12n
0379
(K12n
0379
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 2 12 3 10 4 8 6 11
Solving Sequence
4,10
9
3,6
2 1 5 8 11 12 7
c
9
c
3
c
2
c
1
c
5
c
8
c
10
c
11
c
7
c
4
, c
6
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
30
− 3u
29
+ ··· + 4b + 4, 3u
30
− 4u
29
+ ··· + 4a + 2, u
31
− 2u
30
+ ··· + 4u − 2i
I
u
2
= hu
3
− u
2
+ b + 1, −u
3
+ 2a + u − 2, u
4
− u
2
+ 2i
I
u
3
= ha
2
u
2
+ a
2
u − u
2
a + au + b + 2a, 2a
2
u
2
+ a
3
+ 2a
2
u + au + a + u, u
3
+ u
2
− 1i
I
u
4
= hb, a + 1, u + 1i
I
u
5
= hb − 1, a + 2, u − 1i
I
u
6
= hb + 1, a, u + 1i
I
u
7
= hb − 1, a + 1, u − 1i
I
u
8
= h−u
2
+ b + u − 1, −u
3
+ u
2
+ a, u
4
+ 1i
I
v
1
= ha, b − 1, v −1i
* 9 irreducible components of dim
C
= 0, with total 53 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
30
−3u
29
+· · ·+4b+4, 3u
30
−4u
29
+· · ·+4a+2, u
31
−2u
30
+· · ·+4u−2i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
3
=
−u
−u
3
+ u
a
6
=
−
3
4
u
30
+ u
29
+ ··· + 3u −
1
2
1
4
u
30
+
3
4
u
29
+ ··· +
1
2
u − 1
a
2
=
1
4
u
30
− u
29
+ ··· − 2u +
1
2
−
3
2
u
30
+ 2u
29
+ ··· + 5u − 2
a
1
=
1
4
u
28
−
5
4
u
26
+ ··· −
1
2
u −
1
2
−
1
4
u
28
+ u
26
+ ··· +
1
2
u
2
+ u
a
5
=
u
13
− 2u
11
+ 5u
9
− 6u
7
+ 6u
5
− 4u
3
+ u
u
15
− 3u
13
+ 6u
11
− 9u
9
+ 8u
7
− 6u
5
+ 2u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
u
4
− u
2
+ 1
−u
4
a
12
=
−
1
4
u
30
+ u
29
+ ··· + 3u −
1
2
1
2
u
30
− u
29
+ ··· −
5
2
u + 1
a
7
=
−u
6
+ u
4
− 2u
2
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −2u
30
+ 4u
29
+ 8u
28
− 16u
27
− 26u
26
+ 56u
25
+ 58u
24
− 122u
23
− 108u
22
+ 230u
21
+
168u
20
− 328u
19
− 224u
18
+ 400u
17
+ 252u
16
− 370u
15
− 246u
14
+ 270u
13
+ 190u
12
−
98u
11
− 122u
10
− 12u
9
+ 54u
8
+ 90u
7
+ 8u
6
− 58u
5
− 6u
4
+ 38u
3
+ 16u
2
+ 10u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 49u
30
+ ··· − 15231u + 529
c
2
, c
5
u
31
+ 3u
30
+ ··· + 77u − 23
c
3
, c
9
u
31
− 2u
30
+ ··· + 4u − 2
c
4
u
31
+ 7u
30
+ ··· + 69324u − 24982
c
6
, c
11
u
31
− 3u
30
+ ··· + 9u − 9
c
7
u
31
+ 2u
30
+ ··· − 1028u − 3866
c
8
, c
10
u
31
− 8u
30
+ ··· + 76u
2
− 4
c
12
u
31
− u
30
+ ··· − 783u − 81
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 121y
30
+ ··· + 137554745y −279841
c
2
, c
5
y
31
− 49y
30
+ ··· − 15231y −529
c
3
, c
9
y
31
− 8y
30
+ ··· + 76y
2
− 4
c
4
y
31
+ 61y
30
+ ··· + 2635081032y −624100324
c
6
, c
11
y
31
− y
30
+ ··· − 783y −81
c
7
y
31
+ 16y
30
+ ··· + 26974448y −14945956
c
8
, c
10
y
31
+ 28y
30
+ ··· + 608y −16
c
12
y
31
+ 71y
30
+ ··· + 24057y −6561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663469 + 0.751213I
a = 0.351205 + 0.923577I
b = 1.105880 − 0.396734I
−3.68245 + 0.08795I −0.712597 + 0.455533I
u = −0.663469 − 0.751213I
a = 0.351205 − 0.923577I
b = 1.105880 + 0.396734I
−3.68245 − 0.08795I −0.712597 − 0.455533I
u = 0.728867 + 0.652617I
a = −0.139459 − 0.952361I
b = 1.33700 + 0.85927I
0.259635 − 0.106495I 9.87430 + 1.04296I
u = 0.728867 − 0.652617I
a = −0.139459 + 0.952361I
b = 1.33700 − 0.85927I
0.259635 + 0.106495I 9.87430 − 1.04296I
u = −0.935170 + 0.222618I
a = 0.574653 + 1.214550I
