11a
231
(K11a
231
)
A knot diagram
1
Linearized knot diagam
7 1 6 10 3 4 2 11 5 8 9
Solving Sequence
4,10 2,5,7
8 1 6 3 9 11
c
4
c
7
c
1
c
6
c
3
c
9
c
11
c
2
, c
5
, 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
= h49503754u
16
− 103286795u
15
+ ··· + 3447876362d − 235456666,
58457271u
16
− 270451180u
15
+ ··· + 13791505448c − 14346071104,
31318034u
16
− 423514703u
15
+ ··· + 6895752724b − 2520805844,
630201461u
16
− 1197766854u
15
+ ··· + 13791505448a − 18642484192, u
17
− 2u
16
+ ··· − 4u
2
+ 8i
I
u
2
= h4u
6
a + 14u
5
a − 3u
6
+ 26u
4
a − 3u
5
+ 26u
3
a − 2u
4
+ 8u
2
a + 3u
3
− 12au + 9u
2
+ 10d − 14a + 9u + 8,
3u
6
a + 3u
5
a − u
6
+ 2u
4
a + 4u
5
− 3u
3
a + 11u
4
− 9u
2
a + 21u
3
− 9au + 18u
2
+ 10c − 8a + 8u + 1,
− u
5
− 2u
4
− 3u
3
+ au − 2u
2
+ b − u,
− 4u
6
− 2u
4
a − 9u
5
− 4u
3
a − 15u
4
− 6u
2
a − 10u
3
+ 2a
2
− 4au − 3u
2
− 2a + 7u + 7,
u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2i
I
u
3
= hu
3
+ d + u, c + u, u
4
− 2u
2
a − u
3
+ au + u
2
+ b − 2a − 1,
− u
4
a + 2u
3
a − 3u
2
a + u
3
+ a
2
+ 2au − u
2
− a + 2u − 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
4
= h−6u
4
a + u
3
a + 2u
4
− 15u
2
a − 8u
3
+ 5au + 5u
2
+ 23d + 2a − 17u + 7,
− 2u
4
a − 15u
3
a − 7u
4
− 5u
2
a + 5u
3
− 6au − 6u
2
+ 23c − 7a − 21u + 10,
− 4u
4
a + 16u
3
a + 9u
4
− 10u
2
a − 13u
3
+ 11au + 11u
2
+ 23b − 14a + 4u − 3,
− u
4
a + 2u
4
− u
2
a + u
3
+ a
2
− 2au + u
2
− a + 4u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
5
= hu
3
+ d + u, c + u, −u
4
+ u
3
− u
2
+ b − 1, −u
4
− u
2
+ a − 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, d + 1, c + a, b − 1, v + 1i
I
v
2
= ha, d, c − 1, b + 1, v − 1i
I
v
3
= ha, d + 1, c + a − 1, b − 1, v − 1i
I
v
4
= hc, d + 1, cb + a − 1, cv + av −c −v, bv − v + 1i
* 8 irreducible components of dim
C
= 0, with total 59 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
= h4.95 × 10
7
u
16
− 1.03 × 10
8
u
15
+ · · · + 3.45 × 10
9
d − 2.35 ×
10
8
, 5.85 × 10
7
u
16
− 2.70 × 10
8
u
15
+ · · · + 1.38 × 10
10
c − 1.43 × 10
10
, 3.13 ×
10
7
u
16
− 4.24 × 10
8
u
15
+ · · · + 6.90 × 10
9
b − 2.52 × 10
9
, 6.30 × 10
8
u
16
−
1.20 × 10
9
u
15
+ · · · + 1.38 × 10
10
a − 1.86 × 10
10
, u
17
− 2u
16
+ · · · − 4u
2
+ 8i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
−0.0456949u
16
+ 0.0868482u
15
+ ··· + 0.0108537u + 1.35174
−0.00454164u
16
+ 0.0614167u
15
+ ··· + 1.35174u + 0.365559
a
5
=
1
u
2
a
7
=
−0.00423864u
16
+ 0.0196100u
15
+ ··· − 0.366884u + 1.04021
−0.0143578u
16
+ 0.0299566u
15
+ ··· − 0.201558u + 0.0682903
a
8
=
0.00853629u
16
− 0.00271483u
15
+ ··· − 0.843158u + 0.201558
−0.0111327u
16
+ 0.00527464u
15
+ ··· − 1.04021u − 0.0339091
a
1
=
0.0196690u
16
− 0.00798947u
15
+ ··· + 0.197053u + 0.235467
0.00442501u
16
+ 0.0219877u
15
+ ··· + 0.882859u − 0.216879
a
6
=
0.0101191u
16
− 0.0103467u
15
+ ··· − 0.165326u + 0.971920
−0.0143578u
16
+ 0.0299566u
15
+ ··· − 0.201558u + 0.0682903
a
3
=
0.0101191u
16
− 0.0103467u
15
+ ··· − 0.165326u + 0.971920
0.0191724u
16
− 0.0450506u
15
+ ··· + 0.120605u − 0.147423
