12n
0556
(K12n
0556
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 10 12 2 4 11 5 7 11
Solving Sequence
3,9 4,7
2 1 8
5,11
10 12 6
c
3
c
2
c
1
c
8
c
4
c
10
c
12
c
6
c
5
, c
7
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
7
+ u
6
+ 2u
5
+ 3u
4
− 2u
3
+ 6u
2
+ 4d − u + 2, −u
7
− u
6
− 4u
5
+ u
4
− 2u
3
+ 8u
2
+ 4c − u,
− u
7
+ u
6
− 6u
5
+ 5u
4
− 12u
3
+ 8u
2
+ 4b − 5u + 2, u
7
− u
6
+ 4u
5
− 5u
4
+ 4u
3
− 6u
2
+ 4a − u,
u
8
+ 5u
6
− 3u
5
+ 7u
4
− 8u
3
+ 5u
2
− u + 2i
I
u
2
= hu
5
− u
4
+ u
3
− u
2
+ 2d − 2u − 2, u
5
+ u
4
+ 3u
3
+ u
2
+ 4c + 4u, −u
5
− u
4
− 3u
3
− 3u
2
+ 2b − 2u − 2,
u
5
+ u
4
− u
3
+ u
2
+ 4a − 4u − 4, u
6
+ u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4i
I
u
3
= hau + d, −u
2
a + 3u
2
+ 2c − a − 2u + 9, −u
2
a + u
2
+ 2b − a + 3, −2u
2
a + a
2
+ au + 4u
2
− 5a − 3u + 10,
u
3
− u
2
+ 3u − 1i
I
u
4
= hd, c − 1, b − u, a, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
5
= hd, c − 1, −u
3
− u
2
+ b − 2u − 1, u
2
+ a + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
6
= hd, c − 1, u
3
+ u
2
+ b + 3u + 1, 3u
3
+ u
2
+ a + 7u + 2, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
7
= h−u
3
+ d − u, c − u, b − u, a, u
4
+ u
3
+ u
2
+ 1i
I
u
8
= h−u
3
+ d − u, c − u, −u
3
− u
2
+ b − 2u − 1, u
2
+ a + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
9
= h−u
3
+ d − u, c − u, −u
3
+ u
2
+ b − u + 1, u
3
− 2u
2
+ 2a − u + 1, u
4
− 2u
3
+ 3u
2
− 3u + 2i
I
u
10
= h2u
3
+ d + 4u − 1, −2u
3
− 2u
2
+ c − 5u − 3, −u
3
− u
2
+ b − 2u − 1, u
2
+ a + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
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
11
= h2u
3
− 2u
2
+ d + 2u − 1, u
3
+ 2c + u + 1, b − u, a, u
4
− 2u
3
+ 3u
2
− 3u + 2i
I
u
12
= hd − 1, c − u, b, a − u, u
2
+ 1i
I
u
13
= hd − u, c, b − u, a + 1, u
2
+ 1i
I
u
14
= hd + 1, c − u, b − u, a − 1, u
2
+ 1i
I
u
15
= hda + u + 1, c − u, b − u, u
2
+ 1i
I
v
1
= ha, d + v, c + a − 1, b − v, v
2
+ 1i
* 15 irreducible components of dim
C
= 0, with total 60 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
= hu
7
+ u
6
+ · · · + 4d + 2, −u
7
− u
6
+ · · · + 4c − u, −u
7
+ u
6
+ · · · +
4b + 2, u
7
− u
6
+ · · · + 4a − u, u
8
+ 5u
6
+ · · · − u + 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−
1
4
u
7
+
1
4
u
6
+ ··· +
3
2
u
2
+
1
4
u
1
4
u
7
−
1
4
u
6
+ ··· +
5
4
u −
1
2
a
2
=
1
2
u
5
+ u
3
−
1
2
u
2
−
1
2
u +
1
2
1
4
u
7
−
1
4
u
6
+ ··· +
1
4
u −
1
2
a
1
=
1
4
u
7
−
1
4
u
6
+ ··· −
3
2
u
2
−
1
4
u
1
4
u
7
−
1
4
u
6
+ ··· +
1
4
u −
1
2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
1
4
u
7
+
1
4
u
6
+ ··· − 2u
2
+
1
4
u
−
1
4
u
7
−
1
4
u
6
+ ··· +
1
4
u −
1
2
a
10
=
−
1
4
u
7
−
1
4
u
6
+ ··· − u
2
−
1
4
u
−
1
2
u
6
− 2u
4
+ ··· −
1
2
u
2
+
3
2
u
a
12
=
1
2
u
7
+
1
2
u
6
+ ··· −
1
2
u
2
+
1
2
−
1
2
u
7
− u
5
+ ··· −
3
2
u
2
− 1
a
6
=
1
4
u
