11a
57
(K11a
57
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 9 10 3 7 5 6
Solving Sequence
3,8
4
1,9
2
5,10
7 6 11
c
3
c
8
c
2
c
4
c
7
c
6
c
11
c
1
, c
5
, c
9
, 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
= h−68209745u
16
+ 103218620u
15
+ ··· + 6895752724d + 558230980,
− 117728333u
16
+ 37441650u
15
+ ··· + 13791505448c − 2779791176,
− 70376587u
16
+ 38764471u
15
+ ··· + 6895752724b + 3895994728,
− 327083412u
16
+ 276473252u
15
+ ··· + 6895752724a − 7902639380, u
17
− 2u
16
+ ··· − 4u
2
+ 8i
I
u
2
= hu
6
c + 2u
5
c + 3u
4
c + 2u
3
c − u
3
− cu − u
2
+ d − u,
− u
6
c − u
5
c − 2u
4
c − u
3
c − u
2
c + 2c
2
− cu − 2u
2
− 2u − 2, −u
4
− u
3
− u
2
+ b + 1,
− u
6
− 3u
5
− 4u
4
− 3u
3
− u
2
+ 2a + u, u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2i
I
u
3
= h−u
4
+ d, −u
2
+ c − 1, −u
4
a − 2u
2
a + u
3
− au + b − a + u + 1,
u
3
a − 2u
2
a − u
3
+ a
2
+ 2au + u
2
− 2a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
4
= h2u
4
a − 2u
4
+ 4u
2
a + 2u
3
+ au − 6u
2
+ d + 4a + 2u − 4, −u
4
a + u
4
− 2u
2
a − u
3
+ 3u
2
+ c − 2a − u + 2,
− u
4
a − 2u
2
a + u
3
− au + b − a + u + 1, u
3
a − 2u
2
a − u
3
+ a
2
+ 2au + u
2
− 2a − u + 1,
u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
5
= h−u
4
+ d, −u
2
+ c − 1, u
4
− u
3
+ u
2
+ b + 1, 2u
4
− u
3
+ 4u
2
+ a + 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= hc, d − 1, b, a − 1, v + 1i
I
v
2
= ha, d, c − 1, b + 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 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
= h−6.82 × 10
7
u
16
+ 1.03 × 10
8
u
15
+ · · · + 6.90 × 10
9
d + 5.58 ×
10
8
, −1.18 × 10
8
u
16
+ 3.74 × 10
7
u
15
+ · · · + 1.38 × 10
10
c − 2.78 × 10
9
, −7.04 ×
10
7
u
16
+ 3.88 × 10
7
u
15
+ · · · + 6.90 × 10
9
b + 3.90 × 10
9
, −3.27 × 10
8
u
16
+
2.76 × 10
8
u
15
+ · · · + 6.90 × 10
9
a − 7.90 × 10
9
, u
17
− 2u
16
+ · · · − 4u
2
+ 8i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
0.0474326u
16
− 0.0400933u
15
+ ··· + 0.133884u + 1.14602
0.0102058u
16
− 0.00562150u
15
+ ··· + 0.589483u − 0.564985
a
9
=
−u
u
a
2
=
−0.0115535u
16
− 0.0103886u
15
+ ··· − 0.835060u + 1.27282
−0.0135318u
16
+ 0.0739510u
15
+ ··· + 1.06137u + 0.141156
a
5
=
0.0576384u
16
− 0.0457148u
15
+ ··· + 0.723367u + 0.581031
−0.0339841u
16
+ 0.0141997u
15
+ ··· − 1.05059u + 0.00848878
a
10
=
0.00853629u
16
− 0.00271483u
15
+ ··· − 0.843158u + 0.201558
0.00989156u
16
− 0.0149684u
15
+ ··· + 0.971920u − 0.0809529
a
7
=
−0.0184279u
16
+ 0.0176833u
15
+ ··· − 0.128762u − 0.120605
0.00989156u
16
− 0.0149684u
15
+ ··· + 0.971920u − 0.0809529
a
6
=
−0.0196690u
16
+ 0.00798947u
15
+ ··· − 0.197053u − 0.235467
0.0111327u
16
− 0.00527464u
15
+ ··· + 1.04021u + 0.0339091
a
11
=
0.0321906u
16
− 0.0342299u
15
+ ··· − 0.170381u + 0.791078
0.00701992u
16
+ 0.00619838u
15
+ ··· + 0.764986u − 0.330652
a
11
=
0.0321906u
16
− 0.0342299u
15
+ ··· − 0.170381u + 0.791078
0.00701992u
16
+ 0.00619838u
15
+ ··· + 0.764986u − 0.330652
(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
4
u
17
− 2u
16
+ ··· − 8u + 4
c
2
u
17
+ 6u
16
+ ··· + 88u + 16
c
3
, c
8
u
17
− 2u
16
+ ··· − 4u
2
+ 8
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
17
+ 2u
16
