12n
0750
(K12n
0750
)
A knot diagram
1
Linearized knot diagam
4 6 8 9 2 11 3 12 5 6 8 9
Solving Sequence
8,11
12
4,9
5 1 3 7 6 2 10
c
11
c
8
c
4
c
12
c
3
c
7
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2u
5
− 10u
4
− 15u
3
+ 13u
2
+ 5b + 45u + 19, −7u
5
− 25u
4
− 20u
3
+ 43u
2
+ 15a + 85u + 24,
u
6
+ 4u
5
+ 5u
4
− 4u
3
− 16u
2
− 12u − 3i
I
u
2
= h−2u
2
+ b + u + 2, a − u, u
3
− u
2
+ 1i
I
u
3
= h−2u
2
a − u
2
+ b + a + u, a
2
+ au − u
2
+ u − 1, u
3
− u
2
+ 1i
I
u
4
= h2u
3
− u
2
+ 3b − 1, u
3
+ 4u
2
+ 3a + 9u + 4, u
4
+ 3u
3
+ 5u
2
+ u − 1i
I
u
5
= hu
2
+ b − 3, −3u
3
+ 4u
2
+ 5a + 7u − 10, u
4
− 3u
3
+ u
2
+ 5u − 5i
I
u
6
= h−3au + 2b + 6a + u, 4a
2
+ 2au − 6a − 5u + 3, u
2
− u + 2i
I
u
7
= hb
2
+ b − 1, a + 1, u + 1i
I
v
1
= ha, b + v −2, v
2
− 3v + 1i
I
v
2
= ha, b − 1, v −1i
* 9 irreducible components of dim
C
= 0, with total 32 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−2u
5
− 10u
4
+ · · · + 5b + 19, −7u
5
− 25u
4
+ · · · + 15a + 24, u
6
+
4u
5
+ 5u
4
− 4u
3
− 16u
2
− 12u − 3i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
7
15
u
5
+
5
3
u
4
+ ··· −
17
3
u −
8
5
2
5
u
5
+ 2u
4
+ 3u
3
−
13
5
u
2
− 9u −
19
5
a
9
=
−u
−u
3
+ u
a
5
=
13
15
u
5
+
8
3
u
4
+ ··· −
29
3
u −
17
5
7
5
u
5
+ 4u
4
+ 2u
3
−
38
5
u
2
− 11u −
19
5
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
7
15
u
5
+
5
3
u
4
+ ··· −
17
3
u −
8
5
3
5
u
5
+ 2u
4
+ 2u
3
−
17
5
u
2
− 8u −
16
5
a
7
=
−
4
15
u
5
−
2
3
u
4
+ ··· +
8
3
u +
6
5
−
1
5
u
5
− u
4
− u
3
+
9
5
u
2
+ 4u +
7
5
a
6
=
−
7
15
u
5
−
5
3
u
4
+ ··· +
20
3
u +
13
5
−
1
5
u
5
− u
4
− u
3
+
9
5
u
2
+ 4u +
7
5
a
2
=
4
15
u
5
+
2
3
u
4
+ ··· −
8
3
u −
1
5
4
5
u
5
+ 2u
4
+ u
3
−
21
5
u
2
− 7u −
13
5
a
10
=
2
15
u
5
+
1
3
u
4
+ ··· −
1
3
u +
7
5
−
2
5
u
5
− u
4
+
8
5
u
2
+ 2u +
4
5
(ii) Obstruction class = −1
(iii) Cusp Shapes =
26
5
u
5
+ 18u
4
+ 16u
3
−
154
5
u
2
− 72u −
192
5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
u
6
− 2u
5
+ 5u
4
+ 2u
3
− 4u
2
− 2u − 1
c
2
, c
5
, c
8
c
11
, c
12
u
6
+ 4u
5
+ 5u
4
− 4u
3
− 16u
2
− 12u − 3
c
4
, c
9
u
6
+ 2u
5
− u
4
− 2u
3
− 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
y
6
+ 6y
5
+ 25y
4
− 54y
3
+ 14y
2
+ 4y + 1
c
2
, c
5
, c
8
c
11
, c
12
y
6
− 6y
5
+ 25y
4
− 86y
3
+ 130y
2
− 48y + 9
c
4
, c
9
y
6
− 6y
5
+ 9y
4
+ 6y
3
− 10y
2
− 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.510485 + 0.215723I
a = 0.602418 − 0.514537I
b = 0.055837 − 1.062600I
−0.807577 + 0.909082I −9.16175 − 7.66066I
u = −0.510485 − 0.215723I
