12n
0605
(K12n
0605
)
A knot diagram
1
Linearized knot diagam
3 7 10 8 9 2 12 5 3 4 1 8
Solving Sequence
2,6
7
3,9
10 1 5 8 4 12 11
c
6
c
2
c
9
c
1
c
5
c
8
c
4
c
12
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
7
− 3u
6
− u
5
+ 9u
4
− 6u
3
− 2u
2
+ 4b + 2, u
7
− 2u
6
− u
5
+ 6u
4
− 6u
3
+ 2u
2
+ 4a + 2u,
u
8
− 2u
7
− 2u
6
+ 8u
5
− 3u
4
− 4u
3
+ 2u
2
+ 2u + 2i
I
u
2
= hb − 1, u
2
+ 2a − u, u
4
− u
2
+ 2i
I
u
3
= h−63u
7
+ 285u
6
− 207u
5
+ 132u
4
− 665u
3
− 273u
2
+ 1121b + 1277u − 919,
6601u
7
− 21641u
6
+ 23931u
5
− 33635u
4
+ 55727u
3
+ 23373u
2
+ 24662a − 106399u + 92305,
u
8
− 4u
7
+ 6u
6
− 8u
5
+ 12u
4
− 2u
3
− 18u
2
+ 26u − 11i
I
u
4
= hau + b − a + 1, 2a
2
− 2au − 4a − u − 1, u
2
+ 2u − 1i
I
u
5
= hb − 2a + 1, 2a
2
− 2a − 1, u + 1i
I
u
6
= hb + 1, −u
3
− u
2
+ 2a + u − 1, u
4
+ 1i
I
u
7
= hb, a + 1, u + 1i
I
u
8
= h−2au + 2b + 2a + u − 3, 4a
2
− 4a + 9, u
2
− 2u + 1i
I
u
9
= hb − 1, u − 1i
I
v
1
= ha, b + 1, v + 1i
* 9 irreducible components of dim
C
= 0, with total 36 representations.
* 1 irreducible components of dim
C
= 1
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
= hu
7
− 3u
6
− u
5
+ 9u
4
− 6u
3
− 2u
2
+ 4b + 2, u
7
− 2u
6
− u
5
+ 6u
4
−
6u
3
+ 2u
2
+ 4a + 2u, u
8
− 2u
7
+ · · · + 2u + 2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−
1
4
u
7
+
1
2
u
6
+ ··· −
1
2
u
2
−
1
2
u
−
1
4
u
7
+
3
4
u
6
+ ··· +
1
2
u
2
−
1
2
a
10
=
−
1
2
u
7
+
3
4
u
6
+ ··· −
1
2
u −
1
2
−
3
4
u
7
+
5
4
u
6
+ ··· + u +
1
2
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
1
4
u
7
−
1
2
u
6
+ ··· −
1
2
u + 1
1
4
u
7
−
3
4
u
6
+ ··· +
1
2
u
2
+
1
2
a
8
=
1
2
u
7
− u
6
−
1
2
u
5
+ 3u
4
− 2u
3
− u + 1
1
2
u
7
− u
6
−
1
2
u
5
+ 2u
4
− 2u
3
+ u
2
− u
a
4
=
−
1
2
u
7
+
3
4
u
6
+ ··· −
1
2
u −
1
2
−
3
4
u
7
+
1
4
u
6
+ ··· + 2u +
1
2
a
12
=
1
2
u
6
− u
5
−
1
2
u
4
+ 3u
3
− 2u
2
− 1
1
2
u
6
− u
5
−
1
2
u
4
+ 2u
3
− 2u
2
− 1
a
11
=
1
2
u
6
− 2u
5
−
1
2
u
4
+ 3u
3
− 2u
2
− 1
−u
7
+
1
2
u
6
−
1
2
u
4
+ u
3
− 2u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1
2
u
7
−
1
2
u
6
−
1
2
u
5
−
1
2
u
4
+ u
3
+ 9u
2
− 8u + 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
8
+ 8u
7
+ 30u
6
+ 64u
5
+ 77u
4
+ 68u
3
+ 8u
2
− 4u + 4
c
2
, c
6
, c
7
c
12
u
8
− 2u
7
− 2u
6
+ 8u
5
− 3u
4
− 4u
3
+ 2u
2
+ 2u + 2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
8
− 2u
7
− 5u
6
+ 16u
5
− 3u
4
− 14u
3
+ u
2
− 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
8
− 4y
7
+ 30y
6
− 548y
5
− 2223y
4
− 2640y
3
+ 1224y
2
+ 48y + 16
c
2
, c
6
, c
7
c
12
y
8
− 8y
7
+ 30y
6
− 64y
5
+ 77y
4
− 68y
3
+ 8y
2
+ 4y + 4
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
8
− 14y
7
+ 83y
6
− 280y
5
+ 443y
4
− 182y
3
+ 13y
2
− 4y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.795087
a = −1.17483
b = −1.67677
10.6824 12.2800
u = 0.973229 + 0.738508I
a = −0.555279 − 0.483622I
