11a
44
(K11a
44
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 9 3 6 7 5 10
Solving Sequence
3,7
8
4,9 1,10
2 6 11 5
c
7
c
3
c
9
c
2
c
6
c
11
c
5
c
1
, c
4
, c
8
, c
10
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
= h295797384u
18
+ 418536515u
17
+ ··· + 3702415268d − 1995040792,
186291706u
18
+ 295294768u
17
+ ··· + 3702415268c − 4955557140,
− 340509075u
18
− 461083130u
17
+ ··· + 3702415268b + 2243928812,
− 1103288949u
18
− 1383517078u
17
+ ··· + 7404830536a + 9000488512,
u
19
+ 2u
18
+ ··· + 4u
2
− 8i
I
u
2
= hu
7
− 2u
6
+ u
5
+ 3u
4
− 5u
3
+ 3u
2
+ d + u − 1, u
7
− 3u
6
+ u
5
+ 4u
4
− 8u
3
+ 5u
2
+ 2c + u − 4,
− u
7
a + 2u
6
a + 2u
7
− 4u
6
− 4u
4
a + 2u
5
+ 5u
3
a + 5u
4
− u
2
a − 9u
3
− 3au + 8u
2
+ b + 2a − u,
3u
7
a − 4u
7
+ ··· − 6a + 8, u
8
− 3u
7
+ 3u
6
+ 2u
5
− 8u
4
+ 9u
3
− 3u
2
− 2u + 2i
I
u
3
= hu
5
a + u
4
a − u
5
− u
3
a − u
4
− u
2
a + u
2
+ d, −u
5
a − u
4
a + u
2
a + u
3
+ au + u
2
+ c − 1,
− u
4
a − u
3
a + u
4
+ 2u
2
a + u
3
+ au + b − a − u, 2u
5
a + 2u
4
a − u
5
− 2u
3
a − u
4
− 3u
2
a + a
2
+ u
2
+ a,
u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
4
= hu
5
c − u
5
− 2u
3
c + u
3
+ 2cu + d − u + 1, −2u
4
c − u
3
c + u
4
+ 2u
2
c + c
2
+ 2cu − u
2
− u, −u
2
+ b,
− u
2
+ a + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
5
= hu
5
− u
3
+ d + u, 2u
5
+ 2u
4
− 3u
3
− 4u
2
+ c + 2u + 2, −u
2
+ b, −u
2
+ a + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 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 − 1, b + 1, v −1i
I
v
4
= hc, d + 1, −av + c −v −1, bv + 1i
* 8 irreducible components of dim
C
= 0, with total 68 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
= h2.96 × 10
8
u
18
+ 4.19 × 10
8
u
17
+ · · · + 3.70 × 10
9
d − 2.00 ×
10
9
, 1.86 × 10
8
u
18
+ 2.95 × 10
8
u
17
+ · · · + 3.70 × 10
9
c − 4.96 × 10
9
, −3.41 ×
10
8
u
18
− 4.61 × 10
8
u
17
+ · · · + 3.70 × 10
9
b + 2.24 × 10
9
, −1.10 × 10
9
u
18
−
1.38 × 10
9
u
17
+ · · · + 7.40 × 10
9
a + 9.00 × 10
9
, u
19
+ 2u
18
+ · · · + 4u
2
− 8i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−0.0503163u
18
− 0.0797573u
17
+ ··· − 0.0228247u + 1.33847
−0.0798931u
18
− 0.113044u
17
+ ··· − 0.992877u + 0.538848
a
1
=
0.148996u
18
+ 0.186840u
17
+ ··· + 0.656789u − 1.21549
0.0919694u
18
+ 0.124536u
17
+ ··· + 1.08046u − 0.606072
a
10
=
−0.130209u
18
− 0.192802u
17
+ ··· − 1.01570u + 1.87731
−0.0798931u
18
− 0.113044u
17
+ ··· − 0.992877u + 0.538848
a
2
=
0.0237009u
18
+ 0.0450696u
17
+ ··· + 0.0621551u − 0.293810
0.0895560u
18
+ 0.0824521u
17
+ ··· + 1.48819u − 0.554949
a
6
=
−0.0503163u
18
− 0.0797573u
17
+ ··· − 0.0228247u + 1.33847
0.133048u
18
+ 0.117935u
17
+ ··· + 1.39541u − 0.705850
a
11
=
0.106508u
18
+ 0.147732u
17
+ ··· + 0.953547u − 1.58350
−0.00966290u
18
+ 0.0305921u
17
+ ··· + 0.504689u + 0.0161009
a
5
=
−0.0570264u
18
− 0.0623040u
17
+ ··· + 0.423674u + 0.609417
0.143944u
18
+ 0.132344u
17
+ ··· + 1.53667u − 1.02006