a = 0.602418 + 0.514537I
b = 0.055837 + 1.062600I
−0.807577 − 0.909082I −9.16175 + 7.66066I
u = 1.52560
a = 0.702173
b = 1.21012
−11.8129 −22.6370
u = −1.70948
a = 0.469310
b = 0.240689
−9.43829 −7.45040
u = −1.39757 + 1.33871I
a = −1.188160 + 0.447062I
b = 3.21876 + 4.79537I
13.9006 + 10.5245I −7.79449 − 4.24029I
u = −1.39757 − 1.33871I
a = −1.188160 − 0.447062I
b = 3.21876 − 4.79537I
13.9006 − 10.5245I −7.79449 + 4.24029I
5
II. I
u
2
= h−2u
2
+ b + u + 2, a − u, u
3
− u
2
+ 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
u
2u
2
− u − 2
a
9
=
−u
−u
2
+ u + 1
a
5
=
−1
0
a
1
=
−u
2
+ 1
u
2
+ u + 1
a
3
=
u
u
2
− u − 1
a
7
=
u
2
− 1
−u
2
a
6
=
−1
−u
2
a
2
=
0
−u
a
10
=
−u
2
+ 1
−u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u − 12
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
3
− u
2
+ 2u − 1
c
2
, c
8
u
3
+ u
2
− 1
c
4
u
3
+ 3u
2
+ 2u − 1
c
5
, c
11
, c
12
u
3
− u
2
+ 1
c
7
, c
10
u
3
+ u
2
+ 2u + 1
c
9
u
3
− 3u
2
+ 2u + 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
y
3
+ 3y
2
+ 2y −1
c
2
, c
5
, c
8
c
11
, c
12
y
3
− y
2
+ 2y −1
c
4
, c
9
y
3
− 5y
2
+ 10y −1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.877439 + 0.744862I
b = −2.44728 + 1.86942I
6.04826 − 5.65624I −4.98049 + 5.95889I
u = 0.877439 − 0.744862I
a = 0.877439 − 0.744862I
b = −2.44728 − 1.86942I
6.04826 + 5.65624I −4.98049 − 5.95889I
u = −0.754878
a = −0.754878
b = −0.105442
−2.22691 −18.0390
9
III. I
u
3
= h−2u
2
a − u
2
+ b + a + u, a
2
+ au − u
2
+ u − 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
a
2u
2
a + u
2
− a − u
a
9
=
−u
−u
2
+ u + 1
a
5
=
u
2
a − au − u
1
a
1
=
−u
2
+ 1
u
2
+ u + 1
a
3
=
a
u
2
a + u
2
− a − u
a
7
=
−u
2
a + u − 1
au
a
6
=
−u
2
a + au + u − 1
au
a
2
=
−u
2
+ u
u
2
− a − u
a
10
=
−u
2
a + 2au − u
2
+ u
u
2
a − u
2
− a + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u − 18
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
u
6
+ u
5
+ 2u
4
− 4u
2
+ 2u − 1
c
2
, c
5
, c
8
c
11
, c
12
(u
3
− u
2
+ 1)
2
c
4
, c
9
u
6
+ 3u
5
− 4u
3
+ 6u
2
+ 14u + 5
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
y
6
+ 3y
5
− 4y
4
− 22y
3
+ 12y
2
+ 4y + 1
c
2
, c
5
, c
8
c
11
, c
12
(y
3
− y
2
+ 2y −1)
2
c
4
, c
9
y
6
− 9y
5
+ 36y
4
− 90y
3
+ 148y
2
− 136y + 25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −1.26420 − 0.91095I
b = 2.43950 − 2.22359I
4.40332 − 5.65624I −10.98049 + 5.95889I
u = 0.877439 + 0.744862I
a = 0.386757 + 0.166085I
b = −1.31694 + 1.47873I
4.40332 − 5.65624I −10.98049 + 5.95889I