+ ··· + 3u + 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
− 6y
16
+ ··· + 88y −16
c
2
y
17
+ 10y
16
+ ··· + 288y −256
c
3
, c
8
y
17
+ 6y
16
+ ··· + 64y −64
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
17
− 20y
16
+ ··· + 27y −1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679716 + 0.561358I
a = 0.469715 + 0.071775I
b = −1.066150 + 0.686891I
c = −0.482279 − 0.453082I
d = 0.255516 + 0.765465I
−3.14388 + 1.09865I −5.52136 − 1.09882I
u = 0.679716 − 0.561358I
a = 0.469715 − 0.071775I
b = −1.066150 − 0.686891I
c = −0.482279 + 0.453082I
d = 0.255516 − 0.765465I
−3.14388 − 1.09865I −5.52136 + 1.09882I
u = 0.555749 + 1.023030I
a = −0.24717 + 1.86349I
b = −0.86669 − 1.12847I
c = −0.493632 − 0.522885I
d = −0.051009 + 0.779355I
−1.71782 − 5.90288I −0.75718 + 7.23695I
u = 0.555749 − 1.023030I
a = −0.24717 − 1.86349I
b = −0.86669 + 1.12847I
c = −0.493632 + 0.522885I
d = −0.051009 − 0.779355I
−1.71782 + 5.90288I −0.75718 − 7.23695I
u = −1.247530 + 0.318357I
a = 0.505620 + 0.282992I
b = 0.454441 + 0.853023I
c = −1.114330 − 0.162230I
d = −0.517027 + 0.098116I
8.60033 − 1.91429I 8.38805 + 0.33236I
u = −1.247530 − 0.318357I
a = 0.505620 − 0.282992I
b = 0.454441 − 0.853023I
c = −1.114330 + 0.162230I
d = −0.517027 − 0.098116I
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 = 1.92972 − 1.22120I
b = −0.342039 + 0.295037I
c = 0.324109 − 0.810541I
d = 0.054070 + 0.438524I
0.88275 + 1.29794I 5.86581 − 6.22804I
u = −0.022849 − 0.695780I
a = 1.92972 + 1.22120I
b = −0.342039 − 0.295037I
c = 0.324109 + 0.810541I
d = 0.054070 − 0.438524I
0.88275 − 1.29794I 5.86581 + 6.22804I
u = 1.235140 + 0.560024I
a = 0.436143 + 0.137389I
b = −0.74733 + 1.42693I
c = 1.046940 − 0.255771I
d = 0.525994 + 0.171484I
6.85439 + 7.49245I 6.04980 − 5.00652I
u = 1.235140 − 0.560024I
a = 0.436143 − 0.137389I
b = −0.74733 − 1.42693I
c = 1.046940 + 0.255771I
d = 0.525994 − 0.171484I
6.85439 − 7.49245I 6.04980 + 5.00652I
u = −0.66454 + 1.33308I
a = 0.446199 + 0.683104I
b = 0.944156 − 0.676727I
c = 0.252205 + 0.988893I
d = −0.30957 − 2.53920I
11.9481 + 8.6770I 9.06927 − 4.38269I
u = −0.66454 − 1.33308I
a = 0.446199 − 0.683104I
b = 0.944156 + 0.676727I
c = 0.252205 − 0.988893I
d = −0.30957 + 2.53920I
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 = −0.46664 + 1.36075I
b = −1.06945 − 1.61168I
c = −0.297727 + 0.961003I
d = 0.35861 − 2.47585I
9.1924 − 14.7354I 6.16899 + 8.15927I
u = 0.79652 − 1.26851I
a = −0.46664 − 1.36075I
b = −1.06945 + 1.61168I
c = −0.297727 − 0.961003I
d = 0.35861 + 2.47585I
9.1924 + 14.7354I 6.16899 − 8.15927I
u = −0.11728 + 1.54547I
a = 0.161885 − 1.071490I
b = 0.08928 + 1.57333I
c = 0.041573 + 1.021680I
d = −0.05064 − 2.64219I
15.7365 + 3.2760I 10.07807 − 2.58290I
u = −0.11728 − 1.54547I
a = 0.161885 + 1.071490I
b = 0.08928 − 1.57333I
c = 0.041573 − 1.021680I
d = −0.05064 + 2.64219I
15.7365 − 3.2760I 10.07807 + 2.58290I
u = −0.429856
a = 0.529049
b = −0.792429
c = 0.446280
d = −0.531893
−1.29941 −8.68290
8
II. I
u
2
= hu
6
c + 2u
5
c + · · · + d − u, −u
6
c − u
5
c + · · · + 2c
2
− 2, −u
4
− u
3
−
u
2
+ b + 1, −u
6
− 3u
5
+ · · · + 2a + u, u
7
+ 3u
6
+ · · · − 2u − 2i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
1
