12n
0553
(K12n
0553
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 12 2 4 3 5 9 6 11
Solving Sequence
3,6
2
1,12 5,9
8 4 7 11 10
c
2
c
1
c
5
c
8
c
3
c
7
c
11
c
10
c
4
, c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
6
− 4u
4
− u
3
− 3u
2
+ 2d − u, u
7
− u
6
+ 4u
5
− 3u
4
+ 2u
3
− 4u
2
+ 4c − 3u − 4, b − u,
− u
6
− 4u
4
− 3u
3
− 3u
2
+ 2a − 7u − 2, u
8
+ 5u
6
+ 3u
5
+ 7u
4
+ 8u
3
+ 5u
2
+ u + 2i
I
u
2
= h−u
4
− u
2
+ d + u + 1, −u
5
− u
4
− u
3
− u
2
+ 4c + 2u, u
5
− u
4
+ 3u
3
− 3u
2
+ 2b + 4u − 2,
u
5
− u
4
+ 3u
3
− u
2
+ 4a + 4u, u
6
− u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4i
I
u
3
= hcu + d − 1, c
2
+ 3u
2
+ c + 2u + 9, b − u, a + 1, u
3
+ u
2
+ 3u + 1i
I
u
4
= h−u
2
+ d, c − 1, b − u, −u
3
+ a − 2u − 1, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
5
= h−u
2
+ d, c − 1, u
2
+ b, −u
3
+ 2u
2
+ a − u, u
4
− u
3
+ u
2
+ 1i
I
u
6
= h−u
2
+ d, c − 1, u
3
+ u
2
+ b + 2u + 1, u
3
+ 2a + u − 1, u
4
+ 2u
3
+ 3u
2
+ 3u + 2i
I
u
7
= h−u
3
+ u
2
+ d − 2u + 1, −u
3
+ c − 2u, b − u, −u
3
+ a − 2u − 1, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
8
= h−u
3
+ u
2
+ d − 2u + 1, −u
3
+ c − 2u, −u
3
+ u
2
+ b − 2u + 1, −2u
3
+ 2u
2
+ a − 5u + 3,
u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
9
= h−u
3
+ u
2
+ d − 2u + 1, −u
3
+ c − 2u, u
3
− u
2
+ b + 3u − 1, a + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
10
= hu
3
+ d + 1, u
3
+ 2c + u + 1, u
3
+ u
2
+ b + 2u + 1, u
3
+ 2a + u − 1, u
4
+ 2u
3
+ 3u
2
+ 3u + 2i
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 + 5u − 4, u
3
+ c + 2u + 1, u
3
− u
2
+ b + 3u − 1, a + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
I
u
12
= hd − u + 1, c − 1, b, a − u, u
2
+ 1i
I
u
13
= hd + 1, c, b + u, a − 1, u
2
+ 1i
I
u
14
= hd + u + 1, c − 1, b + u, a − 1, u
2
+ 1i
I
u
15
= hda + a + u + 1, c − 1, b + u, u
2
+ 1i
I
v
1
= ha, d − 1, −av + c − v −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
= h−u
6
− 4u
4
+ · · · + 2d − u, u
7
− u
6
+ · · · + 4c − 4, b − u, −u
6
−
4u
4
+ · · · + 2a − 2, u
8
+ 5u
6
+ · · · + u + 2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
−
1
4
u
7
+
1
4
u
6
+ ··· +
3
4
u + 1
1
2
u
6
+ 2u
4
+
1
2
u
3
+
3
2
u
2
+
1
2
u
a
5
=
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
9
=
1
2
u
6
+ 2u
4
+ ··· +
7
2
u + 1
u
a
8
=
1
2
u
6
+ 2u
4
+ ··· +
5
2
u + 1
u
a
4
=
−
1
2
u
7
− 2u
5
+ ··· − u + 1
−u
2
a
7
=
u
u
3
+ u
a
11
=
−
1
4
u
7
+
1
4
u
6
+ ··· +
3
4
u + 1
−
1
4
u
7
+
1
4
u
6
+ ··· +
1
4
u +
1
2
a
10
=
1
4
u
7
+
1
4
u
6
+ ··· +
11
4
u + 1
−
1
2
u
6
− u
4
+ ··· +
1
2
u
2
+
1
2
u
(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
u
8
+ 10u
7
+ 39u
6
+ 71u
5
+ 55u
4
+ 20u
3
+ 37u
2
+ 19u + 4
c
2
, c
3
, c
6