u = 0.877439 − 0.744862I
a = −1.26420 + 0.91095I
b = 2.43950 + 2.22359I
4.40332 + 5.65624I −10.98049 − 5.95889I
u = 0.877439 − 0.744862I
a = 0.386757 − 0.166085I
b = −1.31694 − 1.47873I
4.40332 + 5.65624I −10.98049 − 5.95889I
u = −0.754878
a = −1.19329
b = 1.15804
−3.87184 −24.0390
u = −0.754878
a = 1.94816
b = 1.59684
−3.87184 −24.0390
13
IV. I
u
4
= h2u
3
− u
2
+ 3b − 1, u
3
+ 4u
2
+ 3a + 9u + 4, u
4
+ 3u
3
+ 5u
2
+ u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
−
1
3
u
3
−
4
3
u
2
− 3u −
4
3
−
2
3
u
3
+
1
3
u
2
+
1
3
a
9
=
−u
−u
3
+ u
a
5
=
−u
3
− 3u
2
− 4u − 1
4
3
u
3
+
4
3
u
2
+
1
3
a
1
=
−u
2
+ 1
3u
3
+ 7u
2
+ u − 1
a
3
=
−
1
3
u
3
−
4
3
u
2
− 3u −
4
3
−
1
3
u
3
−
1
3
u
2
+
2
3
a
7
=
1
3
u
3
+
1
3
u
2
+ 2u +
4
3
1
3
u
3
+
4
3
u
2
+ u −
2
3
a
6
=
2
3
u
3
+
5
3
u
2
+ 3u +
2
3
1
3
u
3
+
4
3
u
2
+ u −
2
3
a
2
=
−
1
3
u
3
−
4
3
u
2
− 2u −
1
3
1
3
u
3
+
4
3
u
2
+
1
3
a
10
=
u + 1
4
3
u
3
+
7
3
u
2
+ u −
2
3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
u
4
+ 2u
3
+ 8u
2
+ 7u + 1
c
2
, c
5
, c
8
c
11
, c
12
u
4
+ 3u
3
+ 5u
2
+ u − 1
c
4
, c
9
(u
2
− u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
y
4
+ 12y
3
+ 38y
2
− 33y + 1
c
2
, c
5
, c
8
c
11
, c
12
y
4
+ y
3
+ 17y
2
− 11y + 1
c
4
, c
9
(y
2
− 3y + 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713039
a = 0.248726
b = 0.744493
−1.31595 −7.00000
u = 0.331073
a = −2.48479
b = 0.345677
−1.31595 −7.00000
u = −1.30902 + 1.58825I
a = 1.118030 − 0.606658I
b = −5.04508 − 4.15810I
14.4754 −7.00000
u = −1.30902 − 1.58825I
a = 1.118030 + 0.606658I
b = −5.04508 + 4.15810I
14.4754 −7.00000
17
V. I
u
5
= hu
2
+ b − 3, −3u
3
+ 4u
2
+ 5a + 7u − 10, u
4
− 3u
3
+ u
2
+ 5u − 5i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
4
=
3
5
u
3
−
4
5
u
2
−
7
5
u + 2
−u
2
+ 3
a
9
=
−u
−u
3
+ u
a
5
=
−
7
5
u
3
+
11
5
u
2
+
8
5
u − 3
−2u
3
+ 4u
2
+ 2u − 7
a
1
=
−u
2
+ 1
−3u
3
+ 3u
2
+ 5u − 5
a
3
=
3
5
u
3
−
4
5
u
2
−
7
5
u + 2
−u
3
+ u
2
+ 2u − 2
a
7
=
−
1
5
u
3
+
3
5
u
2
+
4
5
u − 2
u
3
− 2u
2
− u + 4
a
6
=
4
5
u
3
−
7
5
u
2
−
1
5
u + 2
u
3
− 2u
2
− u + 4
a
2
=
−
1
5
u
3
−
2
5
u
2
+
4
5
u − 1
−u
3
+ 2u − 1
a
10
=
−
6
5
u
3
+
8
5
u
2
+
9
5
u − 3
−2u
3
+ 3u
2
+ 3u − 6
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
u
4
+ 2u
3
+ 2u
2
+ u − 1
c
2
, c
8
u
4
+ 3u
3
+ u
2
− 5u − 5
c
4
(u
2
− u − 1)
2
c
5
, c
11
, c
12
u
4
− 3u
3
+ u
2
+ 5u − 5
c
7
, c
10
u
4
− 2u
3
+ 2u
2
− u − 1
c
9
(u
2
+ u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
y
4
− 2y
2
− 5y + 1
c
2
, c
5
, c
8
c
11