7
−
3
4
u
6
+ ··· +
5
4
u − 1
1
4
u
7
+
5
4
u
6
+ ··· −
1
4
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
7
+ u
6
− 2u
5
+ 9u
4
+ 12u
2
− 9u
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
8
+ 2u
7
+ 7u
6
+ 7u
5
+ 23u
4
+ 28u
3
+ 37u
2
+ 19u + 4
c
2
, c
5
, c
7
c
10
u
8
+ u
6
− 3u
5
+ 3u
4
+ 5u
2
− u + 2
c
3
, c
4
, c
6
c
8
, c
11
u
8
+ 5u
6
− 3u
5
+ 7u
4
− 8u
3
+ 5u
2
− u + 2
c
12
u
8
− 10u
7
+ 39u
6
− 71u
5
+ 55u
4
− 20u
3
+ 37u
2
− 19u + 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
8
+ 10y
7
+ 67y
6
+ 235y
5
+ 587y
4
+ 708y
3
+ 489y
2
− 65y + 16
c
2
, c
5
, c
7
c
10
y
8
+ 2y
7
+ 7y
6
+ 7y
5
+ 23y
4
+ 28y
3
+ 37y
2
+ 19y + 4
c
3
, c
4
, c
6
c
8
, c
11
y
8
+ 10y
7
+ 39y
6
+ 71y
5
+ 55y
4
+ 20y
3
+ 37y
2
+ 19y + 4
c
12
y
8
− 22y
7
+ ··· − 65y + 16
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758942 + 0.438317I
a = 0.817358 + 0.864251I
b = −0.595440 + 0.936067I
c = −1.151560 − 0.803744I
d = −0.241512 − 1.014180I
−1.16700 − 5.71173I −4.09501 + 8.31811I
u = 0.758942 − 0.438317I
a = 0.817358 − 0.864251I
b = −0.595440 − 0.936067I
c = −1.151560 + 0.803744I
d = −0.241512 + 1.014180I
−1.16700 + 5.71173I −4.09501 − 8.31811I
u = −0.179745 + 0.559373I
a = −0.512845 + 0.085661I
b = 0.174356 + 0.612892I
c = 0.526077 + 0.448139I
d = −0.044265 + 0.302269I
−0.095264 + 1.253510I −1.27264 − 6.48719I
u = −0.179745 − 0.559373I
a = −0.512845 − 0.085661I
b = 0.174356 − 0.612892I
c = 0.526077 − 0.448139I
d = −0.044265 − 0.302269I
−0.095264 − 1.253510I −1.27264 + 6.48719I
u = −0.41760 + 1.54917I
a = 1.46083 − 0.22749I
b = −0.75243 − 1.27936I
c = 1.332250 + 0.331963I
d = 0.25762 − 2.35809I
11.6096 + 14.8655I 0.93475 − 7.40876I
u = −0.41760 − 1.54917I
a = 1.46083 + 0.22749I
b = −0.75243 + 1.27936I
c = 1.332250 − 0.331963I
d = 0.25762 + 2.35809I
11.6096 − 14.8655I 0.93475 + 7.40876I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16160 + 1.70407I
a = −1.015350 + 0.406227I
b = 1.173510 − 0.663027I
c = −0.956761 − 0.459439I
d = 0.52816 + 1.79586I
15.9716 + 0.6364I 4.43290 + 0.86524I
u = −0.16160 − 1.70407I
a = −1.015350 − 0.406227I
b = 1.173510 + 0.663027I
c = −0.956761 + 0.459439I
d = 0.52816 − 1.79586I
15.9716 − 0.6364I 4.43290 − 0.86524I
7
II. I
u
2
= hu
5
− u
4
+ · · · + 2d − 2, u
5
+ u
4
+ · · · + 4c + 4u, −u
5
− u
4
+ · · · +
2b − 2, u
5
+ u
4
+ · · · + 4a − 4, u
6
+ u
5
+ · · · + 4u + 4i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−
1
4
u
5
−
1
4
u
4
+ ··· + u + 1
1
2
u
5
+
1
2
u
4
+ ··· + u + 1
a
2
=
−
1
4
u
5
−
3
4
u
4
+ ··· −
3
2
u − 1
u
3
+ u + 1
a
1
=
−
1
4
u
5
−
3
4
u
4
+ ··· −
7
4
u
2
−
1
2
u
u
3
+ u + 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
−
1
4
u
5
−
1
4
u
4
+ ··· −
1
4
u
2
− u
−
1
2
u
5
+
1
2
u
4
+ ··· + u + 1
a
10
=
−
3
4
u
5
+
1
4
u
4
+ ··· −
3
4
u
2
− 1
−
1
2
u
5
+
1
2
u
4
+ ··· + u − 3
a
12
=
−
1
2
u
4
−