2
u
6
+
3
2
u
5
+ ··· +
1
2
u
2
−
1
2
u
u
4
+ u
3
+ u
2
− 1
a
9
=
−u
u
a
2
=
−
1
2
u
6
−
1
2
u
5
+ ··· +
1
2
u + 1
−u
5
− u
4
− 2u
3
− u
2
+ 1
a
5
=
1
2
u
6
+
3
2
u
5
+ ··· −
1
2
u − 1
−u
5
− 2u
4
− 2u
3
− u
2
+ u + 1
a
10
=
c
−u
6
c − 2u
5
c − 3u
4
c − 2u
3
c + u
3
+ cu + u
2
+ u
a
7
=
u
6
c + 2u
5
c + 3u
4
c + 2u
3
c − u
3
− cu − u
2
− c − u
−u
6
c − 2u
5
c − 3u
4
c − 2u
3
c + u
3
+ cu + u
2
+ u
a
6
=
u
6
c + 2u
5
c + 3u
4
c + 2u
3
c + u
2
c − u
3
− cu − u
2
− c − u
−u
6
c − 2u
5
c − 3u
4
c − 2u
3
c − u
2
c + u
3
+ cu + u
2
+ u
a
11
=
1
2
u
6
+
1
2
u
5
+ ··· +
1
2
u
2
−
1
2
u
−u
4
c + u
5
− u
3
c + 2u
4
− u
2
c + 3u
3
+ 2u
2
+ u − 1
a
11
=
1
2
u
6
+
1
2
u
5
+ ··· +
1
2
u
2
−
1
2
u
−u
4
c + u
5
− u
3
c + 2u
4
− u
2
c + 3u
3
+ 2u
2
+ u − 1
(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
4
(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
8
(u
7
+ 3u
6
+ 6u
5
+ 7u
4
+ 5u
3
+ u
2
− 2u − 2)
2
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
14
+ u
13
+ ··· − 4u − 4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(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
8
(y
7
+ 3y
6
+ 4y
5
+ y
4
− y
3
+ 7y
2
+ 8y − 4)
2
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
14
− 11y
13
+ ··· − 40y + 16
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984140 + 0.426152I
a = 0.472917 − 0.120643I
b = −0.714380 − 0.998080I
c = −1.198550 − 0.312556I
d = −0.438334 + 0.145757I
1.19445 − 3.93070I 1.74059 + 4.87230I
u = −0.984140 + 0.426152I
a = 0.472917 − 0.120643I
b = −0.714380 − 0.998080I
c = 0.543084 − 0.485903I
d = −0.376079 + 1.030380I
1.19445 − 3.93070I 1.74059 + 4.87230I
u = −0.984140 − 0.426152I
a = 0.472917 + 0.120643I
b = −0.714380 + 0.998080I
c = −1.198550 + 0.312556I
d = −0.438334 − 0.145757I
1.19445 + 3.93070I 1.74059 − 4.87230I
u = −0.984140 − 0.426152I
a = 0.472917 + 0.120643I
b = −0.714380 + 0.998080I
c = 0.543084 + 0.485903I
d = −0.376079 − 1.030380I
1.19445 + 3.93070I 1.74059 − 4.87230I
u = −0.167785 + 1.218780I
a = 0.529166 + 1.016880I
b = 0.242061 − 0.924444I
c = −0.650809 − 0.592102I
d = −0.300734 + 0.551723I
7.14223 − 0.95540I 8.68929 + 2.37083I
u = −0.167785 + 1.218780I
a = 0.529166 + 1.016880I
b = 0.242061 − 0.924444I
c = 0.093897 + 1.158860I
d = −0.13529 − 2.82138I
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 = 0.529166 − 1.016880I
b = 0.242061 + 0.924444I
c = −0.650809 + 0.592102I
d = −0.300734 − 0.551723I
7.14223 + 0.95540I 8.68929 − 2.37083I
u = −0.167785 − 1.218780I
a = 0.529166 − 1.016880I
b = 0.242061 + 0.924444I
c = 0.093897 − 1.158860I
d = −0.13529 + 2.82138I
7.14223 + 0.95540I 8.68929 − 2.37083I
u = −0.654547 + 1.202470I
a = −0.33478 − 1.51279I
b = −0.90125 + 1.43610I
c = 0.292391 + 1.022450I
d = −0.38305 − 2.56809I
3.65356 + 9.93065I 3.53972 − 7.33664I
u = −0.654547 + 1.202470I
a = −0.33478 − 1.51279I
b = −0.90125 + 1.43610I
c = 0.509792 − 0.511513I
d = 0.118485 + 0.850766I
3.65356 + 9.93065I 3.53972 − 7.33664I
u = −0.654547 − 1.202470I
a = −0.33478 + 1.51279I
b = −0.90125 − 1.43610I
c = 0.292391 − 1.022450I
d = −0.38305 + 2.56809I
3.65356 − 9.93065I 3.53972 + 7.33664I
u = −0.654547 − 1.202470I
a = −0.33478 + 1.51279I
b = −0.90125 − 1.43610I
c = 0.509792 + 0.511513I