a
5
=
−0.0570264u
18
− 0.0623040u
17
+ ··· + 0.423674u + 0.609417
0.143944u
18
+ 0.132344u
17
+ ··· + 1.53667u − 1.02006
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1436975081
1851207634
u
18
−
348795105
1851207634
u
17
+ ··· −
4741127818
925603817
u +
7721567164
925603817
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
19
− 2u
18
+ ··· + 3u − 1
c
2
, c
11
u
19
+ 8u
18
+ ··· + 19u + 1
c
3
, c
7
u
19
+ 2u
18
+ ··· + 4u
2
− 8
c
6
, c
8
, c
9
u
19
+ 2u
18
+ ··· − 8u − 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
19
− 8y
18
+ ··· + 19y −1
c
2
, c
11
y
19
+ 12y
18
+ ··· + 195y −1
c
3
, c
7
y
19
− 6y
18
+ ··· + 64y −64
c
6
, c
8
, c
9
y
19
− 18y
18
+ ··· + 88y −16
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.085440 + 0.040618I
a = −0.082939 − 0.820035I
b = −0.548223 − 0.458686I
c = 0.526397 + 0.204170I
d = −0.651290 + 0.640476I
2.40223 − 3.63220I 3.52732 + 6.81616I
u = −1.085440 − 0.040618I
a = −0.082939 + 0.820035I
b = −0.548223 + 0.458686I
c = 0.526397 − 0.204170I
d = −0.651290 − 0.640476I
2.40223 + 3.63220I 3.52732 − 6.81616I
u = −0.122471 + 1.080680I
a = 0.718026 + 0.002764I
b = 1.002700 + 0.800999I
c = 0.423035 − 0.010382I
d = −1.362450 − 0.057980I
4.14406 − 1.22871I 4.10945 + 3.37998I
u = −0.122471 − 1.080680I
a = 0.718026 − 0.002764I
b = 1.002700 − 0.800999I
c = 0.423035 + 0.010382I
d = −1.362450 + 0.057980I
4.14406 + 1.22871I 4.10945 − 3.37998I
u = 0.583709 + 0.932517I
a = 1.248640 − 0.243760I
b = 0.757420 − 1.122890I
c = 0.663350 − 0.622962I
d = 0.198964 − 0.752266I
−4.29720 − 4.85510I −5.63265 + 5.33490I
u = 0.583709 − 0.932517I
a = 1.248640 + 0.243760I
b = 0.757420 + 1.122890I
c = 0.663350 + 0.622962I
d = 0.198964 + 0.752266I
−4.29720 + 4.85510I −5.63265 − 5.33490I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628638 + 1.123100I
a = −1.232770 − 0.120292I
b = −1.30952 − 1.42851I
c = 0.413232 − 0.052969I
d = −1.380830 − 0.305181I
0.71510 + 8.68076I −0.47305 − 6.48182I
u = −0.628638 − 1.123100I
a = −1.232770 + 0.120292I
b = −1.30952 + 1.42851I
c = 0.413232 + 0.052969I
d = −1.380830 + 0.305181I
0.71510 − 8.68076I −0.47305 + 6.48182I
u = 1.114960 + 0.705316I
a = 0.111878 − 1.272940I
b = −1.46155 − 1.34018I
c = 0.523314 − 0.396742I
d = −0.213448 − 0.919956I
−2.61225 + 10.89710I −3.23641 − 8.50579I
u = 1.114960 − 0.705316I
a = 0.111878 + 1.272940I
b = −1.46155 + 1.34018I
c = 0.523314 + 0.396742I
d = −0.213448 + 0.919956I
−2.61225 − 10.89710I −3.23641 + 8.50579I
u = −0.072034 + 0.667244I
a = −0.502161 − 0.640166I
b = −0.246691 + 0.049771I
c = 1.56560 + 0.68284I
d = 0.463352 + 0.234060I
−1.32552 + 1.22673I −3.58366 − 5.47914I
u = −0.072034 − 0.667244I
a = −0.502161 + 0.640166I
b = −0.246691 − 0.049771I
c = 1.56560 − 0.68284I
d = 0.463352 − 0.234060I
−1.32552 − 1.22673I −3.58366 + 5.47914I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.241950 + 0.516338I
a = 0.276604 + 0.673540I