a
9
=
u
u
3
+ u
a
11
=
0.0184279u
16
− 0.0176833u
15
+ ··· + 0.128762u + 0.120605
0.00318587u
16
− 0.0118199u
15
+ ··· + 0.824498u − 0.234332
a
11
=
0.0184279u
16
− 0.0176833u
15
+ ··· + 0.128762u + 0.120605
0.00318587u
16
− 0.0118199u
15
+ ··· + 0.824498u − 0.234332
(ii) Obstruction class = −1
(iii) Cusp Shapes =
975451789
3447876362
u
16
−
210120269
3447876362
u
15
+ ··· +
8037027246
1723938181
u −
2146878348
1723938181
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
17
− 2u
16
+ ··· − 8u + 4
c
2
u
17
+ 6u
16
+ ··· + 88u + 16
c
3
, c
5
, c
6
c
8
, c
10
, c
11
u
17
+ 2u
16
+ ··· + 3u + 1
c
4
, c
9
u
17
− 2u
16
+ ··· − 4u
2
+ 8
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
17
− 6y
16
+ ··· + 88y −16
c
2
y
17
+ 10y
16
+ ··· + 288y −256
c
3
, c
5
, c
6
c
8
, c
10
, c
11
y
17
− 20y
16
+ ··· + 27y −1
c
4
, c
9
y
17
+ 6y
16
+ ··· + 64y −64
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679716 + 0.561358I
a = 0.75464 + 1.62593I
b = −0.39979 + 1.52879I
c = 0.849883 + 1.063640I
d = 0.073472 + 0.578699I
−3.14388 + 1.09865I −5.52136 − 1.09882I
u = 0.679716 − 0.561358I
a = 0.75464 − 1.62593I
b = −0.39979 − 1.52879I
c = 0.849883 − 1.063640I
d = 0.073472 − 0.578699I
−3.14388 − 1.09865I −5.52136 + 1.09882I
u = 0.555749 + 1.023030I
a = −1.22318 − 0.96405I
b = 0.30647 − 1.78712I
c = 0.306715 + 1.153640I
d = −0.260592 + 0.795594I
−1.71782 − 5.90288I −0.75718 + 7.23695I
u = 0.555749 − 1.023030I
a = −1.22318 + 0.96405I
b = 0.30647 + 1.78712I
c = 0.306715 − 1.153640I
d = −0.260592 − 0.795594I
−1.71782 + 5.90288I −0.75718 − 7.23695I
u = −1.247530 + 0.318357I
a = −0.254428 + 0.248211I
b = 0.238386 − 0.390648I
c = −1.033850 + 0.177824I
d = −1.44180 + 0.15237I
8.60033 − 1.91429I 8.38805 + 0.33236I
u = −1.247530 − 0.318357I
a = −0.254428 − 0.248211I
b = 0.238386 + 0.390648I
c = −1.033850 − 0.177824I
d = −1.44180 − 0.15237I
8.60033 + 1.91429I 8.38805 − 0.33236I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.022849 + 0.695780I
a = 0.596447 − 0.521515I
b = 0.349231 + 0.426912I
c = 0.070481 − 0.342332I
d = −0.556553 − 0.244029I
0.88275 + 1.29794I 5.86581 − 6.22804I
u = −0.022849 − 0.695780I
a = 0.596447 + 0.521515I
b = 0.349231 − 0.426912I
c = 0.070481 + 0.342332I
d = −0.556553 + 0.244029I
0.88275 − 1.29794I 5.86581 + 6.22804I
u = 1.235140 + 0.560024I
a = −1.37636 − 0.88777I
b = −1.20283 − 1.86731I
c = −1.030900 − 0.315398I
d = −1.43635 − 0.27040I
6.85439 + 7.49245I 6.04980 − 5.00652I
u = 1.235140 − 0.560024I
a = −1.37636 + 0.88777I
b = −1.20283 + 1.86731I
c = −1.030900 + 0.315398I
d = −1.43635 + 0.27040I
6.85439 − 7.49245I 6.04980 + 5.00652I
u = −0.66454 + 1.33308I
a = −0.189517 − 0.255094I
b = 0.466001 − 0.083122I
c = 0.052946 + 1.267480I
d = 1.48587 + 0.32095I
11.9481 + 8.6770I 9.06927 − 4.38269I
u = −0.66454 − 1.33308I
a = −0.189517 + 0.255094I
b = 0.466001 + 0.083122I
c = 0.052946 − 1.267480I
d = 1.48587 − 0.32095I
11.9481 − 8.6770I 9.06927 + 4.38269I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.79652 + 1.26851I
a = 0.52130 + 1.70360I
b = −1.74580 + 2.01822I