1
2
u
3
+ ··· −
3
2
u + 1
−
1
2
u
5
+
1
2
u
4
+ ··· + u + 2
a
6
=
−
3
4
u
5
−
1
4
u
4
+ ··· −
3
2
u − 1
−u
5
− 3u
3
− 3u
2
− u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
5
− 3u
4
− 9u
3
− 9u
2
− 6u − 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
3
+ u
2
+ 3u − 1)
2
c
2
, c
5
, c
7
c
10
(u
3
− u
2
+ u + 1)
2
c
3
, c
4
, c
6
c
8
, c
11
u
6
+ u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4
c
12
u
6
− 5u
5
+ 7u
4
+ u
3
− 16u + 16
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y
3
+ 5y
2
+ 11y −1)
2
c
2
, c
5
, c
7
c
10
(y
3
+ y
2
+ 3y −1)
2
c
3
, c
4
, c
6
c
8
, c
11
y
6
+ 5y
5
+ 7y
4
− y
3
+ 16y + 16
c
12
y
6
− 11y
5
+ 59y
4
− 129y
3
+ 256y
2
− 256y + 256
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.047560 + 0.418092I
a = −0.596209 + 0.934931I
b = 0.771845 + 1.115140I
c = 1.09915 − 1.20459I
d = 0.46183 − 2.34381I
5.31927 + 9.53188I −0.63107 − 6.69086I
u = −1.047560 − 0.418092I
a = −0.596209 − 0.934931I
b = 0.771845 − 1.115140I
c = 1.09915 + 1.20459I
d = 0.46183 + 2.34381I
5.31927 − 9.53188I −0.63107 + 6.69086I
u = 0.271845 + 1.105310I
a = 0.629465 + 0.853123I
b = −0.543689
c = 0.062023 − 0.252181I
d = 0.771845 + 0.927668I
4.16586 7.26213 + 0.I
u = 0.271845 − 1.105310I
a = 0.629465 − 0.853123I
b = −0.543689
c = 0.062023 + 0.252181I
d = 0.771845 − 0.927668I
4.16586 7.26213 + 0.I
u = 0.27572 + 1.53323I
a = −1.53326 + 0.02549I
b = 0.771845 − 1.115140I
c = −1.161170 + 0.213694I
d = −0.233679 − 1.228670I
5.31927 − 9.53188I −0.63107 + 6.69086I
u = 0.27572 − 1.53323I
a = −1.53326 − 0.02549I
b = 0.771845 + 1.115140I
c = −1.161170 − 0.213694I
d = −0.233679 + 1.228670I
5.31927 + 9.53188I −0.63107 − 6.69086I
11
III. I
u
3
= hau + d, −u
2
a + 3u
2
+ · · · − a + 9, −u
2
a + u
2
+ 2b − a +
3, −2u
2
a + 4u
2
+ · · · − 5a + 10, u
3
− u
2
+ 3u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
a
1
2
u
2
a −
1
2
u
2
+
1
2
a −
3
2
a
2
=
1
2
u
2
a −
3
2
u
2
+ ··· +
3
2
a −
9
2
−
1
2
u
2
a −
1
2
u
2
+ ··· −
1
2
a −
1
2
a
1
=
−2u
2
+ a + u − 5
−
1
2
u
2
a −
1
2
u
2
+ ··· −
1
2
a −
1
2
a
8
=
u
u
2
− 2u + 1
a
5
=
u
2
+ 1
−2u + 1
a
11
=
1
2
u
2
a −
3
2
u
2
+
1
2
a + u −
9
2
−au
a
10
=
1
2
u
2
a − au −
3
2
u
2
+
3
2
a −
11
2
−
1
2
u
2
a −
3
2
u
2
+ ··· −
1
2
a −
1
2
a
12
=
1
2
u
2
a −
3
2
u
2
+ ··· +
1
2
a −
9
2
1
2
u
2
a − 2au −
1
2
u
2
+
1
2
a −
1
2
a
6
=
3
2
u
2
a − au −
1
2
u
2
+
3
2
a −
3
2
−u
2
a − au − u
2
+ a + u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6u
2
+ 6u − 14
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
6
+ u
5
+ 3u
4
− u
3
+ 16u + 16
c
2
, c
5
, c
7
c
10
u
6
+ u
5
+ u
4
+ 3u
3
+ 4u
2
+ 4u + 4
c
3
, c
4
, c
6
c
8
, c
11
(u
3
− u
2
+ 3u − 1)
2
c
12
(u
3
− 5u
2
+ 7u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
6
+ 5y
5
+ 11y
4
− y
3
+ 128y
2
− 256y + 256
c
2
, c
5
, c
7
c
10
y
6
+ y
5
+ 3y
4
− y
3