b = −1.46152 + 0.68811I
c = −1.72308 − 0.97561I
d = 1.43947 − 0.24883I
7.80660 − 4.21764I 6.24313 + 1.77538I
u = −1.241950 − 0.516338I
a = 0.276604 − 0.673540I
b = −1.46152 − 0.68811I
c = −1.72308 + 0.97561I
d = 1.43947 + 0.24883I
7.80660 + 4.21764I 6.24313 − 1.77538I
u = 1.391220 + 0.215371I
a = −0.043768 − 1.017560I
b = −0.031342 + 0.273386I
c = −1.88210 + 0.37845I
d = 1.51067 + 0.10269I
9.74824 + 5.99256I 5.35093 − 5.49640I
u = 1.391220 − 0.215371I
a = −0.043768 + 1.017560I
b = −0.031342 − 0.273386I
c = −1.88210 − 0.37845I
d = 1.51067 − 0.10269I
9.74824 − 5.99256I 5.35093 + 5.49640I
u = −1.18800 + 0.79635I
a = −0.064734 − 1.301180I
b = 1.97753 − 1.24306I
c = −1.28148 − 1.20067I
d = 1.41555 − 0.38935I
2.5538 − 15.5977I 0.09598 + 9.40344I
u = −1.18800 − 0.79635I
a = −0.064734 + 1.301180I
b = 1.97753 + 1.24306I
c = −1.28148 + 1.20067I
d = 1.41555 + 0.38935I
2.5538 + 15.5977I 0.09598 − 9.40344I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.497291
a = 0.142445
b = 0.642422
c = 0.543479
d = −0.839998
1.20822 9.19790
9
II. I
u
2
= hu
7
− 2u
6
+ · · · + d − 1, u
7
− 3u
6
+ · · · + 2c − 4, −u
7
a + 2u
7
+ · · · +
b + 2a, 3u
7
a − 4u
7
+ · · · − 6a + 8, u
8
− 3u
7
+ · · · − 2u + 2i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−
1
2
u
7
+
3
2
u
6
+ ··· −
1
2
u + 2
−u
7
+ 2u
6
− u
5
− 3u
4
+ 5u
3
− 3u
2
− u + 1
a
1
=
a
u
7
a − 2u
7
+ ··· − 2a + u
a
10
=
−
3
2
u
7
+
7
2
u
6
+ ··· −
3
2
u + 3
−u
7
+ 2u
6
− u
5
− 3u
4
+ 5u
3
− 3u
2
− u + 1
a
2
=
u
6
a + 2u
7
+ ··· + 3a − 4
−u
7
a + 3u
6
a + ··· + 2a − 2
a
6
=
−
1
2
u
7
+
3
2
u
6
+ ··· −
1
2
u + 2
−u
6
+ u
5
+ u
4
− 3u
3
+ 2u
2
− 1
a
11
=
−u
7
a +
5
2
u
7
+ ··· + 4a − 5
−u
7
+ 2u
6
+ ··· + 2u − 1
a
5
=
u
7
a − 2u
7
+ ··· − 3a + u
u
7
a − u
6
a + ··· + u − 4
a
5
=
u
7
a − 2u
7
+ ··· − 3a + u
u
7
a − u
6
a + ··· + u − 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
7
+ 4u
5
− 6u
4
− 4u
3
+ 6u
2
− 8u − 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
10
u
16
− u
15
+ ··· + 4u − 4
c
2
, c
11
u
16
+ 7u
15
+ ··· + 40u + 16
c
3
, c
7
(u
8
− 3u
7
+ 3u
6
+ 2u
5
− 8u
4
+ 9u
3
− 3u
2
− 2u + 2)
2
c
6
, c
8
, c
9
(u
8
+ u
7
− 4u
6
− 3u
5
+ 5u
4
+ u
3
− u
2
+ 3u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y
16
− 7y
15
+ ··· − 40y + 16
c
2
, c
11
y
16
+ y
15
+ ··· − 544y + 256
c
3
, c
7
(y
8
− 3y
7
+ 5y
6
− 4y
5
+ 2y
4
− 13y
3
+ 13y
2
− 16y + 4)
2
c
6
, c
8
, c
9
(y
8
− 9y
7
+ 32y
6
− 53y
5
+ 31y
4
+ 15y
3
− 15y
2
− 7y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.821613 + 0.567011I
a = 0.327841 − 1.281680I
b = −0.32411 − 2.07852I
c = 0.647330 − 0.378425I
d = −0.151337 − 0.673064I
−4.77492 + 2.26376I −6.05872 − 4.53378I
u = 0.821613 + 0.567011I
a = 1.55977 − 0.26895I
b = −0.408126 − 1.151440I
c = 0.647330 − 0.378425I
d = −0.151337 − 0.673064I
−4.77492 + 2.26376I −6.05872 − 4.53378I
u = 0.821613 − 0.567011I
a = 0.327841 + 1.281680I
b = −0.32411 + 2.07852I
c = 0.647330 + 0.378425I