c
7
, c
8
u
8
+ 5u
6
+ 3u
5
+ 7u
4
+ 8u
3
+ 5u
2
+ u + 2
c
4
, c
5
, c
9
c
11
u
8
+ u
6
+ 3u
5
+ 3u
4
+ 5u
2
+ u + 2
c
10
, c
12
u
8
− 2u
7
+ 7u
6
− 7u
5
+ 23u
4
− 28u
3
+ 37u
2
− 19u + 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 22y
7
+ ··· − 65y + 16
c
2
, c
3
, c
6
c
7
, c
8
y
8
+ 10y
7
+ 39y
6
+ 71y
5
+ 55y
4
+ 20y
3
+ 37y
2
+ 19y + 4
c
4
, c
5
, c
9
c
11
y
8
+ 2y
7
+ 7y
6
+ 7y
5
+ 23y
4
+ 28y
3
+ 37y
2
+ 19y + 4
c
10
, c
12
y
8
+ 10y
7
+ 67y
6
+ 235y
5
+ 587y
4
+ 708y
3
+ 489y
2
− 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 = −1.89723 + 0.52453I
b = −0.758942 + 0.438317I
c = −0.054172 − 1.264670I
d = −0.62069 − 1.46361I
1.16700 − 5.71173I 4.09501 + 8.31811I
u = −0.758942 − 0.438317I
a = −1.89723 − 0.52453I
b = −0.758942 − 0.438317I
c = −0.054172 + 1.264670I
d = −0.62069 + 1.46361I
1.16700 + 5.71173I 4.09501 − 8.31811I
u = 0.179745 + 0.559373I
a = 1.04641 + 1.87221I
b = 0.179745 + 0.559373I
c = 0.902346 + 0.601652I
d = −0.329909 + 0.314903I
0.095264 + 1.253510I 1.27264 − 6.48719I
u = 0.179745 − 0.559373I
a = 1.04641 − 1.87221I
b = 0.179745 − 0.559373I
c = 0.902346 − 0.601652I
d = −0.329909 − 0.314903I
0.095264 − 1.253510I 1.27264 + 6.48719I
u = 0.41760 + 1.54917I
a = 1.357530 + 0.013373I
b = 0.41760 + 1.54917I
c = −0.647833 − 0.660328I
d = 2.03855 − 1.72671I
−11.6096 + 14.8655I −0.93475 − 7.40876I
u = 0.41760 − 1.54917I
a = 1.357530 − 0.013373I
b = 0.41760 − 1.54917I
c = −0.647833 + 0.660328I
d = 2.03855 + 1.72671I
−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 = 0.493297 − 0.013672I
b = 0.16160 + 1.70407I
c = −0.450341 + 0.645947I
d = 0.412046 − 0.311025I
−15.9716 + 0.6364I −4.43290 + 0.86524I
u = 0.16160 − 1.70407I
a = 0.493297 + 0.013672I
b = 0.16160 − 1.70407I
c = −0.450341 − 0.645947I
d = 0.412046 + 0.311025I
−15.9716 − 0.6364I −4.43290 − 0.86524I
7
II. I
u
2
= h−u
4
− u
2
+ d + u + 1, −u
5
− u
4
+ · · · + 4c + 2u, u
5
− u
4
+ · · · +
2b − 2, u
5
− u
4
+ · · · + 4a + 4u, u
6
− u
5
+ · · · − 4u + 4i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
1
4
u
5
+
1
4
u
4
+ ··· +
1
4
u
2
−
1
2
u
u
4
+ u
2
− u − 1
a
5
=
−
1
4
u
5
+
1
4
u
4
+ ··· +
1
4
u
2
− u
−
1
2
u
5
−
1
2
u
4
+ ··· + u − 1
a
9
=
−
1
4
u
5
+
1
4
u
4
+ ··· +
1
4
u
2
− u
−
1
2
u
5
+
1
2
u
4
+ ··· − 2u + 1
a
8
=
1
4
u
5
−
1
4
u
4
+ ··· + u − 1
−
1
2
u
5
+
1
2
u
4
+ ··· − 2u + 1
a
4
=
−
1
4
u
5
−
1
4
u
4
+ ··· −
1
4
u
2
+
1
2
u
−u
3
+ u
2
− u + 3
a
7
=
u
u
3
+ u
a
11
=
1
4
u
5
+
1
4
u
4
+ ··· +
1
4
u
2
−
1
2
u
u
4
− u
3
+ 2u
2
− 2u + 1
a
10
=
−
1
2
u
5
− u
3
+ u
2
−
1
2
u + 1
−
1
2
u
5
+
1
2
u
4
+ ··· − u + 2
(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
u
6
+ 5u
5
+ 7u
4
− u
3
+ 16u + 16
c
2
, c
3
, c
6
c
7
, c
8
u
6
− u
5
+ 3u