+ 16y + 16
c
3
, c
4
, c
6
c
8
, c
11
(y
3
+ 5y
2
+ 7y −1)
2
c
12
(y
3
− 11y
2
+ 59y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.361103
a = 2.44984 + 1.85379I
b = −0.180552 + 1.047760I
c = −2.94984 + 1.04776I
d = −0.884646 − 0.669409I
−3.88548 −12.6160
u = 0.361103
a = 2.44984 − 1.85379I
b = −0.180552 − 1.047760I
c = −2.94984 − 1.04776I
d = −0.884646 + 0.669409I
−3.88548 −12.6160
u = 0.31945 + 1.63317I
a = 0.912386 + 0.501068I
b = −1.192850 − 0.437845I
c = −1.308200 + 0.151898I
d = 0.52687 − 1.65015I
14.2797 − 7.9406I 3.30788 + 3.53846I
u = 0.31945 + 1.63317I
a = −1.362230 − 0.047383I
b = 0.87340 − 1.19533I
c = 0.758045 − 0.605583I
d = 0.35778 + 2.23989I
14.2797 − 7.9406I 3.30788 + 3.53846I
u = 0.31945 − 1.63317I
a = 0.912386 − 0.501068I
b = −1.192850 + 0.437845I
c = −1.308200 − 0.151898I
d = 0.52687 + 1.65015I
14.2797 + 7.9406I 3.30788 − 3.53846I
u = 0.31945 − 1.63317I
a = −1.362230 + 0.047383I
b = 0.87340 + 1.19533I
c = 0.758045 + 0.605583I
d = 0.35778 − 2.23989I
14.2797 + 7.9406I 3.30788 − 3.53846I
15
IV. I
u
4
= hd, c − 1, b − u, a, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
11
=
1
0
a
10
=
−u
u
a
12
=
1
u
2
a
6
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
5
, c
10
u
4
+ u
3
+ u
2
+ 1
c
12
u
4
− 5u
3
+ 7u
2
− 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
5
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0
b = −0.395123 + 0.506844I
c = 1.00000
d = 0
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = 0
b = −0.395123 − 0.506844I
c = 1.00000
d = 0
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = 0
b = −0.10488 + 1.55249I
c = 1.00000
d = 0
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 0
b = −0.10488 − 1.55249I
c = 1.00000
d = 0
6.79074 − 3.16396I 1.82674 + 2.56480I
19
V. I
u
5
= hd, c − 1, −u
3
− u
2
+ b − 2u − 1, u
2
+ a + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−u
2
− 1
u
3
+ u
2
+ 2u + 1
a
2
=
−u
u
a
1
=
0
u
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
11
=
1
0
a
10
=
−u
u
a
12
=
−u
u
a
6
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
9
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
5
, c
6
c
7
, c
10
, c
11
u
4
+ u
3
+ u
2
+ 1
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
, c
9
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
, c
6
c
7
, c
10
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.899232 + 0.400532I
b = 0.351808 + 0.720342I
c = 1.00000
d = 0
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = −0.899232 − 0.400532I
b = 0.351808 − 0.720342I
c = 1.00000
d = 0
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = 1.39923 + 0.32564I
b = −0.851808 − 0.911292I
c = 1.00000
d = 0
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 1.39923 − 0.32564I
b = −0.851808 + 0.911292I
c = 1.00000
d = 0
6.79074 − 3.16396I 1.82674 + 2.56480I
23
VI.