d = −0.151337 + 0.673064I
−4.77492 − 2.26376I −6.05872 + 4.53378I
u = 0.821613 − 0.567011I
a = 1.55977 + 0.26895I
b = −0.408126 + 1.151440I
c = 0.647330 + 0.378425I
d = −0.151337 + 0.673064I
−4.77492 − 2.26376I −6.05872 + 4.53378I
u = 0.432344 + 1.079150I
a = 1.115680 − 0.168353I
b = 1.27697 − 0.76242I
c = 0.420583 + 0.036953I
d = −1.359440 + 0.207304I
2.93531 − 3.55755I 2.52739 + 2.62489I
u = 0.432344 + 1.079150I
a = −0.603271 + 0.193035I
b = −0.50994 + 1.48491I
c = 0.420583 + 0.036953I
d = −1.359440 + 0.207304I
2.93531 − 3.55755I 2.52739 + 2.62489I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432344 − 1.079150I
a = 1.115680 + 0.168353I
b = 1.27697 + 0.76242I
c = 0.420583 − 0.036953I
d = −1.359440 − 0.207304I
2.93531 + 3.55755I 2.52739 − 2.62489I
u = 0.432344 − 1.079150I
a = −0.603271 − 0.193035I
b = −0.50994 − 1.48491I
c = 0.420583 − 0.036953I
d = −1.359440 − 0.207304I
2.93531 + 3.55755I 2.52739 − 2.62489I
u = −1.38845
a = 0.099908 + 0.914602I
b = −0.636148 − 0.242515I
c = −1.96418
d = 1.50912
10.1546 6.33750
u = −1.38845
a = 0.099908 − 0.914602I
b = −0.636148 + 0.242515I
c = −1.96418
d = 1.50912
10.1546 6.33750
u = 1.215250 + 0.684012I
a = 0.067480 − 1.248660I
b = −1.57665 − 0.90527I
c = −1.45820 + 1.13316I
d = 1.42757 + 0.33227I
5.44991 + 9.88301I 3.28252 − 6.06963I
u = 1.215250 + 0.684012I
a = −0.355893 + 0.630356I
b = 1.56027 + 1.09581I
c = −1.45820 + 1.13316I
d = 1.42757 + 0.33227I
5.44991 + 9.88301I 3.28252 − 6.06963I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.215250 − 0.684012I
a = 0.067480 + 1.248660I
b = −1.57665 + 0.90527I
c = −1.45820 − 1.13316I
d = 1.42757 − 0.33227I
5.44991 − 9.88301I 3.28252 + 6.06963I
u = 1.215250 − 0.684012I
a = −0.355893 − 0.630356I
b = 1.56027 − 1.09581I
c = −1.45820 − 1.13316I
d = 1.42757 − 0.33227I
5.44991 − 9.88301I 3.28252 + 6.06963I
u = −0.549965
a = −1.11644
b = −2.20354
c = 0.744760
d = −0.342714
−2.57083 2.16010
u = −0.549965
a = −2.30659
b = 0.439006
c = 0.744760
d = −0.342714
−2.57083 2.16010
15
III. I
u
3
= hu
5
a − u
5
+ · · · + u
2
+ d, −u
5
a − u
4
a + · · · + c − 1, −u
4
a + u
4
+
· · · + b − a, 2u
5
a − u
5
+ · · · + a
2
+ a, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
u
5
a + u
4
a − u
2
a − u
3
− au − u
2
+ 1
−u
5
a − u
4
a + u
5
+ u
3
a + u
4
+ u
2
a − u
2
a
1
=
a
u
4
a + u
3
a − u
4
− 2u
2
a − u
3
− au + a + u
a
10
=
u
5
+ u
3
a + u
4
− u
3
− au − 2u
2
+ 1
−u
5
a − u
4
a + u
5
+ u
3
a + u
4
+ u
2
a − u
2
a
2
=
−u
3
a + u
4
+ u
3
+ au + 2a − u − 1
u
5
a + u
4
a − u
3
a − u
4
− 3u
2
a − u
3
+ u
2
+ 2a + u
a
6
=
u
5
a + u
4
a − u
2
a − u
3
− au − u
2
+ 1
au
a
11
=
u
5
a + u
4
a − 2u
3
a − u
2
a + au + u
2
+ 2a − 1
u
5
a + u
4
a − u
3
a − u
4
− 3u
2
a − u
3
+ u
2
+ 2a + u
a
5
=
u
4
a + u
3
a − u
4
− 2u
2
a − u
3
− au + u
2u
4
a − 2u
2
a + 2a − 1
a
5
=
u
4
a + u
3
a − u
4
− 2u
2
a − u
3
− au + u
2u
4
a − 2u
2
a + 2a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 2
