10
120
(K10a
102
)
A knot diagram
1
Linearized knot diagam
5 9 6 2 8 10 4 1 7 3
Solving Sequence
1,5 2,8
6 9 4 3 7 10
c
1
c
5
c
8
c
4
c
3
c
7
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
6
− u
5
− 2u
4
− u
3
− u
2
+ b − u + 1,
− u
10
− 3u
9
− 8u
8
− 13u
7
− 19u
6
− 20u
5
− 19u
4
− 13u
3
− 7u
2
+ 2a − 2u + 2,
u
11
+ 3u
10
+ 8u
9
+ 13u
8
+ 19u
7
+ 22u
6
+ 21u
5
+ 17u
4
+ 9u
3
+ 4u
2
− 2i
I
u
2
= h−u
17
− 7u
16
+ ··· + b − 13, −13u
17
− 60u
16
+ ··· + 5a + 4, u
18
+ 5u
17
+ ··· + 27u + 5i
I
u
3
= h−3u
11
+ 11u
10
− 29u
9
+ 50u
8
− 66u
7
+ 71u
6
− 59u
5
+ 43u
4
− 22u
3
− au + 7u
2
+ b − 4u,
3u
10
a + u
11
+ ··· + 4a − 4, u
12
− 3u
11
+ 8u
10
− 13u
9
+ 18u
8
− 21u
7
+ 19u
6
− 17u
5
+ 10u
4
− 6u
3
+ 4u
2
+ 1i
I
u
4
= h−au + u
2
+ b − u + 1, −u
2
a + a
2
+ u
2
− a + 1, u
3
− u
2
+ 2u − 1i
I
u
5
= hu
2
+ b − u + 1, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
I
u
6
= hu
6
− 4u
5
+ 8u
4
− 11u
3
+ 9u
2
+ b − 5u + 3, −3u
7
+ 12u
6
− 25u
5
+ 34u
4
− 29u
3
+ 17u
2
+ 2a − 9u + 2,
u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2i
I
u
7
= h−au + b + u − 1, a
2
− au − 1, u
2
− u + 1i
* 7 irreducible components of dim
C
= 0, with total 74 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).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−u
6
− u
5
− 2u
4
− u
3
− u
2
+ b − u + 1, −u
10
− 3u
9
+ · · · + 2a +
2, u
11
+ 3u
10
+ · · · + 4u
2
− 2i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
1
2
u
10
+
3
2
u
9
+ ··· + u − 1
u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u − 1
a
6
=
1
2
u
10
+
3
2
u
9
+ ··· −
1
2
u
2
− u
u
9
+ 2u
8
+ 5u
7
+ 6u
6
+ 8u
5
+ 7u
4
+ 5u
3
+ 3u
2
+ u − 1
a
9
=
1
2
u
10
+
3
2
u
9
+ ··· +
11
2
u
3
+
5
2
u
2
u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u − 1
a
4
=
u
u
3
+ u
a
3
=
−
1
2
u
10
−
3
2
u
9
+ ··· + u + 1
−u
6
− u
5
− 2u
4
− u
3
− u
2
− u + 1
a
7
=
1
2
u
10
+
5
2
u
9
+ ··· +
7
2
u
2
− 1
−u
10
− 3u
9
− 7u
8
− 11u
7
− 14u
6
− 15u
5
− 12u
4
− 8u
3
− 3u
2
+ 1
a
10
=
−
1
2
u
10
−
1
2
u
9
+ ··· + u − 1
−u
9
− 2u
8
− 5u
7
− 6u
6
− 8u
5
− 7u
4
− 5u
3
− 3u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
8
− 6u
7
− 14u
6
− 18u
5
− 24u
4
− 18u
3
− 16u
2
− 6u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
11
− 3u
10
+ 8u
9
− 13u
8
+ 19u
7
− 22u
6
+ 21u
5
− 17u
4
+ 9u
3
− 4u
2
+ 2
c
2
, c
7
u
11
+ 5u
10
+ ··· + 10u + 4
c
3
, c
5
, c
8
c
10
u
11
+ 4u
9
+ u
8
+ 11u
7
+ 4u
6
+ 15u
5
+ 3u
4
+ 9u
3
− u
2
+ 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
11
+ 7y
10
+ ··· + 16y −4
c
2
, c
7
y
11
− 5y
10
+ ··· + 60y −16
c
3
, c
5
, c
8
c
10
y
11
+ 8y
10
+ ··· + 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.955959 + 0.181916I