I
u
6
= hd, c−1, u
3
+u
2
+b+3u+1, 3u
3
+u
2
+a+7u+2, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−3u
3
− u
2
− 7u − 2
−u
3
− u
2
− 3u − 1
a
2
=
−u
3
− 2u
2
− 2u − 4
−u
2
− u − 2
a
1
=
−u
3
− 3u
2
− 3u − 6
−u
2
− u − 2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
11
=
1
0
a
10
=
−u
u
a
12
=
−u
3
− 2u
2
− 2u − 4
−u
2
− u − 2
a
6
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
6
, c
7
c
11
u
4
− 2u
3
+ 3u
2
− 3u + 2
c
3
, c
4
, c
8
c
9
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
5
, c
10
u
4
+ u
3
+ u
2
+ 1
c
12
u
4
− 2u
3
+ u
2
− 3u + 4
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
4
− 2y
3
− 3y
2
− y + 16
c
2
, c
6
, c
7
c
11
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
3
, c
4
, c
8
c
9
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
5
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.13816 − 3.46893I
b = 0.043315 − 1.227190I
c = 1.00000
d = 0
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = 0.13816 + 3.46893I
b = 0.043315 + 1.227190I
c = 1.00000
d = 0
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = −1.138160 + 0.530104I
b = 0.956685 − 0.641200I
c = 1.00000
d = 0
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = −1.138160 − 0.530104I
b = 0.956685 + 0.641200I
c = 1.00000
d = 0
6.79074 − 3.16396I 1.82674 + 2.56480I
27
VII. I
u
7
= h−u
3
+ d − u, c − u, b − u, a, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
−u
3
+ u
2
− 1
a
11
=
u
u
3
+ u
a
10
=
−u
3
−u
3
− u
2
+ 2u − 1
a
12
=
u
2u
3
+ u
a
6
=
u
3
u
3
+ 2u
2
− u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 2
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
9
c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
u
4
+ u
3
+ u
2
+ 1
c
12
u
4
− 5u
3
+ 7u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 0
b = 0.351808 + 0.720342I
c = 0.351808 + 0.720342I
d = −0.152300 + 0.614030I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = 0.351808 − 0.720342I
a = 0
b = 0.351808 − 0.720342I
c = 0.351808 − 0.720342I
d = −0.152300 − 0.614030I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.851808 + 0.911292I
a = 0
b = −0.851808 + 0.911292I
c = −0.851808 + 0.911292I
d = 0.65230 + 2.13814I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = −0.851808 − 0.911292I
a = 0
b = −0.851808 − 0.911292I
c = −0.851808 − 0.911292I
d = 0.65230 − 2.13814I
6.79074 + 3.16396I 1.82674 − 2.56480I
31
VIII.
I
u
8
= h−u
3
+d−u, c−u, −u
3
−u
2
+b−2u−1, u
2
+a+1, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−u
2
− 1
u
3
+ u
2
+ 2u + 1
a
2
=
−u
u
a
1
=
0
u
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
11
=
u
u
3
+ u
a
10
=
−u
3
u
3
− u
2
− 1
a
12
=
−u
3
u
3
− u
2
− 1
a
6
=
u
3
+ 2u
2
+ 2u
−u
3
− 2u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
7
u
4
+ u
3
+ u
2
+ 1
c
9
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
c
12
u
4
− 5u
3
+ 7u
2
− 2u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
8
c
10
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
7
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
9
, c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.899232 + 0.400532I
b = 0.351808 + 0.720342I
c = −0.395123 + 0.506844I
d = −0.152300 + 0.614030I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = −0.899232 − 0.400532I
b = 0.351808 − 0.720342I
c = −0.395123 − 0.506844I
d = −0.152300 − 0.614030I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = 1.39923 + 0.32564I
b = −0.851808 − 0.911292I