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
, c
9
u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1
c
2
u
12
+ 9u
11
+ ··· − 4u + 1
c
3
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
5
, c
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
11
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
8
, c
9
y
12
− 9y
11
+ ··· + 4y + 1
c
2
y
12
− 13y
11
+ ··· − 12y + 1
c
3
, c
5
, c
7
c
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
11
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.228720 − 1.004780I
b = 0.103539 − 0.942817I
c = 0.490081 + 0.135670I
d = −0.895235 + 0.524661I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 + 0.295542I
a = 1.69020 − 0.12901I
b = −1.18901 − 0.78206I
c = −2.60446 + 1.12615I
d = 1.323480 + 0.139870I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 − 0.295542I
a = 0.228720 + 1.004780I
b = 0.103539 + 0.942817I
c = 0.490081 − 0.135670I
d = −0.895235 − 0.524661I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.002190 − 0.295542I
a = 1.69020 + 0.12901I
b = −1.18901 + 0.78206I
c = −2.60446 − 1.12615I
d = 1.323480 − 0.139870I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.428243 + 0.664531I
a = 0.305248 + 0.125739I
b = −0.101098 + 0.828455I
c = 0.886780 + 0.510268I
d = 0.152828 + 0.487477I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = −0.41743 − 1.68310I
b = −0.15460 − 3.71488I
c = 0.460381 − 0.041004I
d = −1.155020 − 0.191936I
−1.89061 + 0.92430I −3.71672 − 0.79423I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = 0.305248 − 0.125739I
b = −0.101098 − 0.828455I
c = 0.886780 − 0.510268I
d = 0.152828 − 0.487477I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = −0.41743 + 1.68310I
b = −0.15460 + 3.71488I
c = 0.460381 + 0.041004I
d = −1.155020 + 0.191936I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.073950 + 0.558752I
a = 0.266694 + 0.574266I
b = −1.16959 + 0.91104I
c = 0.550084 + 0.355577I
d = −0.282166 + 0.828798I
− 5.69302I 0. + 5.51057I
u = −1.073950 + 0.558752I
a = −1.57343 − 0.13663I
b = 1.01075 − 1.59090I
c = −1.78287 − 1.35197I
d = 1.356120 − 0.270046I
− 5.69302I 0. + 5.51057I
u = −1.073950 − 0.558752I
a = 0.266694 − 0.574266I
b = −1.16959 − 0.91104I
c = 0.550084 − 0.355577I
d = −0.282166 − 0.828798I
5.69302I 0. − 5.51057I
u = −1.073950 − 0.558752I
a = −1.57343 + 0.13663I
b = 1.01075 + 1.59090I
c = −1.78287 + 1.35197I
d = 1.356120 + 0.270046I
5.69302I 0. − 5.51057I
20
IV. I
u
4
= hu
5
c − u
5
+ · · · + d + 1, −2u
4
c + u
4
+ · · · + c
2
− u, −u
2
+ b, −u
2
+
a + 1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
c
−u
5
c + u
5
+ 2u
3
c − u
3
− 2cu + u − 1
a
1
=
u
2
− 1
u
2
a
10
=
−u
5
c + u
5
+ 2u
3
c − u
3
− 2cu + c + u − 1
−u
5
c + u
5
+ 2u
3
c − u
3
− 2cu + u − 1
a
2
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
6
=
c
u
5
c − u
5
− 2u
3
c − u
2
c + u
3
+ 2cu − u + 1
a
11
=
−c
u
5
c − u
5
− 2u
3
c + u
3
+ 2cu − u + 1