b = 0.655349 − 0.111756I
2.80118 − 5.76470I −0.66223 + 7.42338I
u = 0.973229 − 0.738508I
a = −0.555279 + 0.483622I
b = 0.655349 + 0.111756I
2.80118 + 5.76470I −0.66223 − 7.42338I
u = −0.253073 + 0.513412I
a = 0.548752 − 0.359255I
b = −0.248429 − 0.443565I
0.076761 + 1.027570I 1.43267 − 6.49756I
u = −0.253073 − 0.513412I
a = 0.548752 + 0.359255I
b = −0.248429 + 0.443565I
0.076761 − 1.027570I 1.43267 + 6.49756I
u = 1.55774 + 0.70350I
a = 0.340083 + 1.296596I
b = −1.80248 + 0.99093I
−13.5641 − 12.7719I 1.06054 + 5.06853I
u = 1.55774 − 0.70350I
a = 0.340083 − 1.296596I
b = −1.80248 − 0.99093I
−13.5641 + 12.7719I 1.06054 − 5.06853I
u = −1.76070
a = 0.507716
b = 2.46790
7.40006 0.0581740
5
II. I
u
2
= hb − 1, u
2
+ 2a − u, u
4
− u
2
+ 2i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−
1
2
u
2
+
1
2
u
1
a
10
=
−
1
2
u
2
+
3
2
u
u
3
− u + 1
a
1
=
u
3
−u
a
5
=
−
1
2
u
2
+
1
2
u + 1
1
a
8
=
−1
0
a
4
=
−
1
2
u
2
+
1
2
u
1
a
12
=
u
3
− u
−u
a
11
=
u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 4
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
− u + 2)
2
c
2
, c
6
, c
7
c
12
u
4
− u
2
+ 2
c
3
, c
8
(u + 1)
4
c
4
, c
5
, c
9
c
10
(u − 1)
4
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
+ 3y + 4)
2
c
2
, c
6
, c
7
c
12
(y
2
− y + 2)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y − 1)
4
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = 0.239159 − 0.323389I
b = 1.00000
4.11234 − 5.33349I 6.00000 + 5.29150I
u = 0.978318 − 0.676097I
a = 0.239159 + 0.323389I
b = 1.00000
4.11234 + 5.33349I 6.00000 − 5.29150I
u = −0.978318 + 0.676097I
a = −0.739159 + 0.999486I
b = 1.00000
4.11234 + 5.33349I 6.00000 − 5.29150I
u = −0.978318 − 0.676097I
a = −0.739159 − 0.999486I
b = 1.00000
4.11234 − 5.33349I 6.00000 + 5.29150I
9
III. I
u
3
= h−63u
7
+ 285u
6
+ · · · + 1121b − 919, 6601u
7
− 21641u
6
+ · · · +
24662a + 92305, u
8
− 4u
7
+ · · · + 26u − 11i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−0.267659u
7
+ 0.877504u
6
+ ··· + 4.31429u − 3.74280
0.0561998u
7
− 0.254237u
6
+ ··· − 1.13916u + 0.819804
a
10
=
−0.238221u
7
+ 1.03005u
6
+ ··· + 4.95568u − 4.36100
0.599465u
7
− 1.71186u
6
+ ··· − 8.48439u + 4.41124
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.0185305u
7
− 0.0362096u
6
+ ··· − 0.502595u + 0.792677
0.0374665u
7
− 0.169492u
6
+ ··· − 0.0927743u + 0.213202
a
8
=
−0.407591u
7
+ 1.17720u
6
+ ··· + 6.03958u − 4.71332
−0.312221u
7
+ 0.745763u
6
+ ··· + 3.43979u − 1.44335
a
4
=
−0.0381559u
7
− 0.0654854u
6
+ ··· − 1.25833u + 0.619455
−0.399643u
7
+ 0.474576u
6
+ ··· + 6.32293u − 2.60749
a
12
=
0.321953u
7
− 1.07550u
6
+ ··· − 4.54181u + 4.51172
−0.00892061u
7
+ 0.135593u
6
+ ··· + 0.926851u + 0.187333
a
11
=
−0.181169u
7
− 0.228043u
6
+ ··· + 1.13259u + 1.07728
−1.87957u
7
+ 6.16949u
6
+ ··· + 21.9875u − 11.5290
(ii) Obstruction class = −1
(iii) Cusp Shapes =