a = −0.517203 − 1.103780I
b = −0.695220 − 0.961079I
−0.51987 − 4.74721I −10.74299 + 5.17166I
u = −0.955959 − 0.181916I
a = −0.517203 + 1.103780I
b = −0.695220 + 0.961079I
−0.51987 + 4.74721I −10.74299 − 5.17166I
u = 0.104833 + 1.064770I
a = −1.051120 − 0.609326I
b = −0.538602 + 1.183080I
5.39093 − 0.52336I −2.07555 − 0.88155I
u = 0.104833 − 1.064770I
a = −1.051120 + 0.609326I
b = −0.538602 − 1.183080I
5.39093 + 0.52336I −2.07555 + 0.88155I
u = 0.375570 + 1.042270I
a = 0.289036 + 0.451507I
b = 0.362037 − 0.470824I
2.05520 − 3.23878I −8.62571 + 3.68812I
u = 0.375570 − 1.042270I
a = 0.289036 − 0.451507I
b = 0.362037 + 0.470824I
2.05520 + 3.23878I −8.62571 − 3.68812I
u = −0.641442 + 1.159660I
a = −0.736546 + 0.484569I
b = 0.089483 + 1.164960I
6.47745 + 4.30838I −1.34168 − 3.93056I
u = −0.641442 − 1.159660I
a = −0.736546 − 0.484569I
b = 0.089483 − 1.164960I
6.47745 − 4.30838I −1.34168 + 3.93056I
u = −0.58305 + 1.34141I
a = 1.128180 + 0.208445I
b = 0.93740 − 1.39182I
6.7235 + 16.2714I −5.72276 − 8.85281I
u = −0.58305 − 1.34141I
a = 1.128180 − 0.208445I
b = 0.93740 + 1.39182I
6.7235 − 16.2714I −5.72276 + 8.85281I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.400093
a = 0.775290
b = −0.310188
−0.775978 −12.9830
6
II. I
u
2
=
h−u
17
−7u
16
+· · ·+b−13, −13u
17
−60u
16
+· · ·+5a+4, u
18
+5u
17
+· · ·+27u+5i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
13
5
u
17
+ 12u
16
+ ··· +
77
5
u −
4
5
u
17
+ 7u
16
+ ··· + 71u + 13
a
6
=
−
11
5
u
17
− 11u
16
+ ··· −
229
5
u −
42
5
−3u
15
− 13u
14
+ ··· − 50u − 11
a
9
=
8
5
u
17
+ 5u
16
+ ··· −
278
5
u −
69
5
u
17
+ 7u
16
+ ··· + 71u + 13
a
4
=
u
u
3
+ u
a
3
=
4
5
u
17
+ 8u
16
+ ··· +
391
5
u +
73
5
−3u
17
− 16u
16
+ ··· − 62u − 11
a
7
=
13
5
u
17
+ 13u
16
+ ··· +
67
5
u −
4
5
u
16
+ 5u
15
+ ··· + 42u + 8
a
10
=
9
5
u
17
+ 6u
16
+ ··· −
189
5
u −
32
5
−u
17
− 4u
16
+ ··· + 16u + 4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 26u
17
+ 130u
16
+ 415u
15
+ 871u
14
+ 1236u
13
+ 1002u
12
− 275u
11
− 2187u
10
−
3562u
9
− 3091u
8
− 569u
7
+ 2567u
6
+ 4603u
5
+ 4614u
4
+ 3181u
3
+ 1560u
2
+ 486u + 63
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
18
− 5u
17
+ ··· − 27u + 5
c
2
, c
7
(u
9
− 2u
8
+ 4u
7
− 5u
6
+ 7u
5
− 5u
4
+ 3u
3
− 2u
2
+ u − 1)
2
c
3
, c
5
, c
8
c
10
u
18
− u
17
+ ··· + 3u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
18
+ 9y
17
+ ··· + 61y + 25
c
2
, c
7
(y
9
+ 4y
8
+ 10y
7
+ 17y
6
+ 17y
5
+ y
4
− 7y
3
− 8y
2
− 3y −1)
2
c
3
, c
5
, c
8
c
10
y
18
+ 9y
17
+ ··· + 43y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198527 + 0.827118I
a = −0.81586 − 1.28949I
b = −1.228530 + 0.418813I
−1.04793 + 1.11007I −17.5535 − 4.7867I
u = −0.198527 − 0.827118I