a
5
=
1
0
a
5
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 2
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
3
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
5
, c
6
, c
8
c
9
, c
10
u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1
c
11
u
12
+ 9u
11
+ ··· − 4u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
5
, c
6
, c
8
c
9
, c
10
y
12
− 9y
11
+ ··· + 4y + 1
c
11
y
12
− 13y
11
+ ··· − 12y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.082955 + 0.592379I
b = 0.917045 + 0.592379I
c = 0.490081 + 0.135670I
d = −0.895235 + 0.524661I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 + 0.295542I
a = −0.082955 + 0.592379I
b = 0.917045 + 0.592379I
c = −2.60446 + 1.12615I
d = 1.323480 + 0.139870I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 − 0.295542I
a = −0.082955 − 0.592379I
b = 0.917045 − 0.592379I
c = 0.490081 − 0.135670I
d = −0.895235 − 0.524661I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 1.002190 − 0.295542I
a = −0.082955 − 0.592379I
b = 0.917045 − 0.592379I
c = −2.60446 − 1.12615I
d = 1.323480 − 0.139870I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.428243 + 0.664531I
a = −1.258210 − 0.569162I
b = −0.258209 − 0.569162I
c = 0.886780 + 0.510268I
d = 0.152828 + 0.487477I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.428243 + 0.664531I
a = −1.258210 − 0.569162I
b = −0.258209 − 0.569162I
c = 0.460381 − 0.041004I
d = −1.155020 − 0.191936I
−1.89061 + 0.92430I −3.71672 − 0.79423I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = −1.258210 + 0.569162I
b = −0.258209 + 0.569162I
c = 0.886780 − 0.510268I
d = 0.152828 − 0.487477I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.428243 − 0.664531I
a = −1.258210 + 0.569162I
b = −0.258209 + 0.569162I
c = 0.460381 + 0.041004I
d = −1.155020 + 0.191936I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.073950 + 0.558752I
a = −0.158836 − 1.200140I
b = 0.84116 − 1.20014I
c = 0.550084 + 0.355577I
d = −0.282166 + 0.828798I
− 5.69302I 0. + 5.51057I
u = −1.073950 + 0.558752I
a = −0.158836 − 1.200140I
b = 0.84116 − 1.20014I
c = −1.78287 − 1.35197I
d = 1.356120 − 0.270046I
− 5.69302I 0. + 5.51057I
u = −1.073950 − 0.558752I
a = −0.158836 + 1.200140I
b = 0.84116 + 1.20014I
c = 0.550084 − 0.355577I
d = −0.282166 − 0.828798I
5.69302I 0. − 5.51057I
u = −1.073950 − 0.558752I
a = −0.158836 + 1.200140I
b = 0.84116 + 1.20014I
c = −1.78287 + 1.35197I
d = 1.356120 + 0.270046I
5.69302I 0. − 5.51057I
25
V. I
u
5
= hu
5
− u
3
+ d + u, 2u
5
+ 2u
4
+ · · · + c + 2, −u
2
+ b, −u
2
+ a +
1, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−2u
5
− 2u
4
+ 3u
3
+ 4u
2
− 2u − 2
−u
5
+ u
3
− u
a
1
=
u
2
− 1
u
2
a
10
=
−3u
5
− 2u
4
+ 4u
3
+ 4u
2
− 3u − 2
−u
5
+ u
3
− u
a
2
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
6
=
−2u
5
− 2u
4
+ 3u
3
+ 4u
2
− 2u − 2
u
3
− u
a
11
=
2u
5
+ 2u
4
− 3u
3
− 4u
2
+ 2u + 2
u
5
− u
3
+ u
a
5
=
1
0
a
5