518
1121
u
7
−
84
59
u
6
+
1702
1121
u
5
−
2580
1121
u
4
+
196
59
u
3
+
2992
1121
u
2
−
8756
1121
u +
9300
1121
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
8
+ 4u
7
− 4u
6
− 28u
5
+ 82u
4
+ 152u
3
+ 164u
2
+ 280u + 121
c
2
, c
6
, c
7
c
12
u
8
− 4u
7
+ 6u
6
− 8u
5
+ 12u
4
− 2u
3
− 18u
2
+ 26u − 11
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(u
4
+ 2u
3
+ 4u
2
− 2u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
8
− 24y
7
+ ··· − 38712y + 14641
c
2
, c
6
, c
7
c
12
y
8
− 4y
7
− 4y
6
+ 28y
5
+ 82y
4
− 152y
3
+ 164y
2
− 280y + 121
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y
4
+ 4y
3
+ 22y
2
− 12y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.737313 + 0.794288I
a = 0.634238 + 0.289969I
b = −0.632293
3.51425 − 61.050747 + 0.10I
u = 0.737313 − 0.794288I
a = 0.634238 − 0.289969I
b = −0.632293
3.51425 − 61.050747 + 0.10I
u = −1.13723
a = 0.132208
b = 0.321336
−2.70122 4.79070
u = 0.741896
a = −1.67811
b = 0.321336
−2.70122 4.79070
u = −0.47349 + 1.60637I
a = −0.607711 + 0.003620I
b = 1.15548 + 1.89385I
−7.80872 + 4.85117I 1.07929 − 2.27864I
u = −0.47349 − 1.60637I
a = −0.607711 − 0.003620I
b = 1.15548 − 1.89385I
−7.80872 − 4.85117I 1.07929 + 2.27864I
u = 1.93385 + 0.46705I
a = −0.162665 − 1.055547I
b = 1.15548 − 1.89385I
−7.80872 − 4.85117I 1.07929 + 2.27864I
u = 1.93385 − 0.46705I
a = −0.162665 + 1.055547I
b = 1.15548 + 1.89385I
−7.80872 + 4.85117I 1.07929 − 2.27864I
13
IV. I
u
4
= hau + b − a + 1, 2a
2
− 2au − 4a − u − 1, u
2
+ 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−2u + 1
a
3
=
−u
−4u + 2
a
9
=
a
−au + a − 1
a
10
=
3au + 2u − 1
13au − 5a + 10u − 5
a
1
=
5u − 2
25u − 10
a
5
=
au + u + 1
4au − 2a + 3u
a
8
=
3u
13u − 5
a
4
=
10au − 3a − 2u + 1
48au − 20a − 10u + 5
a
12
=
−u + 1
−6u + 3
a
11
=
−30u + 13
−151u + 63
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
+ 6u + 1)
2
c
2
, c
6
, c
7
c
12
(u
2
+ 2u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
4
− 4u
3
+ 12u
2
− 4u − 7
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
2
− 34y + 1)
2
c
2
, c
6
, c
7
c
12
(y
2
− 6y + 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
4
+ 8y
3
+ 98y
2
− 184y + 49
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.414214
a = −0.264020
b = −1.15466
2.46740 0
u = 0.414214
a = 2.67823
b = 0.568873
2.46740 0
u = −2.41421
a = −0.207107 + 0.814993I
b = −1.70711 + 2.78256I
−17.2718 0
u = −2.41421
a = −0.207107 − 0.814993I
b = −1.70711 − 2.78256I
−17.2718 0
17
V. I
u
5
= hb − 2a + 1, 2a
2
− 2a − 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
9
=
a
2a − 1
a
10
=
3a − 1
2a − 1
a
1
=
−1
−1
a
5
=
a + 2
3
a
8
=
−4a + 1
−4a + 2
a
4
=
−a − 3
−3
a
12
=
−4a
−4a + 1
a
11
=
−4a + 1
−4a + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
(u − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
2
− 3
c
6
, c
12