b = −0.079692 − 1.257260I
1.12870 − 3.87074I 8.86243 + 7.64140I
u = −0.935170 − 0.222618I
a = 0.574653 − 1.214550I
b = −0.079692 + 1.257260I
1.12870 + 3.87074I 8.86243 − 7.64140I
u = −1.068290 + 0.325898I
a = −1.043310 − 0.044790I
b = 1.40274 + 1.11223I
−7.45526 + 0.17674I 5.77037 + 1.13403I
u = −1.068290 − 0.325898I
a = −1.043310 + 0.044790I
b = 1.40274 − 1.11223I
−7.45526 − 0.17674I 5.77037 − 1.13403I
u = 1.095710 + 0.242215I
a = 1.26095 − 0.95798I
b = −0.735307 + 1.042830I
−6.91990 + 7.21748I 6.74465 − 5.27304I
u = 1.095710 − 0.242215I
a = 1.26095 + 0.95798I
b = −0.735307 − 1.042830I
−6.91990 − 7.21748I 6.74465 + 5.27304I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.781352 + 0.817214I
a = −1.37993 + 0.39344I
b = −0.10938 − 2.09740I
−5.48154 − 2.37155I 1.17244 + 2.28435I
u = 0.781352 − 0.817214I
a = −1.37993 − 0.39344I
b = −0.10938 + 2.09740I
−5.48154 + 2.37155I 1.17244 − 2.28435I
u = −0.720251 + 0.881314I
a = −1.63175 − 1.06162I
b = −0.47498 + 2.37274I
−14.4731 + 7.0018I 1.25090 − 2.32641I
u = −0.720251 − 0.881314I
a = −1.63175 + 1.06162I
b = −0.47498 − 2.37274I
−14.4731 − 7.0018I 1.25090 + 2.32641I
u = 0.963769 + 0.665989I
a = 1.008580 + 0.085082I
b = −0.50239 + 1.42848I
0.98115 + 5.27885I 11.70308 − 5.96602I
u = 0.963769 − 0.665989I
a = 1.008580 − 0.085082I
b = −0.50239 − 1.42848I
0.98115 − 5.27885I 11.70308 + 5.96602I
u = 0.773274 + 0.881332I
a = 0.987775 − 0.615547I
b = 0.713092 + 0.884815I
−15.4700 + 1.2037I 0.44734 − 1.88848I
u = 0.773274 − 0.881332I
a = 0.987775 + 0.615547I
b = 0.713092 − 0.884815I
−15.4700 − 1.2037I 0.44734 + 1.88848I
u = −1.001840 + 0.678352I
a = 0.875242 + 0.190119I
b = −0.99047 − 1.70764I
−2.66141 − 5.53232I 1.04333 + 5.08829I
u = −1.001840 − 0.678352I
a = 0.875242 − 0.190119I
b = −0.99047 + 1.70764I
−2.66141 + 5.53232I 1.04333 − 5.08829I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.055960 + 0.767487I
a = 0.29212 − 2.05873I
b = −0.610484 + 0.959338I
−10.76740 − 3.89804I 0.78804 + 2.34042I
u = −0.055960 − 0.767487I
a = 0.29212 + 2.05873I
b = −0.610484 − 0.959338I
−10.76740 + 3.89804I 0.78804 − 2.34042I
u = 0.970212 + 0.761534I
a = −0.416925 + 1.343310I
b = −1.61267 − 2.44399I
−4.90025 + 8.29290I 2.65243 − 7.48178I
u = 0.970212 − 0.761534I
a = −0.416925 − 1.343310I
b = −1.61267 + 2.44399I
−4.90025 − 8.29290I 2.65243 + 7.48178I
u = 1.002290 + 0.793385I
a = 0.462370 − 0.838920I
b = −0.06322 + 2.17897I
−14.7566 + 5.0057I 1.43866 − 2.92043I
u = 1.002290 − 0.793385I
a = 0.462370 + 0.838920I
b = −0.06322 − 2.17897I
−14.7566 − 5.0057I 1.43866 + 2.92043I
u = −1.028320 + 0.765921I
a = −0.95391 − 1.51050I
b = −0.93688 + 3.31151I
−13.5166 − 13.1152I 2.72835 + 7.05424I
u = −1.028320 − 0.765921I
a = −0.95391 + 1.51050I
b = −0.93688 − 3.31151I
−13.5166 + 13.1152I 2.72835 − 7.05424I
u = −0.082878 + 0.511912I
a = 1.27490 + 1.44891I
b = −0.387924 − 0.478500I
−1.45714 + 1.31342I −0.58494 − 2.75883I
u = −0.082878 − 0.511912I
a = 1.27490 − 1.44891I
b = −0.387924 + 0.478500I
−1.45714 − 1.31342I −0.58494 + 2.75883I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.481415