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 2
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
9
c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
2
, c
11
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
3
, c
7
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.082955 + 0.592379I
b = 0.917045 + 0.592379I
c = 0.575561 − 0.267796I
d = −0.428243 − 0.664531I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 1.002190 − 0.295542I
a = −0.082955 − 0.592379I
b = 0.917045 − 0.592379I
c = 0.575561 + 0.267796I
d = −0.428243 + 0.664531I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.428243 + 0.664531I
a = −1.258210 − 0.569162I
b = −0.258209 − 0.569162I
c = −0.02510 − 3.38343I
d = 1.002190 − 0.295542I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.428243 − 0.664531I
a = −1.258210 + 0.569162I
b = −0.258209 + 0.569162I
c = −0.02510 + 3.38343I
d = 1.002190 + 0.295542I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.073950 + 0.558752I
a = −0.158836 − 1.200140I
b = 0.84116 − 1.20014I
c = 0.449542 − 0.121113I
d = −1.073950 − 0.558752I
− 5.69302I 0. + 5.51057I
u = −1.073950 − 0.558752I
a = −0.158836 + 1.200140I
b = 0.84116 + 1.20014I
c = 0.449542 + 0.121113I
d = −1.073950 + 0.558752I
5.69302I 0. − 5.51057I
29
VI. I
v
1
= ha, d, c − 1, b − 1, v + 1i
(i) Arc colorings
a
3
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
4
=
−1
0
a
9
=
1
0
a
1
=
0
1
a
10
=
1
0
a
2
=
−1
1
a
6
=
1
0
a
11
=
1
1
a
5
=
0
−1
a
5
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u − 1
c
2
, c
4
, c
10
c
11
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
, c
11
y −1
c
3
, c
6
, c
7
c
8
, c
9
y
32
(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
33
VII. I
v
2
= hc, d + 1, b, a − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
8
=
1
0
a
4
=
1
0
a
9
=
0
−1
a
1
=
1
0
a
10
=
−1
−1
a
2
=
1
0
a
6
=
1
1
a
11
=
0
−1
a
5
=
1
0
a
5
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
c
5
, c
6
, c
11
u + 1
c
8
, c
9
, c
10
u − 1
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y −1
36
(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
0 0
37
VIII. I
v
3
= ha, d + 1, c − a − 1, b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
8
=
1
0
a
4
=
1
0
a
9
=
1
−1
a
1
=
0
−1
a
10
=
0
−1
a
2
=
1
−1
a
6
=
0
1
a
11
=
0
−1
a
5
=
0
1
a
5
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
9
u − 1
c
2
, c
4
, c
6
u + 1
c
3
, c
5
, c
7
c
10
, c
11
u
39
(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
y
40
(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 = 1.00000
d = −1.00000
0 0
41
IX. I
v
4
= hc, d + 1, −av + c − v − 1, bv + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
v
0
a
9
=
0
−1
a
1
=
a
a + 1
a
10
=
−1
−1
a
2
=
a + v
a + 1
a
6
=
1
1
a
11
=
a + 1
a + 2
a
5
=
−a
−a − 1
a
5
=
−a
−a − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −a
2
− v
2
− 2a − 5
(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.
