616488 + 0.534141I
b = −0.073457 − 0.802780I
c = 1.61569 + 1.41115I
d = 1.64564 − 0.80187I
−6.31400 + 2.82812I −9.50976 − 2.97945I
u = −0.877439 − 0.744862I
a = 0.432401 − 0.070043I
b = 1.253530 + 0.365043I
c = −1.14863 − 0.86295I
d = −1.67261 + 0.38662I
−6.31400 + 2.82812I −9.50976 − 2.97945I
u = −0.877439 − 0.744862I
a = 0.432401 − 0.070043I
b = 1.253530 + 0.365043I
c = 1.28781 + 0.94152I
d = 2.02696 + 0.41525I
−6.31400 + 2.82812I −9.50976 − 2.97945I
u = −0.877439 − 0.744862I
a = −0.80377 − 1.95382I
b = −1.180080 + 0.437737I
c = −1.14863 − 0.86295I
d = −1.67261 + 0.38662I
−6.31400 + 2.82812I −9.50976 − 2.97945I
u = −0.877439 − 0.744862I
a = −0.80377 − 1.95382I
b = −1.180080 + 0.437737I
c = 1.61569 + 1.41115I
d = 1.64564 − 0.80187I
−6.31400 + 2.82812I −9.50976 − 2.97945I
34
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.754878
a = 0.451991
b = 1.21243
c = 0.603023 + 0.131096I
d = 0.610449 + 0.570600I
−2.17641 −2.98050
u = 0.754878
a = 0.451991
b = 1.21243
c = 0.603023 − 0.131096I
d = 0.610449 − 0.570600I
−2.17641 −2.98050
u = 0.754878
a = 1.52888 + 1.24301I
b = −0.606217 − 0.320153I
c = 0.603023 − 0.131096I
d = 0.610449 − 0.570600I
−2.17641 −2.98050
u = 0.754878
a = 1.52888 + 1.24301I
b = −0.606217 − 0.320153I
c = −2.71580
d = 0.779103
−2.17641 −2.98050
u = 0.754878
a = 1.52888 − 1.24301I
b = −0.606217 + 0.320153I
c = 0.603023 + 0.131096I
d = 0.610449 + 0.570600I
−2.17641 −2.98050
u = 0.754878
a = 1.52888 − 1.24301I
b = −0.606217 + 0.320153I
c = −2.71580
d = 0.779103
−2.17641 −2.98050
35
VI. I
v
1
= ha, d, c + 1, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
−1
0
a
12
=
−1
−1
a
7
=
−1
0
a
10
=
−1
0
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
11
u − 1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
u
c
4
, c
12
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
11
, c
12
y −1
c
3
, c
6
, c
7
c
8
, c
9
, c
10
y
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = −1.00000
d = 0
−3.28987 −12.0000
39
VII. I
v
2
= hc, d + 1, b, a − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
5
=
1
0
a
9
=
−1
0
a
2
=
1
0
a
1
=
1
0
a
11
=
0
−1
a
12
=
1
−1
a
7
=
−1
0
a
10
=
−1
−1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
u
c
5
, c
10
u + 1
c
6
, c
9
, c
11
c
12
u − 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
, c
8
y
c
5
, c
6
, c
9
c
10
, c
11
, c
12
y −1
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 1.00000
b = 0
c = 0
d = −1.00000
−3.28987 −12.0000
43
VIII. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
9
=
−1
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
0
−1
a
12
=
0
−1
a
7
=
−1
0
a
10
=
−1
−1
a
6
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
9
u − 1
c
3
, c
5
, c
7
c
8
, c
11
, c
12
u
c
4
, c
10
u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
9
, c
10
y −1
c
3
, c
5
, c
7
c
8
, c
11
, c
12
y
46
(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
47
IX. I
v
4
= ha, da − c + 1, dv − 1, cv − a − v, b − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
9
=
v
0
a
2
=
1
−1
a
1
=
0
−1
a
11
=
1
d
a
12
=
1
d + 1
a
7
=
v
0
a
10
=
v + 1
d
a
6
=
−1
−d
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
− 16
(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.
48
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−4.93480 −15.5916 − 0.1902I
49
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u(u − 1)
2
· (u
9
+ 6u
8
+ 15u
7
+ 17u
6
+ 3u
5
− 12u
4
− 9u
3
+ u
2
+ 2u + 1)
2
· (u
14
+ 7u
13
+ ··· + 3u + 1)(u
23
+ 12u
22
+ ··· + 7u + 1)
2
· (u
23
+ 14u
22
+ ··· + 24u + 16)
c
2
, c
6
u(u − 1)
2
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
2
· (u
14
− u
13
+ ··· + u + 1)(u
23
− 7u
21
+ ··· − 3u
2
+ 4)
· (u
23
− 2u
22
+ ··· + 3u − 1)
2
c
3
, c
8
u
3
(u
3
− u
2
+ 1)
6
(u
14
+ u
13
+ ··· + 4u
2
+ 4)(u
23
+ 2u
22
+ ··· + 2u + 2)
3
c
4
, c
10
u(u + 1)
2
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
2
· (u
14
− u
13
+ ··· + u + 1)(u
23
− 7u
21
+ ··· − 3u
2
+ 4)
· (u
23
− 2u
22
+ ··· + 3u − 1)
2
c
5
, c
12
u(u − 1)(u + 1)(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
2
· (u
14
− u
13
+ ··· + u + 1)(u
23
− 7u
21
+ ··· − 3u
2
+ 4)
· (u
23
− 2u
22
+ ··· + 3u − 1)
2
c
7
u
3
(u
3
− u
2
+ 2u − 1)
6
(u
14
− 3u
13
+ ··· + 32u + 16)
· (u
23
− 6u
22
+ ··· + 8u − 4)
3
50
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y(y − 1)
2
· (y
9
− 6y
8
+ 27y
7
− 73y
6
+ 139y
5
− 184y
4
+ 83y
3
− 13y
2
+ 2y −1)
2
· (y
14
+ 5y
13
+ ··· + 9y + 1)(y
23
+ 32y
21
+ ··· + 31y −1)
2
· (y
23
− 14y
22
+ ··· − 736y −256)
c
2
, c
4
, c
5
c
6
, c
10
, c
12
y(y − 1)
2
· (y
9
− 6y
8
+ 15y
7
− 17y
6
+ 3y
5
+ 12y
4
− 9y
3
− y
2
+ 2y −1)
2
· (y
14
− 7y
13
+ ··· − 3y + 1)(y
23
− 14y
22
+ ··· + 24y −16)
· (y
23
− 12y
22
+ ··· + 7y −1)
2
c
3
, c
8
y
3
(y
3
− y
2
+ 2y −1)
6
(y
14
− 3y
13
+ ··· + 32y + 16)
· (y
23
− 6y
22
+ ··· + 8y −4)
3
c
7
y
3
(y
3
+ 3y
2
+ 2y −1)
6
(y
14
+ 9y
13
+ ··· − 1536y + 256)
· (y
23
+ 18y
22
+ ··· − 8y −16)
3
51