(u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
(y − 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y − 3)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 1.36603
b = 1.73205
9.86960 0
u = −1.00000
a = −0.366025
b = −1.73205
9.86960 0
21
VI. I
u
6
= hb + 1, −u
3
− u
2
+ 2a + u − 1, u
4
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
1
2
u
3
+
1
2
u
2
−
1
2
u +
1
2
−1
a
10
=
1
2
u
3
+
1
2
u
2
−
3
2
u +
1
2
−u
3
+ u − 1
a
1
=
u
3
−u
3
a
5
=
−
1
2
u
3
−
1
2
u
2
+
1
2
u +
1
2
1
a
8
=
1
0
a
4
=
−
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
1
a
12
=
0
−u
3
a
11
=
−u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
2
+ 1)
2
c
2
, c
6
, c
7
c
12
u
4
+ 1
c
3
, c
8
(u − 1)
4
c
4
, c
5
, c
9
c
10
(u + 1)
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y + 1)
4
c
2
, c
6
, c
7
c
12
(y
2
+ 1)
2
c
3
, c
4
, c
5
c
8
, c
9
, c
10
(y − 1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = −0.207107 + 0.500000I
b = −1.00000
4.93480 8.00000
u = 0.707107 − 0.707107I
a = −0.207107 − 0.500000I
b = −1.00000
4.93480 8.00000
u = −0.707107 + 0.707107I
a = 1.207107 − 0.500000I
b = −1.00000
4.93480 8.00000
u = −0.707107 − 0.707107I
a = 1.207107 + 0.500000I
b = −1.00000
4.93480 8.00000
25
VII. I
u
7
= hb, a + 1, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
6
=
1
0
a
7
=
1
1
a
3
=
1
0
a
9
=
−1
0
a
10
=
−1
0
a
1
=
−1
−1
a
5
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
12
=
−2
−1
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
11
u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
c
6
, c
12
u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
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
−3.28987 −12.0000
29
VIII. I
u
8
= h−2au + 2b + 2a + u − 3, 4a
2
− 4a + 9, u
2
− 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
2u − 1
a
3
=
−u
−2u + 2
a
9
=
a
au − a −
1
2
u +
3
2
a
10
=
−au + 2a +
3
2
u −
1
2
au − a +
3
2
u −
1
2
a
1
=
3u − 2
3u − 2
a
5
=
1
2
au +
1
2
a −
9
4
u +
13
4
2au − 2a − u + 2
a
8
=
−2au + 2a + 5u − 6
−2au + 2a + u − 1
a
4
=
−
5
2
au +
7
2
a +
13
4
u −
13
4
1
a
12
=
2au − 2a − 3u + 5
2au − 2a + 2u − 1
a
11
=
2au − 2a − 4u + 5
2au − 2a + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
10
c
11
, c
12
(u − 1)
4
c
2
, c
3
, c
7
c
8
(u + 1)
4
31
(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 − 1)
4
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.50000 + 1.41421I
b = 1.00000
0 0
u = 1.00000
a = 0.50000 + 1.41421I
b = 1.00000
0 0
u = 1.00000
a = 0.50000 − 1.41421I
b = 1.00000
0 0
u = 1.00000
a = 0.50000 − 1.41421I
b = 1.00000
0 0
33
IX. I
u
9
= hb − 1, u − 1i
(i) Arc colorings
a
2
=
0
1
a
6
=
1
0
a
7
=
1
1
a
3
=
−1
0
a
9
=
a
1
a
10
=
a + 1
1
a
1
=
1
1
a
5
=
a + 1
1
a
8
=
−1
0
a
4
=
a
1
a
12
=
2
1
a
11
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(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.