a = −0.81586 + 1.28949I
b = −1.228530 − 0.418813I
−1.04793 − 1.11007I −17.5535 + 4.7867I
u = −0.079308 + 0.836177I
a = 1.38823 + 0.30834I
b = 0.367922 − 1.136350I
4.23983 −2.85705 + 0.I
u = −0.079308 − 0.836177I
a = 1.38823 − 0.30834I
b = 0.367922 + 1.136350I
4.23983 −2.85705 + 0.I
u = −1.156420 + 0.102576I
a = 0.521985 + 0.890705I
b = 0.694998 + 0.976484I
2.81259 − 10.16840I −7.74812 + 7.64867I
u = −1.156420 − 0.102576I
a = 0.521985 − 0.890705I
b = 0.694998 − 0.976484I
2.81259 + 10.16840I −7.74812 − 7.64867I
u = 1.160130 + 0.229157I
a = 0.035605 − 0.158300I
b = −0.077582 + 0.175489I
−1.04793 − 1.11007I −17.5535 + 4.7867I
u = 1.160130 − 0.229157I
a = 0.035605 + 0.158300I
b = −0.077582 − 0.175489I
−1.04793 + 1.11007I −17.5535 − 4.7867I
u = −0.311796 + 1.205210I
a = 0.814403 − 0.074315I
b = 0.164362 − 1.004700I
4.26456 − 0.69984I −4.65022 + 1.89978I
u = −0.311796 − 1.205210I
a = 0.814403 + 0.074315I
b = 0.164362 + 1.004700I
4.26456 + 0.69984I −4.65022 − 1.89978I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.369880 + 1.229190I
a = 1.216830 + 0.459753I
b = 1.01520 − 1.32566I
8.30021 + 4.38855I −1.11965 − 3.68700I
u = −0.369880 − 1.229190I
a = 1.216830 − 0.459753I
b = 1.01520 + 1.32566I
8.30021 − 4.38855I −1.11965 + 3.68700I
u = −0.642487 + 0.199869I
a = 1.21195 − 1.14348I
b = 0.550112 − 0.976904I
4.26456 + 0.69984I −4.65022 − 1.89978I
u = −0.642487 − 0.199869I
a = 1.21195 + 1.14348I
b = 0.550112 + 0.976904I
4.26456 − 0.69984I −4.65022 + 1.89978I
u = −0.545158 + 1.253180I
a = −1.229130 − 0.230487I
b = −0.95891 + 1.41466I
2.81259 + 10.16840I −7.74812 − 7.64867I
u = −0.545158 − 1.253180I
a = −1.229130 + 0.230487I
b = −0.95891 − 1.41466I
2.81259 − 10.16840I −7.74812 + 7.64867I
u = −0.35655 + 1.50992I
a = −0.544015 + 0.110198I
b = −0.027580 + 0.860709I
8.30021 − 4.38855I −1.11965 + 3.68700I
u = −0.35655 − 1.50992I
a = −0.544015 − 0.110198I
b = −0.027580 − 0.860709I
8.30021 + 4.38855I −1.11965 − 3.68700I
11
III. I
u
3
=
h−3u
11
+11u
10
+· · ·+b−4u, 3u
10
a+u
11
+· · ·+4a−4, u
12
−3u
11
+· · ·+4u
2
+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
a
3u
11
− 11u
10
+ ··· + au + 4u
a
6
=
3u
11
a − u
11
+ ··· − 4u − 1
1
a
9
=
−3u
11
+ 11u
10
+ ··· + a − 4u
3u
11
− 11u
10
+ ··· + au + 4u
a
4
=
u
u
3
+ u
a
3
=
−2u
11
a + u
11
+ ··· − a + 2
−u
10
a + 4u
9
a + ··· − 2a + 1
a
7
=
−u
11
+ 5u
10
+ ··· + a + 2
2u
11
− 7u
10
+ ··· + au + 2u
a
10
=
−u
10
a − u
11
+ ··· + a − 2
−u
7
a + u
6
a + ··· + a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
11
− 16u
10
+ 44u
9
− 80u
8
+ 112u
7
− 124u
6
+ 116u
5
− 92u
4
+ 60u
3
− 28u
2
+ 8u − 18
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
2
c
2
, c