, c
12
y
4
− 7y
3
+ 21y
2
− 35y + 25
c
4
, c
9
(y
2
− 3y + 1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.31651
a = 1.08748
b = 1.26680
−11.1856 −7.00000
u = 1.30902 + 0.72287I
a = −0.670820 − 0.523074I
b = 1.80902 − 1.89250I
4.60582 −7.00000
u = 1.30902 − 0.72287I
a = −0.670820 + 0.523074I
b = 1.80902 + 1.89250I
4.60582 −7.00000
u = 1.69848
a = 0.254159
b = 0.115171
−11.1856 −7.00000
21
VI. I
u
6
= h−3au + 2b + 6a + u, 4a
2
+ 2au − 6a − 5u + 3, u
2
− u + 2i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u − 2
a
4
=
a
3
2
au − 3a −
1
2
u
a
9
=
−u
2u + 2
a
5
=
−
1
2
au +
1
2
u + 1
3
2
au + a −
1
2
u − 4
a
1
=
−u + 3
5u − 6
a
3
=
a
1
2
au − a −
1
2
u
a
7
=
au + a +
1
2
u −
5
2
−
1
2
au − a −
1
2
u + 2
a
6
=
1
2
au −
1
2
−
1
2
au − a −
1
2
u + 2
a
2
=
−
1
2
u +
1
2
−
1
2
au + a +
3
2
u − 1
a
10
=
−a −
1
2
u +
1
2
−
1
2
au + 3a +
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
u
4
− 3u
3
+ 8u
2
− 13u + 11
c
2
, c
5
, c
8
c
11
, c
12
(u
2
− u + 2)
2
c
4
, c
9
(u
2
− u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
y
4
+ 7y
3
+ 8y
2
+ 7y + 121
c
2
, c
5
, c
8
c
11
, c
12
(y
2
+ 3y + 4)
2
c
4
, c
9
(y
2
− 3y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = −0.213525 − 1.070230I
b = 2.35410 + 1.32288I
6.57974 −7.00000
u = 0.50000 + 1.32288I
a = 1.46353 + 0.40879I
b = −4.35410 + 1.32288I
6.57974 −7.00000
u = 0.50000 − 1.32288I
a = −0.213525 + 1.070230I
b = 2.35410 − 1.32288I
6.57974 −7.00000
u = 0.50000 − 1.32288I
a = 1.46353 − 0.40879I
b = −4.35410 − 1.32288I
6.57974 −7.00000
25
VII. I
u
7
= hb
2
+ b − 1, a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
11
=
1
0
a
12
=
1
1
a
4
=
−1
b
a
9
=
1
0
a
5
=
b − 1
b
a
1
=
0
1
a
3
=
−1
b + 1
a
7
=
−1
b
a
6
=
b − 1
b
a
2
=
−1
b + 1
a
10
=
2b
b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
8
(u − 1)
2
c
2
, c
5
u
2
c
4
, c
6
u
2
− u − 1
c
7
, c
11
, c
12
(u + 1)
2
c
9
, c
10
u
2
+ u − 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
c
8
, c
11
, c
12
(y −1)
2
c
2
, c
5
y
2
c
4
, c
6
, c
9
c
10
y
2
− 3y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0.618034
−3.28987 −7.00000
u = −1.00000
a = −1.00000
b = −1.61803
−3.28987 −7.00000
29
VIII. I
v
1
= ha, b + v − 2, v
2
− 3v + 1i
(i) Arc colorings
a
8
=
v
0
a
11
=
1
0
a
12
=
1
0
a
4
=
0
−v + 2
a
9
=
v
0
a
5
=
−2v + 1
−v + 2
a
1
=
1
0
a
3
=
−2v + 1
−v + 2
a
7
=
−2v + 1
−1
a
6
=
−2v
−1
a
2
=
1
−v + 3
a
10
=
−2v + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
2
− u − 1
c
2
, c
6
(u − 1)
2
c
5
, c
10