c = 0.18365 − 1.46954I
d = 1.45618 − 0.38779I
9.1924 − 14.7354I 6.16899 + 8.15927I
u = 0.79652 − 1.26851I
a = 0.52130 − 1.70360I
b = −1.74580 − 2.01822I
c = 0.18365 + 1.46954I
d = 1.45618 + 0.38779I
9.1924 + 14.7354I 6.16899 − 8.15927I
u = −0.11728 + 1.54547I
a = −0.380984 + 0.529958I
b = −0.774348 − 0.650953I
c = −0.113527 + 0.217154I
d = 1.58385 + 0.05558I
15.7365 + 3.2760I 10.07807 − 2.58290I
u = −0.11728 − 1.54547I
a = −0.380984 − 0.529958I
b = −0.774348 + 0.650953I
c = −0.113527 − 0.217154I
d = 1.58385 − 0.05558I
15.7365 − 3.2760I 10.07807 + 2.58290I
u = −0.429856
a = 1.10419
b = −0.474641
c = 1.42921
d = 0.191836
−1.29941 −8.68290
8
II. I
u
2
= h4u
6
a − 3u
6
+ · · · − 14a + 8, 3u
6
a − u
6
+ · · · − 8a + 1, −u
5
− 2u
4
+
· · · + b − u, −4u
6
− 9u
5
+ · · · − 2a + 7, u
7
+ 3u
6
+ · · · − 2u − 2i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
u
5
+ 2u
4
+ 3u
3
− au + 2u
2
+ u
a
5
=
1
u
2
a
7
=
−
3
10
u
6
a +
1
10
u
6
+ ··· +
4
5
a −
1
10
−
2
5
u
6
a +
3
10
u
6
+ ··· +
7
5
a −
4
5
a
8
=
7
10
u
6
a +
1
10
u
6
+ ··· −
1
5
a −
1
10
3
5
u
6
a +
3
10
u
6
+ ··· −
3
5
a −
4
5
a
1
=
1
10
u
6
a −
1
5
u
6
+ ··· +
2
5
a +
7
10
−
1
5
u
6
a −
1
10
u
6
+ ··· +
1
5
a +
3
5
a
6
=
1
10
u
6
a −
1
5
u
6
+ ··· −
3
5
a +
7
10
−
2
5
u
6
a +
3
10
u
6
+ ··· +
7
5
a −
4
5
a
3
=
1
10
u
6
a −
1
5
u
6
+ ··· −
3
5
a +
7
10
−
1
5
u
6
a −
1
10
u
6
+ ··· +
1
5
a +
3
5
a
9
=
u
u
3
+ u
a
11
=
−
1
10
u
6
a +
1
5
u
6
+ ··· −
2
5
a −
7
10
−
1
5
u
6
a −
1
10
u
6
+ ··· +
1
5
a −
2
5
a
11
=
−
1
10
u
6
a +
1
5
u
6
+ ··· −
2
5
a −
7
10
−
1
5
u
6
a −
1
10
u
6
+ ··· +
1
5
a −
2
5
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
6
+ 8u
5
+ 10u
4
+ 10u
3
− 4u
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
7
− u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
+ u + 1)
2
c
2
(u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
2
c
3
, c
5
, c
6
c
8
, c
10
, c
11
u
14
+ u
13
+ ··· − 4u − 4
c
4
, c
9
(u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
7
− 3y
6
+ 7y
5
− 8y
4
+ 9y
3
− 6y
2
+ 5y −1)
2
c
2
(y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y −1)
2
c
3
, c
5
, c
6
c
8
, c
10
, c
11
y
14
− 11y
13
+ ··· − 40y + 16
c
4
, c
9
(y
7
+ 3y
6
+ 4y
5
+ y
4
− y
3
+ 7y
2
+ 8y −4)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984140 + 0.426152I
a = −0.84548 + 1.17216I
b = −0.51690 + 2.36796I
c = −0.883662 + 0.240859I
d = −1.312740 + 0.203166I
1.19445 − 3.93070I 1.74059 + 4.87230I
u = −0.984140 + 0.426152I
a = 1.31968 − 1.83467I
b = 0.33256 − 1.51387I
c = 1.03098 − 1.45195I
d = 0.327402 − 0.709633I
1.19445 − 3.93070I 1.74059 + 4.87230I
u = −0.984140 − 0.426152I
a = −0.84548 − 1.17216I
b = −0.51690 − 2.36796I
c = −0.883662 − 0.240859I
d = −1.312740 − 0.203166I
1.19445 + 3.93070I 1.74059 − 4.87230I
u = −0.984140 − 0.426152I
a = 1.31968 + 1.83467I
b = 0.33256 + 1.51387I
c = 1.03098 + 1.45195I
d = 0.327402 + 0.709633I
1.19445 + 3.93070I 1.74059 − 4.87230I
u = −0.167785 + 1.218780I
a = −0.774541 − 0.827762I
b = 0.139458 + 0.651897I
c = −0.828730 + 0.501700I