7
(u
12
+ u
10
− 6u
9
+ 10u
8
− 2u
7
+ 2u
6
− 2u
4
+ 2u
2
+ 1)
2
c
3
, c
5
, c
8
c
10
u
24
− 3u
23
+ ··· − 4u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(y
12
+ 7y
11
+ ··· + 8y + 1)
2
c
2
, c
7
(y
12
+ 2y
11
+ ··· + 4y + 1)
2
c
3
, c
5
, c
8
c
10
y
24
− 11y
23
+ ··· − 8y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234552 + 1.002020I
a = 0.647681 + 0.298955I
b = 2.11054 + 0.48664I
3.72285 + 6.96551I −5.97171 − 10.57440I
u = −0.234552 + 1.002020I
a = 0.00700 + 2.10465I
b = 0.451474 − 0.578868I
3.72285 + 6.96551I −5.97171 − 10.57440I
u = −0.234552 − 1.002020I
a = 0.647681 − 0.298955I
b = 2.11054 − 0.48664I
3.72285 − 6.96551I −5.97171 + 10.57440I
u = −0.234552 − 1.002020I
a = 0.00700 − 2.10465I
b = 0.451474 + 0.578868I
3.72285 − 6.96551I −5.97171 + 10.57440I
u = 1.090290 + 0.140460I
a = −0.240626 − 0.291610I
b = −0.401743 + 0.003834I
−1.05784 − 1.08263I −14.2815 + 5.6276I
u = 1.090290 + 0.140460I
a = 0.362012 − 0.050153I
b = 0.221393 + 0.351739I
−1.05784 − 1.08263I −14.2815 + 5.6276I
u = 1.090290 − 0.140460I
a = −0.240626 + 0.291610I
b = −0.401743 − 0.003834I
−1.05784 + 1.08263I −14.2815 − 5.6276I
u = 1.090290 − 0.140460I
a = 0.362012 + 0.050153I
b = 0.221393 − 0.351739I
−1.05784 + 1.08263I −14.2815 − 5.6276I
u = −0.185688 + 0.817666I
a = −0.762192 − 0.903819I
b = −1.44128 + 0.18321I
−1.05784 + 1.08263I −14.2815 − 5.6276I
u = −0.185688 + 0.817666I
a = −0.59374 − 1.62783I
b = −0.880553 + 0.455390I
−1.05784 + 1.08263I −14.2815 − 5.6276I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185688 − 0.817666I
a = −0.762192 + 0.903819I
b = −1.44128 − 0.18321I
−1.05784 − 1.08263I −14.2815 + 5.6276I
u = −0.185688 − 0.817666I
a = −0.59374 + 1.62783I
b = −0.880553 − 0.455390I
−1.05784 − 1.08263I −14.2815 + 5.6276I
u = 0.529049 + 1.245360I
a = 0.970902 − 0.051810I
b = 0.692981 + 0.737589I
2.26979 − 4.55813I −9.74676 + 1.77049I
u = 0.529049 + 1.245360I
a = −0.701975 + 0.258240I
b = −0.578176 − 1.181710I
2.26979 − 4.55813I −9.74676 + 1.77049I
u = 0.529049 − 1.245360I
a = 0.970902 + 0.051810I
b = 0.692981 − 0.737589I
2.26979 + 4.55813I −9.74676 − 1.77049I
u = 0.529049 − 1.245360I
a = −0.701975 − 0.258240I
b = −0.578176 + 1.181710I
2.26979 + 4.55813I −9.74676 − 1.77049I
u = −0.251512 + 0.449740I
a = 0.04323 + 2.16308I
b = 0.800711 − 0.884208I
2.26979 − 4.55813I −9.74676 + 1.77049I
u = −0.251512 + 0.449740I
a = 2.25611 + 0.51868I
b = 0.983696 + 0.524600I
2.26979 − 4.55813I −9.74676 + 1.77049I
u = −0.251512 − 0.449740I
a = 0.04323 − 2.16308I
b = 0.800711 + 0.884208I
2.26979 + 4.55813I −9.74676 − 1.77049I
u = −0.251512 − 0.449740I
a = 2.25611 − 0.51868I
b = 0.983696 − 0.524600I