c = −0.10488 + 1.55249I
d = 0.65230 − 2.13814I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 1.39923 − 0.32564I
b = −0.851808 + 0.911292I
c = −0.10488 − 1.55249I
d = 0.65230 + 2.13814I
6.79074 − 3.16396I 1.82674 + 2.56480I
35
IX. I
u
9
= h−u
3
+ d − u, c − u, −u
3
+ u
2
+ b − u + 1, u
3
− 2u
2
+ 2a − u +
1, u
4
− 2u
3
+ 3u
2
− 3u + 2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−
1
2
u
3
+ u
2
+
1
2
u −
1
2
u
3
− u
2
+ u − 1
a
2
=
1
2
u
3
− 2u
2
+
5
2
u −
3
2
−u
3
+ u
2
− 2u + 1
a
1
=
−
1
2
u
3
− u
2
+
1
2
u −
1
2
−u
3
+ u
2
− 2u + 1
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
2u
3
− u
2
+ 3u − 2
a
11
=
u
u
3
+ u
a
10
=
−u
3
−2u
3
+ 3u
2
− 3u + 4
a
12
=
−
1
2
u
3
+
1
2
u +
3
2
u
3
+ u
2
+ u + 1
a
6
=
−2u
3
+ 2u
2
− 3u + 1
−3u
3
+ 4u
2
− 5u + 6
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
7
u
4
+ u
3
+ u
2
+ 1
c
3
, c
4
, c
5
c
8
, c
10
u
4
− 2u
3
+ 3u
2
− 3u + 2
c
9
u
4
+ 2u
3
+ u
2
+ 3u + 4
c
12
u
4
− 5u
3
+ 7u
2
− 2u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
7
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
, c
4
, c
5
c
8
, c
10
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
9
y
4
− 2y
3
− 3y
2
− y + 16
c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956685 + 0.641200I
a = 0.634643 + 0.798979I
b = −0.851808 + 0.911292I
c = 0.956685 + 0.641200I
d = 0.65230 + 2.13814I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = 0.956685 − 0.641200I
a = 0.634643 − 0.798979I
b = −0.851808 − 0.911292I
c = 0.956685 − 0.641200I
d = 0.65230 − 2.13814I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = 0.043315 + 1.227190I
a = −1.88464 + 1.64051I
b = 0.351808 − 0.720342I
c = 0.043315 + 1.227190I
d = −0.152300 − 0.614030I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = 0.043315 − 1.227190I
a = −1.88464 − 1.64051I
b = 0.351808 + 0.720342I
c = 0.043315 − 1.227190I
d = −0.152300 + 0.614030I
−0.21101 + 1.41510I −1.82674 − 4.90874I
39
X. I
u
10
= h2u
3
+ d + 4u − 1, −2u
3
− 2u
2
+ c − 5u − 3, −u
3
− u
2
+ b − 2u −
1, u
2
+ a + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
−u
2
− 1
u
3
+ u
2
+ 2u + 1
a
2
=
−u
u
a
1
=
0
u
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
−u
3
− u
2
− 2u − 1
a
11
=
2u
3
+ 2u
2
+ 5u + 3
−2u
3
− 4u + 1
a
10
=
3u
3
+ 2u
2
+ 7u + 4
−2u
3
+ u
2
− 4u + 2
a
12
=
3u
3
+ 2u
2
+ 7u + 4
−2u
3
+ u
2
− 4u + 2
a
6
=
−u
3
− 3u + 2
−3u
3
− 2u
2
− 7u − 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
7
u
4
+ u
3
+ u
2
+ 1
c
5
, c
6
, c
10
c
11
u
4
− 2u
3
+ 3u
2
− 3u + 2
c
9
u
4
+ 2u
3
+ u
2
+ 3u + 4
c
12
u
4
− 2u
3
+ u
2
− 3u + 4
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
7
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
5
, c
6
, c
10
c
11
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
9
, c
12
y
4
− 2y
3
− 3y
2
− y + 16
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −0.899232 + 0.400532I
b = 0.351808 + 0.720342I
c = 1.30849 + 1.94753I
d = 2.09485 − 2.24175I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = −0.899232 − 0.400532I
b = 0.351808 − 0.720342I
c = 1.30849 − 1.94753I
d = 2.09485 + 2.24175I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = 1.39923 + 0.32564I
b = −0.851808 − 0.911292I
c = −0.808493 − 0.270093I
d = −0.094848 + 1.171300I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 1.39923 − 0.32564I
b = −0.851808 + 0.911292I
c = −0.808493 + 0.270093I
d = −0.094848 − 1.171300I
6.79074 − 3.16396I 1.82674 + 2.56480I
43
XI.