d = 1.42814 + 0.08000I
7.14223 − 0.95540I 8.68929 + 2.37083I
u = −0.167785 + 1.218780I
a = 0.509470 − 0.184562I
b = 1.138810 − 0.805107I
c = −0.353234 + 0.874846I
d = −0.830837 + 0.693845I
7.14223 − 0.95540I 8.68929 + 2.37083I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.167785 − 1.218780I
a = −0.774541 + 0.827762I
b = 0.139458 − 0.651897I
c = −0.828730 − 0.501700I
d = 1.42814 − 0.08000I
7.14223 + 0.95540I 8.68929 − 2.37083I
u = −0.167785 − 1.218780I
a = 0.509470 + 0.184562I
b = 1.138810 + 0.805107I
c = −0.353234 − 0.874846I
d = −0.830837 − 0.693845I
7.14223 + 0.95540I 8.68929 − 2.37083I
u = −0.654547 + 1.202470I
a = 1.13788 − 1.10109I
b = −1.38518 − 2.03898I
c = −0.09289 + 1.46019I
d = 1.42086 + 0.31765I
3.65356 + 9.93065I 3.53972 − 7.33664I
u = −0.654547 + 1.202470I
a = −0.82436 + 1.60067I
b = 0.57924 + 2.08898I
c = 0.223021 − 1.320930I
d = −0.281398 − 0.947821I
3.65356 + 9.93065I 3.53972 − 7.33664I
u = −0.654547 − 1.202470I
a = 1.13788 + 1.10109I
b = −1.38518 + 2.03898I
c = −0.09289 − 1.46019I
d = 1.42086 − 0.31765I
3.65356 − 9.93065I 3.53972 + 7.33664I
u = −0.654547 − 1.202470I
a = −0.82436 − 1.60067I
b = 0.57924 − 2.08898I
c = 0.223021 + 1.320930I
d = −0.281398 + 0.947821I
3.65356 − 9.93065I 3.53972 + 7.33664I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612945
a = 0.738956
b = 1.97108
c = −0.686858
d = −1.15162
2.33847 2.06080
u = 0.612945
a = 3.21576
b = 0.452939
c = 3.49590
d = 0.648769
2.33847 2.06080
14
III. I
u
3
= hu
3
+ d + u, c + u, u
4
− u
3
+ · · · − 2a − 1, −u
4
a + 2u
3
a + · · · − a −
1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
−u
4
+ 2u
2
a + u
3
− au − u
2
+ 2a + 1
a
5
=
1
u
2
a
7
=
−u
−u
3
− u
a
8
=
u
4
− u
2
a − u
3
+ au + u
2
− a − 1
−u
4
a + u
3
a − 2u
2
a + au − u
2
− 2a + u − 1
a
1
=
u
4
a − u
3
a + u
4
+ u
2
a − u
3
+ 2u
2
+ a − u
2u
2
a + 2a + 1
a
6
=
u
3
−u
3
− u
a
3
=
u
3
u
4
− u
3
+ u
2
+ 1
a
9
=
u
u
3
+ u
a
11
=
a
−u
4
+ 2u
2
a + u
3
− au − u
2
+ 2a + 1
a
11
=
a
−u
4
+ 2u
2
a + u
3
− au − u
2
+ 2a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 4u + 6
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
8
c
10
, c
11
u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1
c
2
u
10
+ 5u
9
+ ··· + 4u + 1
c
3
, c
5
, c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
4
, c
9
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
8
c
10
, c
11
y
10
− 5y
9
+ ··· − 4y + 1
c
2
y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1
c
3
, c
5
, c
6
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
4
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −1.058210 − 0.418624I
b = 0.107804 + 1.200570I
c = 0.339110 − 0.822375I
d = −0.309916 − 0.549911I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 + 0.822375I
a = −0.24156 − 1.72831I
b = −1.43677 − 1.97522I
c = 0.339110 − 0.822375I
d = −0.309916 − 0.549911I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 − 0.822375I
a = −1.058210 + 0.418624I
b = 0.107804 − 1.200570I
c = 0.339110 + 0.822375I
d = −0.309916 + 0.549911I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −0.339110 − 0.822375I