4
− 5u
3
+ 4u
2
− 4u + 4
c
4
, c
5
, c
9
c
11
(u
3
+ u
2
+ u − 1)
2
c
10
, c
12
(u
3
− u
2
+ 3u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
6
− 11y
5
+ 59y
4
− 129y
3
+ 256y
2
− 256y + 256
c
2
, c
3
, c
6
c
7
, c
8
y
6
+ 5y
5
+ 7y
4
− y
3
+ 16y + 16
c
4
, c
5
, c
9
c
11
(y
3
+ y
2
+ 3y −1)
2
c
10
, c
12
(y
3
+ 5y
2
+ 11y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.047560 + 0.418092I
a = −1.09915 − 1.20459I
b = −0.27572 − 1.53323I
c = −0.269083 + 1.171910I
d = −1.04111 + 2.07415I
−5.31927 + 9.53188I 0.63107 − 6.69086I
u = 1.047560 − 0.418092I
a = −1.09915 + 1.20459I
b = −0.27572 + 1.53323I
c = −0.269083 − 1.171910I
d = −1.04111 − 2.07415I
−5.31927 − 9.53188I 0.63107 + 6.69086I
u = −0.271845 + 1.105310I
a = −0.062023 − 0.252181I
b = −0.271845 − 1.105310I
c = −0.114078 − 0.463834I
d = −0.919643 − 0.326726I
−4.16586 −7.26213 + 0.I
u = −0.271845 − 1.105310I
a = −0.062023 + 0.252181I
b = −0.271845 + 1.105310I
c = −0.114078 + 0.463834I
d = −0.919643 + 0.326726I
−4.16586 −7.26213 + 0.I
u = −0.27572 + 1.53323I
a = 1.161170 + 0.213694I
b = 1.047560 − 0.418092I
c = −0.616840 + 0.614334I
d = 1.46075 + 1.46786I
−5.31927 − 9.53188I 0.63107 + 6.69086I
u = −0.27572 − 1.53323I
a = 1.161170 − 0.213694I
b = 1.047560 + 0.418092I
c = −0.616840 − 0.614334I
d = 1.46075 − 1.46786I
−5.31927 + 9.53188I 0.63107 − 6.69086I
11
III. I
u
3
= hcu + d − 1, c
2
+ 3 u
2
+ c + 2u + 9, b − u, a + 1, u
3
+ u
2
+ 3 u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
c
−cu + 1
a
5
=
−cu + u
2
+ 3
u
2
c + cu + u
2
+ u + 1
a
9
=
−1
u
a
8
=
−u − 1
u
a
4
=
u
2
+ u + 1
−u
2
a
7
=
u
−u
2
− 2u − 1
a
11
=
c
−u
2
c − cu + 1
a
10
=
u
2
c + c − 1
2cu + c + u + 1
(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
(u
3
+ 5u
2
+ 7u − 1)
2
c
2
, c
3
, c
6
c
7
, c
8
(u
3
+ u
2
+ 3u + 1)
2
c
4
, c
5
, c
9
c
11
u
6
− u
5
+ u
4
− 3u
3
+ 4u
2
− 4u + 4
c
10
, c
12
u
6
− u
5
+ 3u
4
+ u
3
− 16u + 16
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
− 11y
2
+ 59y −1)
2
c
2
, c
3
, c
6
c
7
, c
8
(y
3
+ 5y
2
+ 7y −1)
2
c
4
, c
5
, c
9
c
11
y
6
+ y
5
+ 3y
4
− y
3
+ 16y + 16
c
10
, c
12
y
6
+ 5y
5
+ 11y
4
− y
3
+ 128y
2
− 256y + 256
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.361103
a = −1.00000
b = −0.361103
c = −0.50000 + 2.90155I
d = 0.819448 + 1.047760I
3.88548 12.6160
u = −0.361103
a = −1.00000
b = −0.361103
c = −0.50000 − 2.90155I
d = 0.819448 − 1.047760I
3.88548 12.6160
u = −0.31945 + 1.63317I
a = −1.00000
b = −0.31945 + 1.63317I
c = −0.604185 + 0.652966I
d = 1.87340 + 1.19533I
−14.2797 − 7.9406I −3.30788 + 3.53846I
u = −0.31945 + 1.63317I
a = −1.00000
b = −0.31945 + 1.63317I
c = −0.395815 − 0.652966I
d = −0.192847 + 0.437845I
−14.2797 − 7.9406I −3.30788 + 3.53846I
