12a
0503
(K12a
0503
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 12 2 4 11 5 1 6
Solving Sequence
2,8
7 3 4 9 5
1,12
6 11 10
c
7
c
2
c
3
c
8
c
4
c
1
c
6
c
11
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
5
− 2u
3
+ b + 1, u
5
+ u
3
+ a − 1, u
7
+ 2u
5
+ 2u
3
− u
2
− u − 1i
I
u
2
= h−u
15
− 5u
13
− u
12
− 12u
11
− 4u
10
− 15u
9
− 8u
8
− 10u
7
− 8u
6
− 2u
5
− 5u
4
+ u
3
− 2u
2
+ b − 1,
u
15
+ 2u
14
+ 5u
13
+ 9u
12
+ 12u
11
+ 19u
10
+ 15u
9
+ 19u
8
+ 10u
7
+ 8u
6
+ 2u
5
− 2u
4
− u
2
+ a + 2u,
u
16
+ u
15
+ 5u
14
+ 5u
13
+ 12u
12
+ 12u
11
+ 15u
10
+ 15u
9
+ 10u
8
+ 10u
7
+ 2u
6
+ 2u
5
+ u
2
+ 1i
I
u
3
= h−u
15
+ 2u
14
− 7u
13
+ 9u
12
− 18u
11
+ 16u
10
− 21u
9
+ 12u
8
− 8u
7
+ 2u
6
+ 4u
5
− u
4
+ 2u
3
+ 2u
2
+ b − 3u + 3,
− u
15
− 3u
13
− 2u
12
− 2u
11
− 6u
10
+ 3u
9
− 6u
8
+ 4u
7
+ 4u
4
− 2u
3
+ 2u
2
+ 2a + u − 1,
u
16
− 2u
15
+ 7u
14
− 10u
13
+ 18u
12
− 20u
11
+ 21u
10
− 18u
9
+ 8u
8
− 4u
7
− 4u
6
+ 4u
5
− 2u
4
+ 3u
2
− 3u + 2i
I
u
4
= hu
15
+ 3u
13
+ 4u
11
− u
9
− 4u
7
− 4u
5
+ u
3
+ b − 1, −u
15
− 3u
13
− 4u
11
+ u
9
+ 4u
7
+ 4u
5
− 2u
3
+ a + 1,
u
16
+ u
15
+ 5u
14
+ 5u
13
+ 12u
12
+ 12u
11
+ 15u
10
+ 15u
9
+ 10u
8
+ 10u
7
+ 2u
6
+ 2u
5
+ u
2
+ 1i
I
u
5
= hb + u − 1, a − u + 2, u
2
− u + 1i
I
u
6
= hu
5
− u
2
a + 2u
3
− u
2
+ b − a + u − 1, −2u
5
a − u
5
− 4u
3
a + u
4
+ 2u
2
a − 2u
3
+ a
2
− au + 4u
2
+ 2a − 2u + 2,
u
6
+ 2u
4
− u
3
+ u
2
− u − 1i
I
u
7
= hb − u − 1, a + 2u + 1, u
2
+ 1i
* 7 irreducible components of dim
C
= 0, with total 71 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
5
− 2u
3
+ b + 1, u
5
+ u
3
+ a − 1, u
7
+ 2u
5
+ 2u
3
− u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
−u
5
+ u
4
− u
3
+ u
2
− u
u
5
− u
4
+ u
3
− 2u
2
− 1
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−u
5
− u
3
+ 1
u
5
+ 2u
3
− 1
a
6
=
−u
6
− u
4
+ u + 1
u
6
+ 2u
4
+ u
2
− u
a
11
=
−u
3
+ 1
u
3
+ u
2
+ u
a
10
=
−u
6
+ u
5
− u
4
− u
2
+ 1
u
6
− u
5
+ u
4
− u
3
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
6
− 6u
4
− 6u
2
+ 6u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
u
7
+ 4u
6
+ 8u
5
+ 6u
4