a = −0.0450372
b = 0.889366
0.952264 11.6420
8
II. I
u
2
= hu
3
− u
2
+ b + 1, −u
3
+ 2a + u − 2, u
4
− u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
3
=
−u
−u
3
+ u
a
6
=
1
2
u
3
−
1
2
u + 1
−u
3
+ u
2
− 1
a
2
=
1
2
u
3
−
3
2
u + 1
−2u
3
+ u
2
+ u − 1
a
1
=
1
2
u
3
−
1
2
u + 1
−u
3
+ u
2
− 1
a
5
=
u
u
3
− u
a
8
=
−u
2
+ 1
u
2
a
11
=
−1
−u
2
+ 2
a
12
=
1
2
u
3
−
1
2
u
−u
3
+ 1
a
7
=
1
u
2
− 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 8
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
12
(u − 1)
4
c
2
, c
11
(u + 1)
4
c
3
, c
4
, c
7
c
9
u
4
− u
2
+ 2
c
8
(u
2
+ u + 2)
2
c
10
(u
2
− u + 2)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y −1)
4
c
3
, c
4
, c
7
c
9
(y
2
− y + 2)
2
c
8
, c
10
(y
2
+ 3y + 4)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978318 + 0.676097I
a = 0.308224 + 0.478073I
b = −0.094767 − 0.309366I
−0.82247 + 5.33349I 6.00000 − 5.29150I
u = 0.978318 − 0.676097I
a = 0.308224 − 0.478073I
b = −0.094767 + 0.309366I
−0.82247 − 5.33349I 6.00000 + 5.29150I
u = −0.978318 + 0.676097I
a = 1.69178 + 0.47807I
b = −0.90523 − 2.95512I
−0.82247 − 5.33349I 6.00000 + 5.29150I
u = −0.978318 − 0.676097I
a = 1.69178 − 0.47807I
b = −0.90523 + 2.95512I
−0.82247 + 5.33349I 6.00000 − 5.29150I
12
III.
I
u
3
= ha
2
u
2
+a
2
u−u
2
a+au+b+2a, 2a
2
u
2
+a
3
+2 a
2
u+au+a+u, u
3
+u
2
−1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
3
=
−u
u
2
+ u − 1
a
6
=
a
−a
2
u
2
− a
2
u + u
2
a − au − 2a
a
2
=
a
2
u
2
+ a
2
u + au + a
−a
2
u
2
− au − a
a
1
=
a
2
u
2
+ a
2
u − u
2
a + au + a
−a
2
u
2
− 2au
a
5
=
0
u
a
8
=
−u
2
+ 1
u
2
a
11
=
u
−u
2
− u + 1
a
12
=
−a
2
u
2
− a
2
u − au − a
a
2
u
2
+ au + a
a
7
=
0
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u + 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 6u
8
+ 15u
7
+ 17u
6
+ 3u
5
− 12u
4
− 9u
3
+ u
2
+ 2u + 1
c
2
, c
5
, c
6
c
11
u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1
c
3
, c
9
(u
3
+ u
2
− 1)
3
c
4
u
9
c
7
, c
8
, c
10
(u
3
− u
2
+ 2u − 1)
3
c
12
u
9
− 6u
8
+ 15u
7
− 17u
6
+ 3u
5
+ 12u
4
− 9u
3
− u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
12
y
9
− 6y
8
+ 27y
7
− 73y
6
+ 139y
5
− 184y
4
+ 83y
3
− 13y
2
+ 2y −1
c
2
, c
5
, c
6
c
11
y
9
− 6y
8
+ 15y
7
− 17y
6
+ 3y
5
+ 12y
4
− 9y
3
− y
2
+ 2y −1
c
3
, c
9
(y
3
− y
2
+ 2y −1)
3
c
4
y
9
c
7
, c
8
, c
10
(y
3
+ 3y
2
+ 2y −1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.214566 + 1.359580I
b = 1.07324 − 2.30110I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 + 0.744862I
a = −0.356972 − 0.437449I
b = −0.79165 + 1.30040I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 + 0.744862I
a = 1.46712 + 0.20243I
b = 0.14857 − 1.61358I
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.877439 − 0.744862I
a = 0.214566 − 1.359580I
b = 1.07324 + 2.30110I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = −0.356972 + 0.437449I
b = −0.79165 − 1.30040I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = 1.46712 − 0.20243I
b = 0.14857 + 1.61358I
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.754878
a = −0.351052 + 0.514208I