u = −0.31945 − 1.63317I
a = −1.00000
b = −0.31945 − 1.63317I
c = −0.604185 − 0.652966I
d = 1.87340 − 1.19533I
−14.2797 + 7.9406I −3.30788 − 3.53846I
u = −0.31945 − 1.63317I
a = −1.00000
b = −0.31945 − 1.63317I
c = −0.395815 + 0.652966I
d = −0.192847 − 0.437845I
−14.2797 + 7.9406I −3.30788 − 3.53846I
15
IV. I
u
4
= h−u
2
+ d, c − 1, b − u, −u
3
+ a − 2u − 1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
3
+ 2u + 1
u
a
8
=
u
3
+ u + 1
u
a
4
=
−u
3
+ 2u
2
− 3u + 2
−u
2
a
7
=
u
u
3
+ u
a
11
=
1
0
a
10
=
u
3
− u
2
+ 3u
u
2
(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
5
c
6
, c
7
, c
8
c
10
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
4
, c
9
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
5
c
6
, c
7
, c
8
c
10
, c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
4
, c
9
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 = 1.54742 + 1.12087I
b = 0.395123 + 0.506844I
c = 1.00000
d = −0.100768 + 0.400532I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = 1.54742 − 1.12087I
b = 0.395123 − 0.506844I
c = 1.00000
d = −0.100768 − 0.400532I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.10488 + 1.55249I
a = 0.452576 − 0.585652I
b = 0.10488 + 1.55249I
c = 1.00000
d = −2.39923 + 0.32564I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = 0.452576 + 0.585652I
b = 0.10488 − 1.55249I
c = 1.00000
d = −2.39923 − 0.32564I
−6.79074 − 3.16396I −1.82674 + 2.56480I
19
V. I
u
5
= h−u
2
+ d, c − 1, u
2
+ b, −u
3
+ 2u
2
+ a − u, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
3
− 2u
2
+ u
−u
2
a
8
=
u
3
− u
2
+ u
−u
2
a
4
=
−u + 1
−u
3
+ u
2
+ 1
a
7
=
u
u
3
+ u
a
11
=
1
0
a
10
=
u
3
− u
2
+ u
u
3
− u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
− 4u + 2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
4
, c
5
c
6
, c
9
, c
11
u
4
− u
3
+ u
2
+ 1
c
3
, c
7
, c
8
c
10
, 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
7
c
8
, c
10
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
4
, c
5
c
6
, c
9
, 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 = −0.351808 + 0.720342I
a = 0.94255 + 1.62772I
b = 0.395123 + 0.506844I
c = 1.00000
d = −0.395123 − 0.506844I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = −0.351808 − 0.720342I
a = 0.94255 − 1.62772I
b = 0.395123 − 0.506844I
c = 1.00000
d = −0.395123 + 0.506844I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.851808 + 0.911292I
a = −0.442547 − 0.966840I
b = 0.10488 − 1.55249I
c = 1.00000
d = −0.10488 + 1.55249I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = 0.851808 − 0.911292I
a = −0.442547 + 0.966840I
b = 0.10488 + 1.55249I
c = 1.00000
d = −0.10488 − 1.55249I
−6.79074 + 3.16396I −1.82674 − 2.56480I
23
VI.