− 5u
2
− u − 1
c
2
, c
5
, c
6
c
7
, c
10
, c
12
u
7
+ 2u
5
+ 2u
3
+ u
2
− u + 1
c
3
, c
4
, c
8
u
7
− 5u
5
− 2u
4
+ 7u
3
+ 4u
2
+ 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
y
7
+ 16y
5
+ 2y
4
+ 52y
3
− 13y
2
− 9y −1
c
2
, c
5
, c
6
c
7
, c
10
, c
12
y
7
+ 4y
6
+ 8y
5
+ 6y
4
− 5y
2
− y −1
c
3
, c
4
, c
8
y
7
− 10y
6
+ 39y
5
− 74y
4
+ 65y
3
− 32y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863824
a = −0.125557
b = 0.770135
−4.43886 0.872100
u = −0.506221 + 1.104710I
a = 1.49617 + 1.94571I
b = 0.22746 − 2.44461I
−5.20269 − 11.20360I −5.65627 + 10.71805I
u = −0.506221 − 1.104710I
a = 1.49617 − 1.94571I
b = 0.22746 + 2.44461I
−5.20269 + 11.20360I −5.65627 − 10.71805I
u = −0.426442 + 0.491723I
a = 0.719469 − 0.043211I
b = −0.487688 + 0.192580I
0.805836 − 1.099860I 4.64625 + 4.74954I
u = −0.426442 − 0.491723I
a = 0.719469 + 0.043211I
b = −0.487688 − 0.192580I
0.805836 + 1.099860I 4.64625 − 4.74954I
u = 0.500751 + 1.264820I
a = −1.15286 + 2.51108I
b = −1.12484 − 3.58304I
−15.5903 + 14.7635I −8.42603 − 8.80481I
u = 0.500751 − 1.264820I
a = −1.15286 − 2.51108I
b = −1.12484 + 3.58304I
−15.5903 − 14.7635I −8.42603 + 8.80481I
5
II.
I
u
2
= h−u
15
−5u
13
+· · ·+b−1, u
15
+2u
14
+· · ·+a+2u, u
16
+u
15
+· · ·+u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−u
15
− 2u
14
+ ··· + u
2
− 2u
u
15
+ 5u
13
+ ··· + 2u
2
+ 1
a
6
=
u
15
+ 3u
13
+ 3u
11
− 3u
9
− 6u
7
− 2u
5
+ 3u
3
+ u − 1
u
11
+ 3u
9
+ 4u
7
+ u
5
− u
3
− u
a
11
=
−u
15
− 2u
14
+ ··· + u
4
− u
u
8
+ 2u
6
+ 2u
4
a
10
=
−u
15
− 2u
14
+ ··· − u
2
− u
−u
10
− 2u
8
− u
6
+ 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
14
− 4u
13
− 16u
12
− 20u
11
− 32u
10
− 44u
9
− 28u
8
− 44u
7
−
12u
6
− 12u
5
+ 4u
4
+ 12u
3
− 4u
2
+ 4u − 6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
16
+ 9u
15
+ ··· + 2u + 1
c
2
, c
5
, c
7
c
10
u
16
− u
15
+ ··· + u
2
+ 1
c
3
, c
4
, c
8
u
16
− 2u
15
+ ··· − u + 2
c
6
, c
12
u
16
+ 2u
15
+ ··· + 3u + 2
c
11
u
16
+ 10u
15
+ ··· + 3u + 4
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
16
− 3y
15
+ ··· − 2y + 1
c
2
, c
5
, c
7
c
10
y
16