d = 0.118485 − 0.850766I
3.65356 − 9.93065I 3.53972 + 7.33664I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.612945
a = 0.665400
b = −0.252863
c = −1.05845
d = 1.74513
2.33847 2.06080
u = 0.612945
a = 0.665400
b = −0.252863
c = 1.87884
d = 0.284876
2.33847 2.06080
14
III. I
u
3
= h−u
4
+ d, −u
2
+ c − 1, −u
4
a + u
3
+ · · · − a + 1, u
3
a − u
3
+ · · · −
2a + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
a
u
4
a + 2u
2
a − u
3
+ au + a − u − 1
a
9
=
−u
u
a
2
=
−u
4
a − u
2
a + u
3
− au + u + 1
u
4
a + u
4
+ u
2
a − 2u
3
+ au + 2u
2
− 2u
a
5
=
u
4
a + 2u
2
a − u
3
+ au + 2a − u − 1
−u
4
+ 2u
3
− au − 2u
2
+ 2u
a
10
=
u
2
+ 1
u
4
a
7
=
−u
4
− u
2
− 1
u
4
a
6
=
−1
−u
2
a
11
=
−u
4
a − u
2
a + u
3
− au + u + 1
u
4
a + u
4
+ u
2
a − 2u
3
+ au + 2u
2
− 2u
a
11
=
−u
4
a − u
2
a + u
3
− au + u + 1
u
4
a + u
4
+ u
2
a − 2u
3
+ au + 2u
2
− 2u
(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
4
, c
5
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
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
6
, c
7
, 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
4
, c
5
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
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
6
, c
7
, c
9
(y
5
− 5y
4
+ 8y
3
− 3y
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 = 0.445032 − 0.031192I
b = −1.50324 − 0.38743I
c = 0.438694 − 0.557752I
d = 0.003977 + 0.626138I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 + 0.822375I
a = 0.46155 − 2.45660I
b = −0.703115 + 0.728284I
c = 0.438694 − 0.557752I
d = 0.003977 + 0.626138I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 − 0.822375I
a = 0.445032 + 0.031192I
b = −1.50324 + 0.38743I
c = 0.438694 + 0.557752I
d = 0.003977 − 0.626138I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −0.339110 − 0.822375I
a = 0.46155 + 2.45660I
b = −0.703115 − 0.728284I
c = 0.438694 + 0.557752I
d = 0.003977 − 0.626138I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.766826
a = 0.595741 + 0.124010I
b = −0.258559 + 0.407825I
c = 1.58802
d = 0.345770
2.40108 3.48110
u = 0.766826
a = 0.595741 − 0.124010I
b = −0.258559 − 0.407825I
c = 1.58802
d = 0.345770
2.40108 3.48110
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = 0.542114 − 0.781069I
b = 0.586363 + 0.691742I
c = −0.232705 + 1.093810I
d = 0.32314 − 2.69669I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 + 1.200150I
a = −0.04444 + 1.54938I
b = −0.62145 − 1.31364I
c = −0.232705 + 1.093810I
d = 0.32314 − 2.69669I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 − 1.200150I
a = 0.542114 + 0.781069I
b = 0.586363 − 0.691742I
c = −0.232705 − 1.093810I
d = 0.32314 + 2.69669I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.455697 − 1.200150I
a = −0.04444 − 1.54938I
b = −0.62145 + 1.31364I
c = −0.232705 − 1.093810I
d = 0.32314 + 2.69669I
5.87256 + 4.40083I 6.74431 − 3.49859I
19
IV. I
u
4
= h2u
4
a − 2u
4
+ · · · + 4a − 4, −u
4
a + u
4
+ · · · − 2a + 2, −u
4
a + u
3
+
· · · − a + 1, u
3
a − u
3
+ · · · − 2a + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
a
u
4
a + 2u
2
a − u
3
+ au + a − u − 1
a
9
=
−u
u
a
2
=
−u
4
a − u
2
a + u
3
− au + u + 1
u
4
a + u
4
+ u
2
a − 2u
3
+ au + 2u
2