I
u
6
= h−u
2
+d, c−1, u
3
+u
2
+b+2u+1, u
3
+2a+u−1, u
4
+2u
3
+3u
2
+3u+2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
−
1
2
u
3
−
1
2
u +
1
2
−u
3
− u
2
− 2u − 1
a
8
=
1
2
u
3
+ u
2
+
3
2
u +
3
2
−u
3
− u
2
− 2u − 1
a
4
=
1
2
u
3
+
1
2
u +
1
2
u
3
+ 2u
2
+ 2u + 3
a
7
=
u
u
3
+ u
a
11
=
1
0
a
10
=
−
3
2
u
3
− 2u
2
−
5
2
u −
3
2
−u
3
− 2u
2
− 2u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 2
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
5
, c
6
c
11
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
3
, c
7
, c
8
c
10
u
4
− u
3
+ 3u
2
− 2u + 1
c
4
, c
9
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
5
, c
6
c
11
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
3
, c
7
, c
8
c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
4
, c
9
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 = −0.956685 + 0.641200I
a = 0.826150 − 1.069070I
b = 0.10488 − 1.55249I
c = 1.00000
d = 0.504108 − 1.226850I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = −0.956685 − 0.641200I
a = 0.826150 + 1.069070I
b = 0.10488 + 1.55249I
c = 1.00000
d = 0.504108 + 1.226850I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = −0.043315 + 1.227190I
a = 0.423850 + 0.307015I
b = 0.395123 − 0.506844I
c = 1.00000
d = −1.50411 − 0.10631I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = −0.043315 − 1.227190I
a = 0.423850 − 0.307015I
b = 0.395123 + 0.506844I
c = 1.00000
d = −1.50411 + 0.10631I
0.21101 + 1.41510I 1.82674 − 4.90874I
27
VII. I
u
7
=
h−u
3
+u
2
+d−2u +1, −u
3
+c−2u, b−u, −u
3
+a−2u −1, u
4
−u
3
+3u
2
−2u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
u
3
+ 2u
u
3
− u
2
+ 2u − 1
a
5
=
−1
0
a
9
=
u
3
+ 2u + 1
u
a
8
=
u
3
+ u + 1
u
a
4
=
−u
3
+ 2u
2
− 3u + 2
−u
2
a
7
=
u
u
3
+ u
a
11
=
u
3
+ 2u
u
3
+ u
a
10
=
u
3
+ u + 1
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 12u + 6
28
(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
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
5
, c
11
u
4
− u
3
+ u
2
+ 1
c
10
u
4
− 5u
3
+ 7u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
5
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 1.54742 + 1.12087I
b = 0.395123 + 0.506844I
c = 0.547424 + 1.120870I
d = −0.351808 + 0.720342I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = 1.54742 − 1.12087I
b = 0.395123 − 0.506844I
c = 0.547424 − 1.120870I
d = −0.351808 − 0.720342I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.10488 + 1.55249I
a = 0.452576 − 0.585652I
b = 0.10488 + 1.55249I
c = −0.547424 − 0.585652I
d = 0.851808 − 0.911292I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = 0.452576 + 0.585652I
b = 0.10488 − 1.55249I
c = −0.547424 + 0.585652I
d = 0.851808 + 0.911292I
−6.79074 − 3.16396I −1.82674 + 2.56480I
31
VIII. I
u
8
= h−u
3
+ u
2
+ d − 2u + 1, −u
3
+ c − 2u, −u
3
+ u
2
+ b − 2u +
1, −2u
3
+ 2u
2
+ a − 5u + 3, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
u
3
+ 2u
u
3
− u
2
+ 2u − 1
a
5
=
−1
0
a
9
=
2u
3
− 2u
2
+ 5u − 3
u
3
− u
2
+ 2u − 1
a
8
=
u
3
− u
2
+ 3u − 2
u
3
− u
2
+ 2u − 1
a
4
=
u
3
+ 2u + 1
u
a
7
=
u
u
3
+ u
a
11
=
u
3
+ 2u
u
3
+ u
a
10
=
u
3
− u
2
+ 3u − 2
u
3
− u
2
+ 2u − 1
(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
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
c
2
, c
6
, c
10
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
3
, c
4