+ 9y
15
+ ··· + 2y + 1
c
3
, c
4
, c
8
y
16
− 18y
15
+ ··· + 19y + 4
c
6
, c
12
y
16
+ 10y
15
+ ··· + 3y + 4
c
11
y
16
− 10y
15
+ ··· − y + 16
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.892953 + 0.035958I
a = −0.652536 + 1.200890I
b = 0.02318 + 2.24381I
−8.19036 + 4.73480I −2.47201 − 3.02289I
u = −0.892953 − 0.035958I
a = −0.652536 − 1.200890I
b = 0.02318 − 2.24381I
−8.19036 − 4.73480I −2.47201 + 3.02289I
u = −0.458901 + 0.734878I
a = −0.104273 − 0.435411I
b = 0.247757 + 0.757374I
0.85997 − 1.95072I 3.06114 + 4.17042I
u = −0.458901 − 0.734878I
a = −0.104273 + 0.435411I
b = 0.247757 − 0.757374I
0.85997 + 1.95072I 3.06114 − 4.17042I
u = −0.379593 + 1.079580I
a = −0.56037 − 2.03187I
b = −1.36347 + 1.32712I
−7.04324 − 3.37292I −8.93248 + 5.20888I
u = −0.379593 − 1.079580I
a = −0.56037 + 2.03187I
b = −1.36347 − 1.32712I
−7.04324 + 3.37292I −8.93248 − 5.20888I
u = 0.469252 + 1.053160I
a = −0.371270 − 0.561834I
b = 0.161095 + 0.362888I
−2.68724 + 6.60937I −2.51664 − 7.40663I
u = 0.469252 − 1.053160I
a = −0.371270 + 0.561834I
b = 0.161095 − 0.362888I
−2.68724 − 6.60937I −2.51664 + 7.40663I
u = 0.190701 + 0.810384I
a = 0.33485 − 2.32194I
b = 0.569648 + 0.391218I
−3.86698 + 1.08438I −3.75949 − 5.90127I
u = 0.190701 − 0.810384I
a = 0.33485 + 2.32194I
b = 0.569648 − 0.391218I
−3.86698 − 1.08438I −3.75949 + 5.90127I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487539 + 1.254270I
a = 0.652357 − 0.643137I
b = −0.736189 + 0.110556I
−11.8837 − 9.6751I −5.50822 + 5.97678I
u = −0.487539 − 1.254270I
a = 0.652357 + 0.643137I
b = −0.736189 − 0.110556I
−11.8837 + 9.6751I −5.50822 − 5.97678I
u = 0.469746 + 1.263010I
a = 0.70256 − 1.98263I
b = 1.83074 + 2.27175I
−16.0195 + 4.8597I −9.14726 − 3.11789I
u = 0.469746 − 1.263010I
a = 0.70256 + 1.98263I
b = 1.83074 − 2.27175I
−16.0195 − 4.8597I −9.14726 + 3.11789I
u = 0.589289 + 0.270476I
a = 0.998682 + 0.324734I
b = −0.232766 + 1.375450I
−0.51702 − 2.45923I 1.27496 + 3.25382I
u = 0.589289 − 0.270476I
a = 0.998682 − 0.324734I
b = −0.232766 − 1.375450I
−0.51702 + 2.45923I 1.27496 − 3.25382I
10
III.