42
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−1.64493 −3.42386 − 0.27749I
43
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1)
· (u
16
− u
15
+ ··· + 4u − 4)(u
19
− 2u
18
+ ··· + 3u − 1)
c
2
, c
11
u(u + 1)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
· (u
12
+ 9u
11
+ ··· − 4u + 1)(u
16
+ 7u
15
+ ··· + 40u + 16)
· (u
19
+ 8u
18
+ ··· + 19u + 1)
c
3
, c
7
u
3
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
5
· (u
8
− 3u
7
+ 3u
6
+ 2u
5
− 8u
4
+ 9u
3
− 3u
2
− 2u + 2)
2
· (u
19
+ 2u
18
+ ··· + 4u
2
− 8)
c
4
u(u + 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1)
· (u
16
− u
15
+ ··· + 4u − 4)(u
19
− 2u
18
+ ··· + 3u − 1)
c
5
, c
10
u(u − 1)(u + 1)(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1)
· (u
16
− u
15
+ ··· + 4u − 4)(u
19
− 2u
18
+ ··· + 3u − 1)
c
6
u(u + 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
· (u
8
+ u
7
− 4u
6
− 3u
5
+ 5u
4
+ u
3
− u
2
+ 3u − 1)
2
· (u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1)
2
· (u
19
+ 2u
18
+ ··· − 8u − 4)
c
8
, c
9
u(u − 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
· (u
8
+ u
7
− 4u
6
− 3u
5
+ 5u
4
+ u
3
− u
2
+ 3u − 1)
2
· (u
12
+ u
11
− 4u
10
− 2u
9
+ 7u
8
− u
7
− 5u
6
+ 5u
5
− u
4
− 3u
3
+ 2u
2
+ 1)
2
· (u
19
+ 2u
18
+ ··· − 8u − 4)
44
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
10
y(y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
12
− 9y
11
+ ··· + 4y + 1)(y
16
− 7y
15
+ ··· − 40y + 16)
· (y
19
− 8y
18
+ ··· + 19y −1)
c
2
, c
11
y(y − 1)
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (y
12
− 13y
11
+ ··· − 12y + 1)(y
16
+ y
15
+ ··· − 544y + 256)
· (y
19
+ 12y
18
+ ··· + 195y −1)
c
3
, c
7
y
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
5
· (y
8
− 3y
7
+ 5y
6
− 4y
5
+ 2y
4
− 13y
3
+ 13y
2
− 16y + 4)
2
· (y
19
− 6y
18
+ ··· + 64y −64)
c
6
, c
8
, c
9
y(y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
8
− 9y
7
+ 32y
6
− 53y
5
+ 31y
4
+ 15y
3
− 15y
2
− 7y + 1)
2
· ((y
12
− 9y
11
+ ··· + 4y + 1)
2
)(y
19
− 18y
18
+ ··· + 88y −16)
45