, c
5
c
7
, c
8
, c
9
c
11
u
4
− u
3
+ u
2
+ 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
6
, c
10
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
4
, c
5
c
7
, c
8
, c
9
c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −1.30849 + 1.94753I
b = −0.351808 + 0.720342I
c = 0.547424 + 1.120870I
d = −0.351808 + 0.720342I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = −1.30849 − 1.94753I
b = −0.351808 − 0.720342I
c = 0.547424 − 1.120870I
d = −0.351808 − 0.720342I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.10488 + 1.55249I
a = 0.808493 − 0.270093I
b = 0.851808 − 0.911292I
c = −0.547424 − 0.585652I
d = 0.851808 − 0.911292I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = 0.808493 + 0.270093I
b = 0.851808 + 0.911292I
c = −0.547424 + 0.585652I
d = 0.851808 + 0.911292I
−6.79074 − 3.16396I −1.82674 + 2.56480I
35
IX. I
u
9
= h−u
3
+ u
2
+ d − 2u + 1, −u
3
+ c − 2u, u
3
− u
2
+ b + 3u − 1, a +
1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
u
3
+ 2u
u
3
− u
2
+ 2u − 1
a
5
=
−1
0
a
9
=
−1
−u
3
+ u
2
− 3u + 1
a
8
=
u
3
− u
2
+ 3u − 2
−u
3
+ u
2
− 3u + 1
a
4
=
−u
3
− 2u
u
2
− u + 2
a
7
=
u
u
3
+ u
a
11
=
u
3
+ 2u
u
3
+ u
a
10
=
u
3
− u
2
+ 3u − 2
−u
3
+ u
2
− 3u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 12u + 6
36
(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
6
, c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
5
, c
11
u
4
− u
3
+ u
2
+ 1
c
10
u
4
− 2u
3
+ u
2
− 3u + 4
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
6
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
4
, c
7
c
8
, c
9
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
5
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
10
y
4
− 2y
3
− 3y
2
− y + 16
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −1.00000
b = −0.043315 − 1.227190I
c = 0.547424 + 1.120870I
d = −0.351808 + 0.720342I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = −1.00000
b = −0.043315 + 1.227190I
c = 0.547424 − 1.120870I
d = −0.351808 − 0.720342I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.10488 + 1.55249I
a = −1.00000
b = −0.956685 − 0.641200I
c = −0.547424 − 0.585652I
d = 0.851808 − 0.911292I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = −1.00000
b = −0.956685 + 0.641200I
c = −0.547424 + 0.585652I
d = 0.851808 + 0.911292I
−6.79074 − 3.16396I −1.82674 + 2.56480I
39
X. I
u
10
= hu
3
+ d + 1, u
3
+ 2c + u + 1, u
3
+ u
2
+ b + 2u + 1, u
3
+ 2a + u −
1, u
4
+ 2u
3
+ 3u
2
+ 3u + 2i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
−
1
2
u
3
−
1
2
u −
1
2
−u
3
− 1
a
5
=
−
1
2
u
3
−
1
2
u +
1
2
−2u
3
− 2u
2
− 2u − 1
a
9
=
−
1
2
u
3
−
1
2
u +
1
2
−u
3
− u
2
− 2u − 1
a
8
=
1
2
u
3
+ u
2
+
3
2
u +
3
2
−u
3
− u
2
− 2u − 1
a
4
=
1
2
u
3
+
1
2
u +
1
2
u
3
+ 2u
2
+ 2u + 3
a
7
=
u
u
3
+ u
a
11
=
−
1
2
u
3
−
1
2
u −
1
2
2u
2
+ 2u + 1
a
10
=
1
2
u
3
+ u
2
+
3
2
u +
3
2
u
3
+ 3u
2
+ 3u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 2
40
(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
4
, c
6
c
9
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
3
, c
7
, c
8
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
c
5
, c
11
u
4
− u
3
+ u
2
+ 1
c
10
u
4
− 2u
3
+ u
2
− 3u + 4
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
4
− 2y
3
− 3y
2
− y + 16
c
2
, c
4
, c
6
c
9
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