I
u
3
= h−u
15
+2u
14
+· · ·+b+3, −u
15
−3u
13
+· · ·+2a−1, u
16
−2u
15
+· · ·−3u+2i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
1
2
u
15
+
3
2
u
13
+ ··· −
1
2
u +
1
2
u
15
− 2u
14
+ ··· + 3u − 3
a
6
=
−
1
2
u
15
+ 2u
14
+ ··· −
3
2
u +
3
2
u
15
− 2u
14
+ ··· + 2u − 1
a
11
=
1
2
u
15
− 2u
14
+ ··· +
5
2
u −
3
2
−u
15
+ 2u
14
+ ··· − 2u + 1
a
10
=
−
1
2
u
15
−
3
2
u
13
+ ··· +
1
2
u +
1
2
−u
15
+ 2u
14
+ ··· − 2u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
13
+ 16u
11
+ 24u
9
+ 4u
7
− 20u
5
− 12u
3
+ 4u − 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 10u
15
+ ··· + 3u + 4
c
2
, c
7
u
16
+ 2u
15
+ ··· + 3u + 2
c
3
, c
4
, c
8
u
16
− 2u
15
+ ··· − u + 2
c
5
, c
6
, c
10
c
12
u
16
− u
15
+ ··· + u
2
+ 1
c
9
, c
11
u
16
+ 9u
15
+ ··· + 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 10y
15
+ ··· − y + 16
c
2
, c
7
y
16
+ 10y
15
+ ··· + 3y + 4
c
3
, c
4
, c
8
y
16
− 18y
15
+ ··· + 19y + 4
c
5
, c
6
, c
10
c
12
y
16
+ 9y
15
+ ··· + 2y + 1
c
9
, c
11
y
16
− 3y
15
+ ··· − 2y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.402991 + 0.968083I
a = 0.222795 − 0.609931I
b = −0.059233 + 0.569202I
−0.51702 − 2.45923I 1.27496 + 3.25382I
u = −0.402991 − 0.968083I
a = 0.222795 + 0.609931I
b = −0.059233 − 0.569202I
−0.51702 + 2.45923I 1.27496 − 3.25382I
u = 0.921586 + 0.049492I
a = 0.594426 + 1.196160I
b = −0.09325 + 2.32148I
−11.8837 − 9.6751I −5.50822 + 5.97678I
u = 0.921586 − 0.049492I
a = 0.594426 − 1.196160I
b = −0.09325 − 2.32148I
−11.8837 + 9.6751I −5.50822 − 5.97678I
u = 0.059705 + 1.152710I
a = 0.23551 − 1.67559I
b = 0.10924 + 1.44246I
−3.86698 − 1.08438I −3.75949 + 5.90127I
u = 0.059705 − 1.152710I
a = 0.23551 + 1.67559I
b = 0.10924 − 1.44246I
−3.86698 + 1.08438I −3.75949 − 5.90127I
u = −0.270509 + 1.207500I
a = −0.55626 − 1.86816I
b = −0.82968 + 1.87098I
−7.04324 + 3.37292I −8.93248 − 5.20888I
u = −0.270509 − 1.207500I
a = −0.55626 + 1.86816I
b = −0.82968 − 1.87098I
−7.04324 − 3.37292I −8.93248 + 5.20888I
u = −0.724264 + 0.230405I
a = −0.784571 + 0.654294I
b = 0.31772 + 1.62349I
−2.68724 + 6.60937I −2.51664 − 7.40663I
u = −0.724264 − 0.230405I
a = −0.784571 − 0.654294I
b = 0.31772 − 1.62349I
−2.68724 − 6.60937I −2.51664 + 7.40663I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.507077 + 0.543596I
a = 0.458679 − 0.248786I
b = −0.339347 + 0.997289I
0.85997 − 1.95072I 3.06114 + 4.17042I
u = 0.507077 − 0.543596I
a = 0.458679 + 0.248786I
b = −0.339347 − 0.997289I
0.85997 + 1.95072I 3.06114 − 4.17042I
u = 0.465530 + 1.245910I
a = −0.629795 − 0.668340I
b = 0.723472 + 0.198002I
−8.19036 + 4.73480I −2.47201 − 3.02289I
u = 0.465530 − 1.245910I
a = −0.629795 + 0.668340I
b = 0.723472 − 0.198002I