2.26979 + 4.55813I −9.74676 − 1.77049I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.55241 + 1.40748I
a = 0.767735 − 0.370784I
b = 0.486934 + 1.037080I
3.72285 − 6.96551I −5.97171 + 10.57440I
u = 0.55241 + 1.40748I
a = −0.756136 + 0.049190I
b = −0.945979 − 0.875748I
3.72285 − 6.96551I −5.97171 + 10.57440I
u = 0.55241 − 1.40748I
a = 0.767735 + 0.370784I
b = 0.486934 − 1.037080I
3.72285 + 6.96551I −5.97171 − 10.57440I
u = 0.55241 − 1.40748I
a = −0.756136 − 0.049190I
b = −0.945979 + 0.875748I
3.72285 + 6.96551I −5.97171 − 10.57440I
17
IV. I
u
4
= h−au + u
2
+ b − u + 1, −u
2
a + a
2
+ u
2
− a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
a
au − u
2
+ u − 1
a
6
=
−u
2
a + au + u
2
− a − u + 1
1
a
9
=
−au + u
2
+ a − u + 1
au − u
2
+ u − 1
a
4
=
u
u
2
− u + 1
a
3
=
2au − a
−au + u
2
− u + 1
a
7
=
u
2
a − au + u
2
+ a − u
−u
2
a + au − 2u
2
+ u − 1
a
10
=
u
2
+ u
−au + a − 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
2
+ 8u − 14
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(u
3
+ u
2
+ 2u + 1)
2
c
2
, c
7
u
6
+ 5u
5
+ 16u
4
+ 28u
3
+ 30u
2
+ 18u + 5
c
3
, c
5
, c
8
c
10
u
6
− u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
7
y
6
+ 7y
5
+ 36y
4
+ 6y
3
+ 52y
2
− 24y + 25
c
3
, c
5
, c
8
c
10
y
6
+ 3y
5
+ 16y
4
+ 18y
3
+ 12y
2
+ 4y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.594305 − 0.123240I
b = 1.16635 + 1.49520I
7.69319 − 5.65624I 1.01951 + 5.95889I
u = 0.215080 + 1.307140I
a = −1.25666 + 0.68552I
b = −0.288915 − 0.750335I
7.69319 − 5.65624I 1.01951 + 5.95889I
u = 0.215080 − 1.307140I
a = 0.594305 + 0.123240I
b = 1.16635 − 1.49520I
7.69319 + 5.65624I 1.01951 − 5.95889I
u = 0.215080 − 1.307140I
a = −1.25666 − 0.68552I
b = −0.288915 + 0.750335I
7.69319 + 5.65624I 1.01951 − 5.95889I
u = 0.569840
a = 0.662359 + 0.941275I
b = −0.377439 + 0.536376I
−0.581975 −12.0390
u = 0.569840
a = 0.662359 − 0.941275I
b = −0.377439 − 0.536376I
−0.581975 −12.0390
21
V. I
u
5
= hu
2
+ b − u + 1, u
2
+ a + 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
−u
2
− 1
−u
2
+ u − 1
a
6
=
−1
0
a
9
=
−u
−u
2
+ u − 1
a
4
=
u
u
2
− u + 1
a
3
=
u
2
+ 1
u
2
− u + 1
a
7
=
−1
−u
2
a
10
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
2
+ 8u − 20
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
3
− u
2
+ 2u − 1
c
2
, c
4
, c
7
c
9
u
3
+ u
2
+ 2u + 1
c
3
, c
5
, c
8
c
10
u
3
+ u
2
− 1
23
(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
3
+ 3y
2
+ 2y −1
c
3
, c
5
, c
8
c
10
y
3
− y
2
+ 2y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.662359 − 0.562280I
b = 0.877439 + 0.744862I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.215080 − 1.307140I
a = 0.662359 + 0.562280I