3
, c
7
, c
8
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
5
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = −0.956685 + 0.641200I
a = 0.826150 − 1.069070I
b = 0.10488 − 1.55249I
c = −0.173850 − 1.069070I
d = −1.30438 − 1.49694I
−6.79074 − 3.16396I −1.82674 + 2.56480I
u = −0.956685 − 0.641200I
a = 0.826150 + 1.069070I
b = 0.10488 + 1.55249I
c = −0.173850 + 1.069070I
d = −1.30438 + 1.49694I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = −0.043315 + 1.227190I
a = 0.423850 + 0.307015I
b = 0.395123 − 0.506844I
c = −0.576150 + 0.307015I
d = −1.19562 + 1.84122I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = −0.043315 − 1.227190I
a = 0.423850 − 0.307015I
b = 0.395123 + 0.506844I
c = −0.576150 − 0.307015I
d = −1.19562 − 1.84122I
0.21101 + 1.41510I 1.82674 − 4.90874I
43
XI. I
u
11
= h2u
3
− 2u
2
+ d + 5u − 4, u
3
+ c + 2u + 1, u
3
− u
2
+ b + 3u − 1, a +
1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
12
=
−u
3
− 2u − 1
−2u
3
+ 2u
2
− 5u + 4
a
5
=
2u
3
− 2u
2
+ 5u − 3
−2u
3
− 4u − 1
a
9
=
−1
−u
3
+ u
2
− 3u + 1
a
8
=
u
3
− u
2
+ 3u − 2
−u
3
+ u
2
− 3u + 1
a
4
=
−u
3
− 2u
u
2
− u + 2
a
7
=
u
u
3
+ u
a
11
=
−u
3
− 2u − 1
−2u
3
+ 2u
2
− 4u + 3
a
10
=
−u
3
− 3u − 1
−2u
3
+ 2u
2
− 5u + 4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 12u + 6
44
(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
6
, c
10
u
4
− u
3
+ 3u
2
− 2u + 1
c
3
, c
5
, c
7
c
8
, c
11
u
4
+ 2u
3
+ 3u
2
+ 3u + 2
c
4
, c
9
u
4
− u
3
+ u
2
+ 1
c
12
u
4
− 2u
3
+ u
2
− 3u + 4
45
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
6
, c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
5
, c
7
c
8
, c
11
y
4
+ 2y
3
+ y
2
+ 3y + 4
c
4
, c
9
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
12
y
4
− 2y
3
− 3y
2
− y + 16
46
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −1.00000
b = −0.043315 − 1.227190I
c = −1.54742 − 1.12087I
d = 2.30849 − 1.94753I
0.21101 + 1.41510I 1.82674 − 4.90874I
u = 0.395123 − 0.506844I
a = −1.00000
b = −0.043315 + 1.227190I
c = −1.54742 + 1.12087I
d = 2.30849 + 1.94753I
0.21101 − 1.41510I 1.82674 + 4.90874I
u = 0.10488 + 1.55249I
a = −1.00000
b = −0.956685 − 0.641200I
c = −0.452576 + 0.585652I
d = 0.191507 + 0.270093I
−6.79074 + 3.16396I −1.82674 − 2.56480I
u = 0.10488 − 1.55249I
a = −1.00000
b = −0.956685 + 0.641200I
c = −0.452576 − 0.585652I
d = 0.191507 − 0.270093I
−6.79074 − 3.16396I −1.82674 + 2.56480I
47
XII. I
u
12
= hd − u + 1, c − 1, b, a − u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−1
a
1
=
0
−1
a
12
=
1
u − 1
a
5
=
u
−1
a
9
=
u
0
a
8
=
u
0
a
4
=
1
0
a
7
=
u
0
a
11
=
1
u
a
10
=
u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
48
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
12
(u − 1)
2
c
2
, c
4
, c
5
c
6
, c
9
, c
11
u
2
+ 1
c
3
, c
7
, c
8
u
2
49
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
, c
12
(y −1)
2
c
2
, c
4
, c
5
c
6
, c
9
, c
11
(y + 1)
2
c
3
, c
7
, c
8
y
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 = 1.00000
d = −1.00000 + 1.00000I
1.64493 8.00000
u = − 1.000000I
a = − 1.000000I
b = 0
c = 1.00000
d = −1.00000 − 1.00000I
1.64493 8.00000
51
XIII. I
u
13
= hd + 1, c, b + u, a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−1
a
1
=
0
−1
a
12
=
0
−1
a
5
=
0
u
a
9
=
1
−u
a
8
=
u + 1
−u
a
4
=
u
1
a
7
=
u
0
a
11
=
0
−1
a
10
=
1