a = −0.24156 + 1.72831I
b = −1.43677 + 1.97522I
c = 0.339110 + 0.822375I
d = −0.309916 + 0.549911I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.766826
a = 0.337181 + 0.531835I
b = 1.32946 + 1.28131I
c = −0.766826
d = −1.21774
2.40108 3.48110
u = 0.766826
a = 0.337181 − 0.531835I
b = 1.32946 − 1.28131I
c = −0.766826
d = −1.21774
2.40108 3.48110
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = 1.128480 − 0.089327I
b = −0.91615 + 1.81852I
c = −0.455697 − 1.200150I
d = 1.41878 − 0.21917I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 + 1.200150I
a = −0.665888 + 0.235737I
b = 0.415657 − 0.252788I
c = −0.455697 − 1.200150I
d = 1.41878 − 0.21917I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 − 1.200150I
a = 1.128480 + 0.089327I
b = −0.91615 − 1.81852I
c = −0.455697 + 1.200150I
d = 1.41878 + 0.21917I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.455697 − 1.200150I
a = −0.665888 − 0.235737I
b = 0.415657 + 0.252788I
c = −0.455697 + 1.200150I
d = 1.41878 + 0.21917I
5.87256 + 4.40083I 6.74431 − 3.49859I
19
IV. I
u
4
= h−6u
4
a + 2u
4
+ · · · + 2a + 7, −2u
4
a − 7u
4
+ · · · − 7a + 10, −4u
4
a +
9u
4
+ · · · − 14a − 3, −u
4
a + 2u
4
+ · · · − a + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
0.173913au
4
− 0.391304u
4
+ ··· + 0.608696a + 0.130435
a
5
=
1
u
2
a
7
=
0.0869565au
4
+ 0.304348u
4
+ ··· + 0.304348a − 0.434783
0.260870au
4
− 0.0869565u
4
+ ··· − 0.0869565a − 0.304348
a
8
=
u
2
+ 1
u
2
a
1
=
1
0
a
6
=
−0.173913au
4
+ 0.391304u
4
+ ··· + 0.391304a − 0.130435
0.260870au
4
− 0.0869565u
4
+ ··· − 0.0869565a − 0.304348
a
3
=
−0.173913au
4
+ 0.391304u
4
+ ··· + 0.391304a − 0.130435
0.173913au
4
− 0.391304u
4
+ ··· + 0.608696a + 0.130435
a
9
=
u
u
3
+ u
a
11
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
a
11
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 4u + 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1
c
2
u
10
+ 5u
9
+ ··· + 4u + 1
c
4
, c
9
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
8
, c
10
, c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
y
10
− 5y
9
+ ··· − 4y + 1
c
2
y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1
c
4
, c
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
8
, c
10
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 1.201520 − 0.626542I
b = 0.703115 − 0.728284I
c = −0.427719 + 0.494930I
d = −0.926127 + 0.393188I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 + 0.822375I
a = −1.43707 + 2.33968I
b = 1.50324 + 0.38743I
c = −1.70427 + 2.10897I
d = 1.236040 + 0.156723I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 − 0.822375I
a = 1.201520 + 0.626542I
b = 0.703115 + 0.728284I
c = −0.427719 − 0.494930I
d = −0.926127 − 0.393188I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −0.339110 − 0.822375I
a = −1.43707 − 2.33968I
b = 1.50324 − 0.38743I
c = −1.70427 − 2.10897I
d = 1.236040 − 0.156723I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.766826
a = 1.73372 + 1.67092I
b = 0.258559 + 0.407825I
c = 2.08403 + 1.59800I