34
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
35
X. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
2
=
−1
0
a
6
=
1
0
a
7
=
1
0
a
3
=
−1
0
a
9
=
0
−1
a
10
=
−1
−1
a
1
=
−1
0
a
5
=
1
1
a
8
=
1
0
a
4
=
0
1
a
12
=
−1
0
a
11
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
u
c
3
, c
8
u − 1
c
4
, c
5
, c
9
c
10
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
11
, c
12
y
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y − 1
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
3.28987 12.0000
39
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
u(u − 1)
7
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
2
+ 6u + 1)
2
· (u
8
+ 4u
7
− 4u
6
− 28u
5
+ 82u
4
+ 152u
3
+ 164u
2
+ 280u + 121)
· (u
8
+ 8u
7
+ 30u
6
+ 64u
5
+ 77u
4
+ 68u
3
+ 8u
2
− 4u + 4)
c
2
, c
7
u(u − 1)
3
(u + 1)
4
(u
2
+ 2u − 1)
2
(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
8
− 4u
7
+ 6u
6
− 8u
5
+ 12u
4
− 2u
3
− 18u
2
+ 26u − 11)
· (u
8
− 2u
7
− 2u
6
+ 8u
5
− 3u
4
− 4u
3
+ 2u
2
+ 2u + 2)
c
3
, c
8
u(u − 1)
5
(u + 1)
8
(u
2
− 3)(u
4
− 4u
3
+ 12u
2
− 4u − 7)
· (u
4
+ 2u
3
+ 4u
2
− 2u − 1)
2
· (u
8
− 2u
7
− 5u
6
+ 16u
5
− 3u
4
− 14u
3
+ u
2
− 2)
c
4
, c
5
, c
9
c
10
u(u − 1)
8
(u + 1)
5
(u
2
− 3)(u
4
− 4u
3
+ 12u
2
− 4u − 7)
· (u
4
+ 2u
3
+ 4u
2
− 2u − 1)
2
· (u
8
− 2u
7
− 5u
6
+ 16u
5
− 3u
4
− 14u
3
+ u
2
− 2)
c
6
, c
12
u(u − 1)
4
(u + 1)
3
(u
2
+ 2u − 1)
2
(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
8
− 4u
7
+ 6u
6
− 8u
5
+ 12u
4
− 2u
3
− 18u
2
+ 26u − 11)
· (u
8
− 2u
7
− 2u
6
+ 8u
5
− 3u
4
− 4u
3
+ 2u
2
+ 2u + 2)
40
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
y(y − 1)
7
(y + 1)
4
(y
2
− 34y + 1)
2
(y
2
+ 3y + 4)
2
· (y
8
− 24y
7
+ ··· − 38712y + 14641)
· (y
8
− 4y
7
+ 30y
6
− 548y
5
− 2223y
4
− 2640y
3
+ 1224y
2
+ 48y + 16)
c
2
, c
6
, c
7
c
12
y(y − 1)
7
(y
2
+ 1)
2
(y
2
− 6y + 1)
2
(y
2
− y + 2)
2
· (y
8
− 8y
7
+ 30y
6
− 64y
5
+ 77y
4
− 68y
3
+ 8y
2
+ 4y + 4)
· (y
8
− 4y
7
− 4y
6
+ 28y
5
+ 82y
4
− 152y
3
+ 164y
2
− 280y + 121)
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y(y − 3)
2
(y − 1)
13
(y
4
+ 4y
3
+ 22y
2
− 12y + 1)
2
· (y
4
+ 8y
3
+ 98y
2
− 184y + 49)
· (y
8
− 14y
7
+ 83y
6
− 280y
5
+ 443y
4
− 182y
3
+ 13y
2
− 4y + 4)
41