b = 0.877439 − 0.744862I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = 0.569840
a = −1.32472
b = −0.754878
−2.22691 −18.0390
25
VI. I
u
6
= hu
6
− 4u
5
+ 8u
4
− 11u
3
+ 9u
2
+ b − 5u + 3, −3u
7
+ 12u
6
+ · · · +
2a + 2, u
8
− 4u
7
+ · · · − 4u + 2i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
3
2
u
7
− 6u
6
+ ··· +
9
2
u − 1
−u
6
+ 4u
5
− 8u
4
+ 11u
3
− 9u
2
+ 5u − 3
a
6
=
1
2
u
7
− 3u
6
+ ··· +
15
2
u − 4
−u
7
+ 3u
6
− 5u
5
+ 6u
4
− 4u
3
+ 3u
2
− u − 1
a
9
=
3
2
u
7
− 5u
6
+ ··· −
1
2
u + 2
−u
6
+ 4u
5
− 8u
4
+ 11u
3
− 9u
2
+ 5u − 3
a
4
=
u
u
3
+ u
a
3
=
−
1
2
u
7
+ 2u
6
+ ··· −
7
2
u + 1
u
2
− u + 1
a
7
=
3
2
u
7
− 6u
6
+ ··· +
3
2
u + 1
−u
7
+ 2u
6
− 2u
5
+ 3u
3
− 2u
2
+ 2u − 1
a
10
=
1
2
u
7
− 2u
6
+ ··· +
3
2
u + 1
−u
4
+ 2u
3
− 3u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
7
+ 16u
6
− 43u
5
+ 71u
4
− 82u
3
+ 68u
2
− 40u + 20
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2
c
2
, c
7
(u
4
− u
3
+ u
2
+ 1)
2
c
3
, c
5
, c
8
c
10
u
8
− 2u
7
+ 3u
5
− 3u
4
+ 3u
2
− u + 1
c
4
, c
9
u
8
+ 4u
7
+ 9u
6
+ 14u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
8
+ 2y
7
− y
6
− 12y
5
− 5y
4
+ 25y
3
+ 37y
2
+ 20y + 4
c
2
, c
7
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
3
, c
5
, c
8
c
10
y
8
− 4y
7
+ 6y
6
− 3y
5
+ 7y
4
− 12y
3
+ 3y
2
+ 5y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.192965 + 0.870342I
a = −0.81301 + 1.44822I
b = −1.41733 − 0.42814I
−0.732875 − 0.991478I 5.28161 − 3.59996I
u = 0.192965 − 0.870342I
a = −0.81301 − 1.44822I
b = −1.41733 + 0.42814I
−0.732875 + 0.991478I 5.28161 + 3.59996I
u = −0.138557 + 0.767522I
a = 0.066843 − 1.409780I
b = 1.072770 + 0.246639I
3.20028 + 5.62938I −5.78161 − 5.27851I
u = −0.138557 − 0.767522I
a = 0.066843 + 1.409780I
b = 1.072770 − 0.246639I
3.20028 − 5.62938I −5.78161 + 5.27851I
u = 1.354460 + 0.250532I
a = 0.008624 + 0.392991I
b = −0.086775 + 0.534450I
−0.732875 − 0.991478I 5.28161 − 3.59996I
u = 1.354460 − 0.250532I
a = 0.008624 − 0.392991I
b = −0.086775 − 0.534450I
−0.732875 + 0.991478I 5.28161 + 3.59996I
u = 0.59113 + 1.35317I
a = −0.762459 + 0.087166I
b = −0.568666 − 0.980213I
3.20028 − 5.62938I −5.78161 + 5.27851I
u = 0.59113 − 1.35317I
a = −0.762459 − 0.087166I
b = −0.568666 + 0.980213I
3.20028 + 5.62938I −5.78161 − 5.27851I
29
VII. I
u
7
= h−au + b + u − 1, a
2
− au − 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u − 1
a
8
=
a
au − u + 1
a
6
=
−au + a − u
1
a
9
=
−au + a + u − 1
au − u + 1
a
4
=
u
u − 1
a
3
=
−au + a + u
au
a
7
=
a + u
au
a
10
=
−2au + a
a − u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u − 14
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(u
2
+ u + 1)
2
c
2
, c
7
(u − 1)
4
c
3
, c
5
, c
8
c