I
u
11
= h2u
3
−2u
2
+d +2u − 1, u
3
+2c +u + 1, b − u, a, u
4
−2u
3
+3u
2
−3u +2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
7
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
2u
3
− u
2
+ 3u − 2
a
11
=
−
1
2
u
3
−
1
2
u −
1
2
−2u
3
+ 2u
2
− 2u + 1
a
10
=
−
3
2
u
3
+ 2u
2
−
5
2
u +
5
2
−u
3
+ 3u
2
− u + 3
a
12
=
−
1
2
u
3
−
1
2
u −
1
2
−3u
3
+ 3u
2
− 4u + 3
a
6
=
3
2
u
3
− 2u
2
+
5
2
u −
5
2
u
3
− 4u
2
+ 3u − 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u − 2
44
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 2u
3
+ u
2
+ 3u + 4
c
2
, c
3
, c
4
c
7
, c
8
u
4
− 2u
3
+ 3u
2
− 3u + 2
c
5
, c
10
u
4
+ u
3
+ u
2
+ 1
c
6
, c
9
, c
11
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
12
u
4
− 5u
3
+ 7u
2
− 2u + 1
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 2y
3
− 3y
2
− y + 16
c
2
, c
3
, c
4
c
7
, c
8
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
5
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
6
, c
9
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956685 + 0.641200I
a = 0
b = 0.956685 + 0.641200I
c = −0.826150 − 1.069070I
d = 0.70362 − 1.82258I
6.79074 − 3.16396I 1.82674 + 2.56480I
u = 0.956685 − 0.641200I
a = 0
b = 0.956685 − 0.641200I
c = −0.826150 + 1.069070I
d = 0.70362 + 1.82258I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = 0.043315 + 1.227190I
a = 0
b = 0.043315 + 1.227190I
c = −0.423850 + 0.307015I
d = −1.70362 + 1.44068I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = 0.043315 − 1.227190I
a = 0
b = 0.043315 − 1.227190I
c = −0.423850 − 0.307015I
d = −1.70362 − 1.44068I
−0.21101 + 1.41510I −1.82674 − 4.90874I
47
XII. I
u
12
= hd − 1, c − u, b, a − u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
7
=
u
0
a
2
=
1
0
a
1
=
1
0
a
8
=
u
0
a
5
=
0
−1
a
11
=
u
1
a
10
=
u
u + 1
a
12
=
u + 1
1
a
6
=
1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
c
3
, c
4
, c
5
c
6
, c
8
, c
10
c
11
u
2
+ 1
c
9
, c
12
(u − 1)
2
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
2
c
3
, c
4
, c
5
c
6
, c
8
, c
10
c
11
(y + 1)
2
c
9
, c
12
(y −1)
2
50
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.000000I
b = 0
c = 1.000000I
d = 1.00000
1.64493 4.00000
u = − 1.000000I
a = − 1.000000I
b = 0
c = − 1.000000I
d = 1.00000
1.64493 4.00000
51
XIII. I
u
13
= hd − u, c, b − u, a + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
7
=
−1
u
a
2
=
−u + 1
−1
a
1
=
−u
−1
a
8
=
u
0
a
5
=
0
−1
a
11
=
0
u
a
10
=
0
u
a
12
=
−u
u − 1
a
6
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
52
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u − 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
11
u
2
+ 1
c
5
, c
9
, c
10
u
2
53
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y −1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
11
(y + 1)
2
c
5
, c
9
, c
10
y
2
54
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
13
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = 1.000000I
c = 0
d = 1.000000I
1.64493 4.00000
u = − 1.000000I
a = −1.00000
b = − 1.000000I
c = 0
d = − 1.000000I
1.64493 4.00000
55
XIV. I
u
14
= hd + 1, c − u, b − u, a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
7
=
1
u
a
2
=
u + 1
−1
a
1
=
u
−1
a
8
=
u
0
a
5
=
0
−1
a
11
=
u
−1
a
10
=
u
u − 1
a
12
=
u
−1
a
6
=
1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
56
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u − 1)
2
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
u
2
+ 1
c
6
, c
11
, c
12
u
2
57
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
10
(y + 1)
2
c
6
, c
11
, c
12
y
2
58
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
14
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.000000I
c = 1.000000I
d = −1.00000
−1.64493 −8.00000
u = − 1.000000I
a = 1.00000
b = − 1.000000I
c = − 1.000000I
d = −1.00000
−1.64493 −8.00000
59
XV. I
u
15
= hda + u + 1, c − u, b − u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−1
a
7
=
a
u
a
2
=
au + 1
−1
a
1
=
au
−1
a
8
=
u
0
a
5
=
0
−1
a
11
=
u
d
a
10
=
u
d + u
a
12
=
au + u
d − 1
a
6
=
−1
du
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
(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.