d = 0.608868 + 0.334904I
2.40108 3.48110
u = 0.766826
a = 1.73372 − 1.67092I
b = 0.258559 − 0.407825I
c = 2.08403 − 1.59800I
d = 0.608868 − 0.334904I
2.40108 3.48110
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = 1.07098 + 1.17002I
b = 0.62145 + 1.31364I
c = −0.568964 − 0.788513I
d = −1.018500 − 0.644891I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 + 1.200150I
a = −0.069156 − 0.372595I
b = −0.586363 − 0.691742I
c = 0.116920 + 1.183200I
d = −0.400287 + 0.864056I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 − 1.200150I
a = 1.07098 − 1.17002I
b = 0.62145 − 1.31364I
c = −0.568964 + 0.788513I
d = −1.018500 + 0.644891I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.455697 − 1.200150I
a = −0.069156 + 0.372595I
b = −0.586363 + 0.691742I
c = 0.116920 − 1.183200I
d = −0.400287 − 0.864056I
5.87256 + 4.40083I 6.74431 − 3.49859I
24
V. I
u
5
=
hu
3
+d+u, c+u, −u
4
+u
3
−u
2
+b−1, −u
4
−u
2
+a−1, u
5
−u
4
+2u
3
−u
2
+u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
a
5
=
1
u
2
a
7
=
−u
−u
3
− u
a
8
=
u
2
+ 1
u
2
a
1
=
1
0
a
6
=
u
3
−u
3
− u
a
3
=
u
3
u
4
− u
3
+ u
2
+ 1
a
9
=
u
u
3
+ u
a
11
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
a
11
=
u
4
+ u
2
+ 1
u
4
− u
3
+ u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 4u + 6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
8
c
10
, c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
2
u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1
c
4
, c
9
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
8
c
10
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
2
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
4
, c
9
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.442672 + 0.068387I
b = −0.206354 + 0.340852I
c = 0.339110 − 0.822375I
d = −0.309916 − 0.549911I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 − 0.822375I
a = 0.442672 − 0.068387I
b = −0.206354 − 0.340852I
c = 0.339110 + 0.822375I
d = −0.309916 + 0.549911I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.766826
a = 1.93379
b = 1.48288
c = −0.766826
d = −1.21774
2.40108 3.48110
u = 0.455697 + 1.200150I
a = 0.09043 − 1.60288I
b = 1.96491 − 0.62190I
c = −0.455697 − 1.200150I
d = 1.41878 − 0.21917I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 − 1.200150I
a = 0.09043 + 1.60288I
b = 1.96491 + 0.62190I
c = −0.455697 + 1.200150I
d = 1.41878 + 0.21917I
5.87256 + 4.40083I 6.74431 − 3.49859I
28
VI. I
v
1
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
−1
0
a
2
=
0
1
a
5
=
1
0
a
7
=
0
−1
a
8
=
0
−1
a
1
=
0
1
a
6
=
1
−1
a
3
=
0
1
a
9
=
−1
0
a
11
=
−1
1
a
11
=
−1
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
4
c
7
, c
9
u
c
3
, c
8
u + 1
c
5
, c
6
, c
10
c
11
u − 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
9
y
c
3
, c
5
, c
6
c
8
, c
10
, c
11
y −1
31
(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 = 0
d = −1.00000
3.28987 12.0000
32
VII. I
v
2
= ha, d, c − 1, b + 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
1
0
a
2
=
0
−1
a
5
=
1
0
a
7
=
1
0
a
8
=