10
u
4
− u
3
+ 2u
2
− 2u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(y
2
+ y + 1)
2
c
2
, c
7
(y −1)
4
c
3
, c
5
, c
8
c
10
y
4
+ 3y
3
+ 2y
2
+ 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.692440 + 0.318148I
b = −0.121744 − 1.306620I
1.64493 − 4.05977I −10.00000 + 6.92820I
u = 0.500000 + 0.866025I
a = 1.192440 + 0.547877I
b = 0.621744 + 0.440597I
1.64493 − 4.05977I −10.00000 + 6.92820I
u = 0.500000 − 0.866025I
a = −0.692440 − 0.318148I
b = −0.121744 + 1.306620I
1.64493 + 4.05977I −10.00000 − 6.92820I
u = 0.500000 − 0.866025I
a = 1.192440 − 0.547877I
b = 0.621744 − 0.440597I
1.64493 + 4.05977I −10.00000 − 6.92820I
33
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
+ u + 1)
2
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
· (u
8
− 4u
7
+ 9u
6
− 14u
5
+ 15u
4
− 13u
3
+ 9u
2
− 4u + 2)
· (u
11
− 3u
10
+ 8u
9
− 13u
8
+ 19u
7
− 22u
6
+ 21u
5
− 17u
4
+ 9u
3
− 4u
2
+ 2)
· ((u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
2
)(u
18
− 5u
17
+ ··· − 27u + 5)
c
2
, c
7
(u − 1)
4
(u
3
+ u
2
+ 2u + 1)(u
4
− u
3
+ u
2
+ 1)
2
· (u
6
+ 5u
5
+ 16u
4
+ 28u
3
+ 30u
2
+ 18u + 5)
· (u
9
− 2u
8
+ 4u
7
− 5u
6
+ 7u
5
− 5u
4
+ 3u
3
− 2u
2
+ u − 1)
2
· (u
11
+ 5u
10
+ ··· + 10u + 4)
· (u
12
+ u
10
− 6u
9
+ 10u
8
− 2u
7
+ 2u
6
− 2u
4
+ 2u
2
+ 1)
2
c
3
, c
5
, c
8
c
10
(u
3
+ u
2
− 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
6
− u
5
+ ··· + 2u + 1)
· (u
8
− 2u
7
+ 3u
5
− 3u
4
+ 3u
2
− u + 1)
· (u
11
+ 4u
9
+ u
8
+ 11u
7
+ 4u
6
+ 15u
5
+ 3u
4
+ 9u
3
− u
2
+ 2u + 1)
· (u
18
− u
17
+ ··· + 3u + 1)(u
24
− 3u
23
+ ··· − 4u
2
+ 1)
c
4
, c
9
(u
2
+ u + 1)
2
(u
3
+ u
2
+ 2u + 1)
3
· (u
8
+ 4u
7
+ 9u
6
+ 14u
5
+ 15u
4
+ 13u
3
+ 9u
2
+ 4u + 2)
· (u
11
− 3u
10
+ 8u
9
− 13u
8
+ 19u
7
− 22u
6
+ 21u
5
− 17u
4
+ 9u
3
− 4u
2
+ 2)
· ((u
12
+ 3u
11
+ ··· + 4u
2
+ 1)
2
)(u
18
− 5u
17
+ ··· − 27u + 5)
34
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(y
2
+ y + 1)
2
(y
3
+ 3y
2
+ 2y −1)
3
· (y
8
+ 2y
7
− y
6
− 12y
5
− 5y
4
+ 25y
3
+ 37y
2
+ 20y + 4)
· (y
11
+ 7y
10
+ ··· + 16y −4)(y
12
+ 7y
11
+ ··· + 8y + 1)
2
· (y
18
+ 9y
17
+ ··· + 61y + 25)
c
2
, c
7
(y −1)
4
(y
3
+ 3y
2
+ 2y −1)(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
· (y
6
+ 7y
5
+ 36y
4
+ 6y
3
+ 52y
2
− 24y + 25)
· (y
9
+ 4y
8
+ 10y
7
+ 17y
6
+ 17y
5
+ y
4
− 7y
3
− 8y
2
− 3y −1)
2
· (y
11
− 5y
10
+ ··· + 60y −16)(y
12
+ 2y
11
+ ··· + 4y + 1)
2
c
3
, c
5
, c
8
c
10
(y
3
− y
2
+ 2y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
6
+ 3y
5
+ 16y
4
+ 18y
3
+ 12y
2
+ 4y + 1)
· (y
8
− 4y
7
+ 6y
6
− 3y
5
+ 7y
4
− 12y
3
+ 3y
2
+ 5y + 1)
· (y
11
+ 8y
10
+ ··· + 6y −1)(y
18
+ 9y
17
+ ··· + 43y + 1)
· (y
24
− 11y
23
+ ··· − 8y + 1)
35