− 2u
a
5
=
u
4
a + 2u
2
a − u
3
+ au + 2a − u − 1
−u
4
+ 2u
3
− au − 2u
2
+ 2u
a
10
=
u
4
a − u
4
+ 2u
2
a + u
3
− 3u
2
+ 2a + u − 2
−2u
4
a + 2u
4
− 4u
2
a − 2u
3
− au + 6u
2
− 4a − 2u + 4
a
7
=
u
4
a − u
4
+ 2u
2
a + u
3
+ au − 3u
2
+ 2a + u − 2
−2u
4
a + 2u
4
− 4u
2
a − 2u
3
− au + 6u
2
− 4a − 2u + 4
a
6
=
2u
4
a − u
3
a − 2u
4
+ 4u
2
a + u
3
+ au − 4u
2
+ 3a − 2
−3u
4
a + u
3
a + 3u
4
− 6u
2
a − 2u
3
− au + 7u
2
− 5a − u + 4
a
11
=
3u
4
a − 2u
4
+ 5u
2
a + u
3
+ au − 4u
2
+ 4a − 3
−3u
4
a + 3u
4
− 5u
2
a − 2u
3
− au + 6u
2
− 4a − u + 4
a
11
=
3u
4
a − 2u
4
+ 5u
2
a + u
3
+ au − 4u
2
+ 4a − 3
−3u
4
a + 3u
4
− 5u
2
a − 2u
3
− au + 6u
2
− 4a − u + 4
(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
4
, c
6
c
7
, c
9
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
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
5
, 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
4
, c
6
c
7
, c
9
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
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
5
, 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 = 0.445032 − 0.031192I
b = −1.50324 − 0.38743I
c = 0.366828 + 1.351750I
d = −0.60839 − 3.08007I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 + 0.822375I
a = 0.46155 − 2.45660I
b = −0.703115 + 0.728284I
c = −0.805522 − 0.794001I
d = −0.252685 + 0.375376I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 − 0.822375I
a = 0.445032 + 0.031192I
b = −1.50324 + 0.38743I
c = 0.366828 − 1.351750I
d = −0.60839 + 3.08007I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = −0.339110 − 0.822375I
a = 0.46155 + 2.45660I
b = −0.703115 − 0.728284I
c = −0.805522 + 0.794001I
d = −0.252685 − 0.375376I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.766826
a = 0.595741 + 0.124010I
b = −0.258559 + 0.407825I
c = −0.794011 + 0.436741I
d = 1.13119 − 0.96858I
2.40108 3.48110
u = 0.766826
a = 0.595741 − 0.124010I
b = −0.258559 − 0.407825I
c = −0.794011 − 0.436741I
d = 1.13119 + 0.96858I
2.40108 3.48110
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = 0.542114 − 0.781069I
b = 0.586363 + 0.691742I
c = −0.518554 − 0.530425I
d = −0.147334 + 0.766162I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 + 1.200150I
a = −0.04444 + 1.54938I
b = −0.62145 − 1.31364I
c = 0.751259 − 0.563387I
d = 0.377218 + 0.474060I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 − 1.200150I
a = 0.542114 + 0.781069I
b = 0.586363 − 0.691742I
c = −0.518554 + 0.530425I
d = −0.147334 − 0.766162I
5.87256 + 4.40083I 6.74431 − 3.49859I
u = 0.455697 − 1.200150I
a = −0.04444 − 1.54938I
b = −0.62145 + 1.31364I
c = 0.751259 + 0.563387I
d = 0.377218 − 0.474060I
5.87256 + 4.40083I 6.74431 − 3.49859I
24
V. I
u
5
= h−u
4
+ d, −u
2
+ c − 1, u
4
− u
3
+ u
2
+ b + 1, 2u
4
− u
3
+ 4u
2
+ a +
2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
1
=
−2u
4
+ u
3
− 4u
2
− 2
−u
4
+ u
3
− u
2
− 1
a
9
=
−u
u
a
2
=
−2u
4
− 4u
2
− u − 2
−2u
4
+ 2u
3
− 2u
2
+ u − 2
a
5
=
−3u
4
+ 2u
3
− 5u
2
− 3
u
4
− 2u
3
− 2u
a
10
=
u
2
+ 1
u
4
a
7
=
−u
4
− u
2
− 1
u
4
a
6
=
−1
−u
2
a
11
=
−2u
4
− 4u
2
− u − 2
−2u
4
+ 2u
3
− 2u
2
+ u − 2
a
11
=
−2u
4
− 4u
2
− u − 2
−2u
4
+ 2u
3
− 2u
2
+ u − 2
(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