60
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
15
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
0 −2.00000
61
XVI. I
v
1
= ha, d + v, c + a − 1, b − v, v
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
7
=
0
v
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
0
a
5
=
1
0
a
11
=
1
−v
a
10
=
v + 1
−v
a
12
=
1
−v −1
a
6
=
v
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
62
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
12
(u − 1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
11
u
2
+ 1
c
3
, c
4
, c
8
u
2
63
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
(y −1)
2
c
2
, c
5
, c
6
c
7
, c
10
, c
11
(y + 1)
2
c
3
, c
4
, c
8
y
2
64
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.000000I
a = 0
b = 1.000000I
c = 1.00000
d = − 1.000000I
−1.64493 −8.00000
v = − 1.000000I
a = 0
b = − 1.000000I
c = 1.00000
d = 1.000000I
−1.64493 −8.00000
65
XVII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
9
u
2
(u − 1)
6
(u
3
+ u
2
+ 3u − 1)
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
5
· (u
4
+ 2u
3
+ u
2
+ 3u + 4)
2
(u
4
+ 5u
3
+ 7u
2
+ 2u + 1)
· (u
6
+ u
5
+ 3u
4
− u
3
+ 16u + 16)
· (u
8
+ 2u
7
+ 7u
6
+ 7u
5
+ 23u
4
+ 28u
3
+ 37u
2
+ 19u + 4)
c
2
, c
5
, c
7
c
10
u
2
(u
2
+ 1)
3
(u
3
− u
2
+ u + 1)
2
(u
4
− 2u
3
+ 3u
2
− 3u + 2)
2
· (u
4
+ u
3
+ u
2
+ 1)
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
6
+ u
5
+ u
4
+ 3u
3
+ 4u
2
+ 4u + 4)(u
8
+ u
6
− 3u
5
+ 3u
4
+ 5u
2
− u + 2)
c
3
, c
4
, c
6
c
8
, c
11
u
2
(u
2
+ 1)
3
(u
3
− u
2
+ 3u − 1)
2
(u
4
− 2u
3
+ 3u
2
− 3u + 2)
2
· (u
4
+ u
3
+ u
2
+ 1)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
5
· (u
6
+ u
5
+ 3u
4
+ 5u
3
+ 4u
2
+ 4u + 4)
· (u
8
+ 5u
6
− 3u
5
+ 7u
4
− 8u
3
+ 5u
2
− u + 2)
c
12
u
2
(u − 1)
6
(u
3
− 5u
2
+ 7u + 1)
2
(u
4
− 5u
3
+ 7u
2
− 2u + 1)
5
· (u
4
− 2u
3
+ u
2
− 3u + 4)
2
(u
4
− u
3
+ 3u
2
− 2u + 1)
· (u
6
− 5u
5
+ 7u
4
+ u
3
− 16u + 16)
· (u
8
− 10u
7
+ 39u
6
− 71u
5
+ 55u
4
− 20u
3
+ 37u
2
− 19u + 4)
66
XVIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
9
y
2
(y −1)
6
(y
3
+ 5y
2
+ 11y −1)
2
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)
· (y
4
− 2y
3
− 3y
2
− y + 16)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
5
· (y
6
+ 5y
5
+ 11y
4
− y
3
+ 128y
2
− 256y + 256)
· (y
8
+ 10y
7
+ 67y
6
+ 235y
5
+ 587y
4
+ 708y
3
+ 489y
2
− 65y + 16)
c
2
, c
5
, c
7
c
10
y
2
(y + 1)
6
(y
3
+ y
2
+ 3y −1)
2
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
5
· (y
4
+ 2y
3
+ y
2
+ 3y + 4)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
6
+ y
5
+ 3y
4
− y
3
+ 16y + 16)
· (y
8
+ 2y
7
+ 7y
6
+ 7y
5
+ 23y
4
+ 28y
3
+ 37y
2
+ 19y + 4)
c
3
, c
4
, c
6
c
8
, c
11
y
2
(y + 1)
6
(y
3
+ 5y
2
+ 7y −1)
2
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
· (y
4
+ 2y
3
+ y
2
+ 3y + 4)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
5
· (y
6
+ 5y
5
+ 7y
4
− y
3
+ 16y + 16)
· (y
8
+ 10y
7
+ 39y
6
+ 71y
5
+ 55y
4
+ 20y
3
+ 37y
2
+ 19y + 4)
c
12
y
2
(y −1)
6
(y
3
− 11y
2
+ 59y −1)
2
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)
5
· (y
4
− 2y
3
− 3y
2
− y + 16)
2
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
6
− 11y
5
+ 59y
4
− 129y
3
+ 256y
2
− 256y + 256)
· (y
8
− 22y
7
+ ··· − 65y + 16)
67