−8.19036 − 4.73480I −2.47201 + 3.02289I
u = 0.443866 + 1.287090I
a = 0.70921 − 1.95738I
b = 1.67108 + 2.40426I
−16.0195 − 4.8597I −9.14726 + 3.11789I
u = 0.443866 − 1.287090I
a = 0.70921 + 1.95738I
b = 1.67108 − 2.40426I
−16.0195 + 4.8597I −9.14726 − 3.11789I
15
IV. I
u
4
= hu
15
+ 3u
13
+ 4u
11
− u
9
− 4u
7
− 4u
5
+ u
3
+ b − 1, −u
15
− 3u
13
+
· · · + a + 1, u
16
+ u
15
+ · · · + u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
u
15
+ 3u
13
+ 4u
11
− u
9
− 4u
7
− 4u
5
+ 2u
3
− 1
−u
15
− 3u
13
− 4u
11
+ u
9
+ 4u
7
+ 4u
5
− u
3
+ 1
a
6
=
−u
15
− 2u
14
+ ··· − u
2
− u
u
15
+ 2u
14
+ ··· + u + 1
a
11
=
u
15
+ 3u
13
+ 4u
11
− u
9
− 4u
7
− 3u
5
+ 2u
3
− 1
−u
15
− 3u
13
− 4u
11
+ u
9
+ 5u
7
+ 5u
5
+ 1
a
10
=
u
15
+ 3u
13
+ 4u
11
− u
10
− u
9
− 3u
8
− 4u
7
− 4u
6
− 4u
5
− u
4
+ u
3
+ u
2
− u
2u
13
+ 8u
11
+ ··· − u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
14
− 4u
13
− 16u
12
− 20u
11
− 32u
10
− 44u
9
− 28u
8
− 44u
7
−
12u
6
− 12u
5
+ 4u
4
+ 12u
3
− 4u
2
+ 4u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
16
+ 9u
15
+ ··· + 2u + 1
c
2
, c
6
, c
7
c
12
u
16
− u
15
+ ··· + u
2
+ 1
c
3
, c
4
, c
8
u
16
− 2u
15
+ ··· − u + 2
c
5
, c
10
u
16
+ 2u
15
+ ··· + 3u + 2
c
9
u
16
+ 10u
15
+ ··· + 3u + 4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
16
− 3y
15
+ ··· − 2y + 1
c
2
, c
6
, c
7
c
12
y
16
+ 9y
15
+ ··· + 2y + 1
c
3
, c
4
, c
8
y
16
− 18y
15
+ ··· + 19y + 4
c
5
, c
10
y
16
+ 10y
15
+ ··· + 3y + 4
c
9
y
16
− 10y
15
+ ··· − y + 16
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.892953 + 0.035958I
a = 0.1015470 + 0.0314751I
b = −0.810093 + 0.054493I
−8.19036 + 4.73480I −2.47201 − 3.02289I
u = −0.892953 − 0.035958I
a = 0.1015470 − 0.0314751I
b = −0.810093 − 0.054493I
−8.19036 − 4.73480I −2.47201 + 3.02289I
u = −0.458901 + 0.734878I
a = 1.317400 + 0.329697I
b = −0.670552 − 0.262290I
0.85997 − 1.95072I 3.06114 + 4.17042I
u = −0.458901 − 0.734878I
a = 1.317400 − 0.329697I
b = −0.670552 + 0.262290I
0.85997 + 1.95072I 3.06114 − 4.17042I
u = −0.379593 + 1.079580I
a = 2.22885 + 2.07396I
b = −0.95631 − 2.86552I
−7.04324 − 3.37292I −8.93248 + 5.20888I
u = −0.379593 − 1.079580I
a = 2.22885 − 2.07396I
b = −0.95631 + 2.86552I
−7.04324 + 3.37292I −8.93248 − 5.20888I
u = 0.469252 + 1.053160I
a = −1.74058 + 1.75441I
b = 0.28250 − 2.22682I
−2.68724 + 6.60937I −2.51664 − 7.40663I
u = 0.469252 − 1.053160I
a = −1.74058 − 1.75441I
b = 0.28250 + 2.22682I
−2.68724 − 6.60937I −2.51664 + 7.40663I
u = 0.190701 + 0.810384I
a = −2.50371 − 1.26517I
b = 2.13493 + 0.82139I
−3.86698 + 1.08438I −3.75949 − 5.90127I
u = 0.190701 − 0.810384I
a = −2.50371 + 1.26517I
b = 2.13493 − 0.82139I