4
, c
5
c
6
, c
7
, c
9
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
3
, c
8
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
4
, c
5
c
6
, c
7
, c
9
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
3
, c
8
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 = 0.886294 + 0.706265I
b = 0.206354 − 0.340852I
c = 0.438694 − 0.557752I
d = 0.003977 + 0.626138I
0.32910 + 1.53058I 2.51511 − 4.43065I
u = −0.339110 − 0.822375I
a = 0.886294 − 0.706265I
b = 0.206354 + 0.340852I
c = 0.438694 + 0.557752I
d = 0.003977 − 0.626138I
0.32910 − 1.53058I 2.51511 + 4.43065I
u = 0.766826
a = −4.59272
b = −1.48288
c = 1.58802
d = 0.345770
2.40108 3.48110
u = 0.455697 + 1.200150I
a = 0.410064 + 0.037156I
b = −1.96491 + 0.62190I
c = −0.232705 + 1.093810I
d = 0.32314 − 2.69669I
5.87256 − 4.40083I 6.74431 + 3.49859I
u = 0.455697 − 1.200150I
a = 0.410064 − 0.037156I
b = −1.96491 − 0.62190I
c = −0.232705 − 1.093810I
d = 0.32314 + 2.69669I
5.87256 + 4.40083I 6.74431 − 3.49859I
28
VI. I
v
1
= hc, d − 1, b, a − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
1
=
1
0
a
9
=
−1
0
a
2
=
1
0
a
5
=
1
0
a
10
=
0
1
a
7
=
−1
−1
a
6
=
0
−1
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
3
c
4
, c
8
u
c
5
, c
9
u − 1
c
6
, c
7
, c
10
c
11
u + 1
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
c
5
, c
6
, c
7
c
9
, 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 = 1.00000
b = 0
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
3
=
1
0
a
8
=
1
0
a
4
=
1
0
a
1
=
0
−1
a
9
=
1
0
a
2
=
1
−1
a
5
=
0
1
a
10
=
1
0
a
7
=
1
0
a
6
=
1
0
a
11
=
1
−1
a
11
=
1
−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
4
, c
5
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
34
(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
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, b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
1
0
a
4
=
1
0
a
1
=
0
−1
a
9
=
1
0
a
2
=
1
−1
a
5
=
0
1
a
10
=
0
−1
a
7
=
1
1
a
6
=
0
1
a
11
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u − 1
c
2
, c
4
, c
6
c
7
u + 1
c
3
, c
5
, c
8
c
10
, c
11
u
38
(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 −1
c
3
, c
5
, c
8
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 = 0
d = −1.00000
0 0
40
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
1
=
0
−1
a
9
=
v
0
a
2
=
1
−1
a
5
=
0
1
a
10
=
1
d
a
7
=
v −1
−d
a
6
=
−1
−d
a
11
=
1
d − 1
a
11
=
1
d − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
+ 4
(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 2.23718 − 0.09992I
42
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(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
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
4
u(u + 1)
2
(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
5
, c
10
, c
11
u(u − 1)(u + 1)(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
6
, c
7
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
9
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
4
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
8
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)
c
5
, c
6
, c
7
c
9
, 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)
44