(u + 1)
2
c
7
, c
9
u
2
+ u − 1
c
8
, c
11
, c
12
u
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
y
2
− 3y + 1
c
2
, c
5
, c
6
c
10
(y − 1)
2
c
8
, c
11
, c
12
y
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = 1.61803
−3.28987 −7.00000
v = 2.61803
a = 0
b = −0.618034
−3.28987 −7.00000
33
IX. I
v
2
= ha, b − 1, v − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
1
0
a
12
=
1
0
a
4
=
0
1
a
9
=
1
0
a
5
=
1
1
a
1
=
1
0
a
3
=
1
1
a
7
=
0
−1
a
6
=
−1
−1
a
2
=
1
1
a
10
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
u + 1
c
2
, c
5
, c
8
c
11
, c
12
u
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
y − 1
c
2
, c
5
, c
8
c
11
, c
12
y
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
37
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
((u − 1)
2
)(u + 1)(u
2
− u − 1)(u
3
− u
2
+ 2u − 1)(u
4
− 3u
3
+ ··· − 13u + 11)
· (u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
4
+ 2u
3
+ 8u
2
+ 7u + 1)
· (u
6
− 2u
5
+ ··· − 2u − 1)(u
6
+ u
5
+ 2u
4
− 4u
2
+ 2u − 1)
c
2
, c
8
u
3
(u − 1)
2
(u
2
− u + 2)
2
(u
3
− u
2
+ 1)
2
(u
3
+ u
2
− 1)
· (u
4
+ 3u
3
+ u
2
− 5u − 5)(u
4
+ 3u
3
+ 5u
2
+ u − 1)
· (u
6
+ 4u
5
+ 5u
4
− 4u
3
− 16u
2
− 12u − 3)
c
4
(u + 1)(u
2
− u − 1)
8
(u
3
+ 3u
2
+ 2u − 1)(u
6
+ 2u
5
+ ··· − 2u + 1)
· (u
6
+ 3u
5
− 4u
3
+ 6u
2
+ 14u + 5)
c
5
, c
11
, c
12
u
3
(u + 1)
2
(u
2
− u + 2)
2
(u
3
− u
2
+ 1)
3
(u
4
− 3u
3
+ u
2
+ 5u − 5)
· (u
4
+ 3u
3
+ 5u
2
+ u − 1)(u
6
+ 4u
5
+ 5u
4
− 4u
3
− 16u
2
− 12u − 3)
c
7
, c
10
((u + 1)
3
)(u
2
+ u − 1)(u
3
+ u
2
+ 2u + 1)(u
4
− 3u
3
+ ··· − 13u + 11)
· (u
4
− 2u
3
+ 2u
2
− u − 1)(u
4
+ 2u
3
+ 8u
2
+ 7u + 1)
· (u
6
− 2u
5
+ ··· − 2u − 1)(u
6
+ u
5
+ 2u
4
− 4u
2
+ 2u − 1)
c
9
(u + 1)(u
2
− u − 1)
4
(u
2
+ u − 1)
4
(u
3
− 3u
2
+ 2u + 1)
· (u
6
+ 2u
5
− u
4
− 2u
3
− 2u + 1)(u
6
+ 3u
5
− 4u
3
+ 6u
2
+ 14u + 5)
38
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
(y − 1)
3
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y − 1)(y
4
− 2y
2
− 5y + 1)
· (y
4
+ 7y
3
+ 8y
2
+ 7y + 121)(y
4
+ 12y
3
+ 38y
2
− 33y + 1)
· (y
6
+ 3y
5
− 4y
4
− 22y
3
+ 12y
2
+ 4y + 1)
· (y
6
+ 6y
5
+ 25y
4
− 54y
3
+ 14y
2
+ 4y + 1)
c
2
, c
5
, c
8
c
11
, c
12
y
3
(y − 1)
2
(y
2
+ 3y + 4)
2
(y
3
− y
2
+ 2y − 1)
3
· (y
4
− 7y
3
+ 21y
2
− 35y + 25)(y
4
+ y
3
+ 17y
2
− 11y + 1)
· (y
6
− 6y
5
+ 25y
4
− 86y
3
+ 130y
2
− 48y + 9)
c
4
, c
9
(y − 1)(y
2
− 3y + 1)
8
(y
3
− 5y
2
+ 10y − 1)
· (y
6
− 9y
5
+ 36y
4
− 90y
3
+ 148y
2
− 136y + 25)
· (y
6
− 6y
5
+ 9y
4
+ 6y
3
− 10y
2
− 4y + 1)
39