−u − 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
10
(u − 1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
u
2
+ 1
c
5
, c
11
, c
12
u
2
53
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
2
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
(y + 1)
2
c
5
, c
11
, c
12
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 = −1.00000
−1.64493 −4.00000
u = − 1.000000I
a = 1.00000
b = 1.000000I
c = 0
d = −1.00000
−1.64493 −4.00000
55
XIV. I
u
14
= hd + u + 1, c − 1, b + u, a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−1
a
1
=
0
−1
a
12
=
1
−u − 1
a
5
=
u
1
a
9
=
1
−u
a
8
=
u + 1
−u
a
4
=
u
1
a
7
=
u
0
a
11
=
1
−u
a
10
=
1
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
56
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
(u − 1)
2
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
11
u
2
+ 1
c
4
, c
9
, c
10
u
2
57
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
(y −1)
2
c
2
, c
3
, c
5
c
6
, c
7
, c
8
c
11
(y + 1)
2
c
4
, c
9
, c
10
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 = 1.00000
d = −1.00000 − 1.00000I
−1.64493 −4.00000
u = − 1.000000I
a = 1.00000
b = 1.000000I
c = 1.00000
d = −1.00000 + 1.00000I
−1.64493 −4.00000
59
XV. I
u
15
= hda + a + u + 1, c − 1, b + u, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−1
a
1
=
0
−1
a
12
=
1
d
a
5
=
u
du + u
a
9
=
a
−u
a
8
=
a + u
−u
a
4
=
au
1
a
7
=
u
0
a
11
=
1
d + 1
a
10
=
a + 1
d − u + 1
(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 − 1, −av + c − v − 1, b + v, v
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
v
0
a
2
=
1
0
a
1
=
1
0
a
12
=
v + 1
1
a
5
=
1
−v
a
9
=
0
−v
a
8
=
v
−v
a
4
=
0
1
a
7
=
v
0
a
11
=
v
1
a
10
=
v
−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
2
, c
6
u
2
c
3
, c
4
, c
5
c
7
, c
8
, c
9
c
11
u
2
+ 1
c
10
, c
12
(u − 1)
2
63
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
2
c
3
, c
4
, c
5
c
7
, c
8
, c
9
c
11
(y + 1)
2
c
10
, c
12
(y −1)
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 + 1.00000I
d = 1.00000
1.64493 8.00000
v = − 1.000000I
a = 0
b = 1.000000I
c = 1.00000 − 1.00000I
d = 1.00000
1.64493 8.00000
65
XVII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
6
(u
3
+ 5u
2
+ 7u − 1)
2
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
4
+ 2u
3
+ u
2
+ 3u + 4)
2
(u
4
+ 5u
3
+ 7u
2
+ 2u + 1)
5
· (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)
c
2
, c
3
, c
6
c
7
, c
8
u
2
(u
2
+ 1)
3
(u
3
+ u
2
+ 3u + 1)
2
(u
4
− u
3
+ u
2
+ 1)
· (u
4
− u
3
+ 3u
2
− 2u + 1)
5
(u
4
+ 2u
3
+ 3u
2
+ 3u + 2)
2
· (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
4
, c
5
, c
9
c
11
u
2
(u
2
+ 1)
3
(u
3
+ u
2
+ u − 1)
2
(u
4
− u
3
+ u
2
+ 1)
5
· (u
4
− u
3
+ 3u
2
− 2u + 1)(u
4
+ 2u
3
+ 3u
2
+ 3u + 2)
2
· (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
10
, c
12
u
2
(u − 1)
6
(u
3
− u
2
+ 3u + 1)
2
(u
4
− 5u
3
+ 7u
2
− 2u + 1)
· (u
4
− 2u
3
+ u
2
− 3u + 4)
2
(u
4
− u
3
+ 3u
2
− 2u + 1)
5
· (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)
66
XVIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
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)
c
2
, c
3
, c
6
c
7
, c
8
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
4
, c
5
, c
9
c
11
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
10
, c
12
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)
67