−3.86698 − 1.08438I −3.75949 + 5.90127I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.487539 + 1.254270I
a = 1.21664 + 2.51902I
b = 0.96843 − 3.59781I
−11.8837 − 9.6751I −5.50822 + 5.97678I
u = −0.487539 − 1.254270I
a = 1.21664 − 2.51902I
b = 0.96843 + 3.59781I
−11.8837 + 9.6751I −5.50822 − 5.97678I
u = 0.469746 + 1.263010I
a = −1.23893 + 2.59409I
b = −0.90542 − 3.77274I
−16.0195 + 4.8597I −9.14726 − 3.11789I
u = 0.469746 − 1.263010I
a = −1.23893 − 2.59409I
b = −0.90542 + 3.77274I
−16.0195 − 4.8597I −9.14726 + 3.11789I
u = 0.589289 + 0.270476I
a = −0.381211 + 0.088717I
b = 0.456516 + 0.173272I
−0.51702 − 2.45923I 1.27496 + 3.25382I
u = 0.589289 − 0.270476I
a = −0.381211 − 0.088717I
b = 0.456516 − 0.173272I
−0.51702 + 2.45923I 1.27496 − 3.25382I
20
V. I
u
5
= hb + u − 1, a − u + 2, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
9
=
u
−u
a
5
=
2
u − 2
a
1
=
−1
0
a
12
=
u − 2
−u + 1
a
6
=
−u
u
a
11
=
−1
−u + 1
a
10
=
2u − 1
−2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12u + 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
7
, c
9
c
10
, c
11
, c
12
u
2
+ u + 1
c
3
, c
4
, c
8
u
2
− u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
2
+ y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −1.50000 + 0.86603I
b = 0.500000 − 0.866025I
6.08965I 0. − 10.39230I
u = 0.500000 − 0.866025I
a = −1.50000 − 0.86603I
b = 0.500000 + 0.866025I
− 6.08965I 0. + 10.39230I
24
VI. I
u
6
= hu
5
− u
2
a + 2u
3
− u
2
+ b − a + u − 1, −2u
5
a − u
5
+ · · · + 2a +
2, u
6
+ 2u
4
− u
3
+ u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
u
4
− u
3
+ u
2
− u
u
3
+ u + 1
a
5
=
−u
4
− u
2
+ 1
−u
3
− u − 1
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
a
−u
5
+ u
2
a − 2u
3
+ u
2
+ a − u + 1
a
6
=
u
5
a + u
5
+ 2u
3
a − u
4
− u
2
a + 2u
3
− 4u
2
− a + 2u − 1
−u
3
a − u
4
− 1
a
11
=
−u
4
a − u
5
+ a
u
4
a − u
3
a − u
4
+ u
2
a − 2u
3
− au − 2u + 1
a
10
=
u
5
+ u
2
a + 2u
3
− u
2
− u − 1
u
4
a − u
5
+ u
2
a − 4u
3
+ u
2
+ a − 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
(u
6
+ 4u
5
+ 6u
4
+ u
3
− 5u
2
− 3u + 1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
(u
6
+ 2u
4
+ u
3
+ u
2
+ u − 1)
2
c
3
, c
4
, c
8
(u
2
+ u − 1)
6
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
(y
6
− 4y
5
+ 18y
4
− 35y
3
+ 43y
2
− 19y + 1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
(y
6
+ 4y
5
+ 6y
4
+ y
3
− 5y
2
− 3y + 1)
2
c
3
, c
4
, c
8
(y
2
− 3y + 1)
6
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.896795
a = 0.66668 + 1.26617I
b = 0.08778 + 2.28447I
−12.1725 −6.00000
u = 0.896795
a = 0.66668 − 1.26617I
b = 0.08778 − 2.28447I
−12.1725 −6.00000
u = 0.248003 + 1.088360I
a = −0.296970 − 0.873464I
b = 0.309017 + 0.820596I
−4.27683 −6.00000