1
1
a
1
=
−1
−1
a
6
=
1
0
a
3
=
1
0
a
9
=
1
0
a
11
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
11
u − 1
c
2
, c
7
, c
8
u + 1
c
3
, c
4
, c
5
c
6
, c
9
u
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
, c
10
, c
11
y −1
c
3
, c
4
, c
5
c
6
, c
9
y
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
c = 1.00000
d = 0
0 0
36
VIII. I
v
3
= ha, d + 1, c + a − 1, b − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
1
0
a
2
=
0
1
a
5
=
1
0
a
7
=
1
−1
a
8
=
1
0
a
1
=
1
0
a
6
=
2
−1
a
3
=
−1
1
a
9
=
1
0
a
11
=
1
0
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
u + 1
c
4
, c
8
, c
9
c
10
, c
11
u
c
5
, c
6
, c
7
u − 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
y −1
c
4
, c
8
, c
9
c
10
, c
11
y
39
(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
40
IX. I
v
4
= hc, d + 1, cb + a − 1, cv + av − c − v, bv − v + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
v
0
a
2
=
1
b
a
5
=
1
0
a
7
=
0
−1
a
8
=
1
b − 1
a
1
=
1
b − 1
a
6
=
1
−1
a
3
=
0
1
a
9
=
v
0
a
11
=
v + 1
b − 1
a
11
=
v + 1
b − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
2
+ v
2
− 2b + 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.
41
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
1.64493 3.74053 + 0.27852I
42
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u(u − 1)(u + 1)(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
7
− u
6
− u
5
+ 2u
4
+ u
3
− 2u
2
+ u + 1)
2
· (u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
2
· (u
17
− 2u
16
+ ··· − 8u + 4)
c
2
u(u + 1)
2
(u
5
+ 5u
4
+ 8u
3
+ 3u
2
− u + 1)
· (u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
2
· ((u
10
+ 5u
9
+ ··· + 4u + 1)
2
)(u
17
+ 6u
16
+ ··· + 88u + 16)
c
3
, c
8
u(u + 1)
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
· (u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
· (u
14
+ u
13
+ ··· − 4u − 4)(u
17
+ 2u
16
+ ··· + 3u + 1)
c
4
, c
9
u
3
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
5
· ((u
7
+ 3u
6
+ ··· − 2u − 2)
2
)(u
17
− 2u
16
+ ··· − 4u
2
+ 8)
c
5
, c
6
, c
10
c
11
u(u − 1)
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
3
· (u
10
− u
9
− 2u
8
+ 4u
7
− 4u
5
+ 3u
4
+ u
3
− 2u
2
+ 1)
· (u
14
+ u
13
+ ··· − 4u − 4)(u
17
+ 2u
16
+ ··· + 3u + 1)
43
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y − 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
7
− 3y
6
+ 7y
5
− 8y
4
+ 9y
3
− 6y
2
+ 5y −1)
2
· ((y
10
− 5y
9
+ ··· − 4y + 1)
2
)(y
17
− 6y
16
+ ··· + 88y −16)
c
2
y(y − 1)
2
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)
· (y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y −1)
2
· (y
10
− y
9
− 6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1)
2
· (y
17
+ 10y
16
+ ··· + 288y −256)
c
3
, c
5
, c
6
c
8
, c
10
, c
11
y(y − 1)
2
(y
5
− 5y
4
+ ··· − y −1)
3
(y
10
− 5y
9
+ ··· − 4y + 1)
· (y
14
− 11y
13
+ ··· − 40y + 16)(y
17
− 20y
16
+ ··· + 27y −1)
c
4
, c
9
y
3
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
5
· (y
7
+ 3y
6
+ 4y
5
+ y
4
− y
3
+ 7y
2
+ 8y −4)
2
· (y
17
+ 6y
16
+ ··· + 64y −64)
44