u = 0.248003 + 1.088360I
a = 0.44704 − 1.96182I
b = 0.80502 + 1.35611I
−4.27683 −6.00000
u = 0.248003 − 1.088360I
a = −0.296970 + 0.873464I
b = 0.309017 − 0.820596I
−4.27683 −6.00000
u = 0.248003 − 1.088360I
a = 0.44704 + 1.96182I
b = 0.80502 − 1.35611I
−4.27683 −6.00000
u = −0.448397 + 1.266170I
a = 0.648271 − 0.701773I
b = −0.809017 + 0.247864I
−12.1725 −6.00000
u = −0.448397 + 1.266170I
a = −0.69692 − 1.96794I
b = −1.70581 + 2.28447I
−12.1725 −6.00000
u = −0.448397 − 1.266170I
a = 0.648271 + 0.701773I
b = −0.809017 − 0.247864I
−12.1725 −6.00000
u = −0.448397 − 1.266170I
a = −0.69692 + 1.96794I
b = −1.70581 − 2.28447I
−12.1725 −6.00000
28
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496006
a = −1.76810 + 1.08835I
b = −0.186989 + 1.356110I
−4.27683 −6.00000
u = −0.496006
a = −1.76810 − 1.08835I
b = −0.186989 − 1.356110I
−4.27683 −6.00000
29
VII. I
u
7
= hb − u − 1, a + 2u + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
−1
a
3
=
u
0
a
4
=
u
0
a
9
=
1
0
a
5
=
u
0
a
1
=
−u
u
a
12
=
−2u − 1
u + 1
a
6
=
u − 1
−u
a
11
=
−u − 1
1
a
10
=
−u
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
9
, c
11
(u − 1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
u
2
+ 1
c
3
, c
4
, c
8
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
(y −1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
(y + 1)
2
c
3
, c
4
, c
8
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000 − 2.00000I
b = 1.00000 + 1.00000I
−4.93480 −12.0000
u = − 1.000000I
a = −1.00000 + 2.00000I
b = 1.00000 − 1.00000I
−4.93480 −12.0000
33
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
11
(u − 1)
2
(u
2
+ u + 1)(u
6
+ 4u
5
+ 6u
4
+ u
3
− 5u
2
− 3u + 1)
2
· (u
7
+ 4u
6
+ 8u
5
+ 6u
4
− 5u
2
− u − 1)(u
16
+ 9u
15
+ ··· + 2u + 1)
2
· (u
16
+ 10u
15
+ ··· + 3u + 4)
c
2
, c
5
, c
6
c
7
, c
10
, c
12
(u
2
+ 1)(u
2
+ u + 1)(u
6
+ 2u
4
+ u
3
+ u
2
+ u − 1)
2
· (u
7
+ 2u
5
+ 2u
3
+ u
2
− u + 1)(u
16
− u
15
+ ··· + u
2
+ 1)
2
· (u
16
+ 2u
15
+ ··· + 3u + 2)
c
3
, c
4
, c
8
u
2
(u
2
− u + 1)(u
2
+ u − 1)
6
(u
7
− 5u
5
− 2u
4
+ 7u
3
+ 4u
2
+ 4)
· (u
16
− 2u
15
+ ··· − u + 2)
3
34
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
11
(y −1)
2
(y
2
+ y + 1)(y
6
− 4y
5
+ 18y
4
− 35y
3
+ 43y
2
− 19y + 1)
2
· (y
7
+ 16y
5
+ ··· − 9y −1)(y
16
− 10y
15
+ ··· − y + 16)
· (y
16
− 3y
15
+ ··· − 2y + 1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
12
(y + 1)
2
(y
2
+ y + 1)(y
6
+ 4y
5
+ 6y
4
+ y
3
− 5y
2
− 3y + 1)
2
· (y
7
+ 4y
6
+ 8y
5
+ 6y
4
− 5y
2
− y −1)(y
16
+ 9y
15
+ ··· + 2y + 1)
2
· (y
16
+ 10y
15
+ ··· + 3y + 4)
c
3
, c
4
, c
8
y
2
(y
2
− 3y + 1)
6
(y
2
+ y + 1)
· (y
7
− 10y
6
+ 39y
5
− 74y
4
+ 65y
3
− 32y −16)
· (y
16
− 18y
15
+ ··· + 19y + 4)
3
35