b = 0.954075 − 0.645303I
1.11345 9.01950
u = 0.754878
a = −0.351052 − 0.514208I
b = 0.954075 + 0.645303I
1.11345 9.01950
u = 0.754878
a = −1.94733
b = −0.768470
1.11345 9.01950
16
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
10
=
1
0
a
9
=
1
1
a
3
=
1
0
a
6
=
−1
0
a
2
=
1
0
a
1
=
1
0
a
5
=
−1
0
a
8
=
0
1
a
11
=
1
−1
a
12
=
0
−1
a
7
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 18
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
c
3
, c
6
, c
7
c
9
, c
11
u + 1
c
4
, c
8
, c
10
c
12
u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
4.93480 18.0000
20
V. I
u
5
= hb − 1, a + 2, u − 1i
(i) Arc colorings
a
4
=
0
1
a
10
=
1
0
a
9
=
1
1
a
3
=
−1
0
a
6
=
−2
1
a
2
=
−3
1
a
1
=
−2
1
a
5
=
1
0
a
8
=
0
1
a
11
=
1
−1
a
12
=
−1
0
a
7
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
9
c
10
, c
12
u − 1
c
2
, c
3
, c
8
c
11
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 − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.00000
b = 1.00000
3.28987 12.0000
24
VI. I
u
6
= hb + 1, a, u + 1i
(i) Arc colorings
a
4
=
0
−1
a
10
=
1
0
a
9
=
1
1
a
3
=
1
0
a
6
=
0
−1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
−1
0
a
8
=
0
1
a
11
=
1
−1
a
12
=
1
−2
a
7
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
10
, c
12
u − 1
c
2
, c
4
, c
7
c
8
, c
9
, c
11
u + 1
26
(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
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = −1.00000
3.28987 12.0000
28
VII. I
u
7
= hb − 1, a + 1, u − 1i
(i) Arc colorings
a
4
=
0
1
a
10
=
1
0
a
9
=
1
1
a
3
=
−1
0
a
6
=
−1
1
a
2
=
−2
1
a
1
=
−1
1
a
5
=
1
0
a
8
=
0
1
a
11
=
1
−1
a
12
=
1
−1
a
7
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u + 1
c
2
, c
3
, c
5
c
7
, c
8
, c
9
c
10
u − 1
c
6
, c
11
, c
12
u
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
, c
9
, c
10
y − 1
c
6
, c
11
, c
12
y
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 1.00000
1.64493 6.00000
32
VIII. I
u
8
= h−u
2
+ b + u − 1, −u
3
+ u
2
+ a, u
4
+ 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
3
=
−u
−u
3
+ u
a
6
=
u
3
− u
2
u
2
− u + 1
a
2
=
−u
3
+ u
2
− u
−u
3
− u
2
+ 2u − 1
a
1
=
−u
3
+ u
2
−u
2
+ u − 1
a
5
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
−u
2
1
a
12
=
−u
3
−u
2
+ u
a
7
=
−u
2
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
c
12
(u − 1)
4
c
3
, c
4
, c
7
c
9
u
4
+ 1
c
5
, c
6
(u + 1)
4
c
8
, c
10
(u
2
+ 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
(y − 1)
4
c
3
, c
4
, c
7
c
9
(y
2
+ 1)
2
c
8
, c
10
(y + 1)
4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707107 + 0.707107I
a = −0.707107 − 0.292893I
b = 0.292893 + 0.292893I
−1.64493 4.00000
u = 0.707107 − 0.707107I
a = −0.707107 + 0.292893I
b = 0.292893 − 0.292893I
−1.64493 4.00000
u = −0.707107 + 0.707107I
a = 0.70711 + 1.70711I
b = 1.70711 − 1.70711I
−1.64493 4.00000
u = −0.707107 − 0.707107I
a = 0.70711 − 1.70711I
b = 1.70711 + 1.70711I
−1.64493 4.00000
36
IX. I
v
1
= ha, b − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
1
0
a
9
=
1
0
a
3
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
5
=
1
0
a
8
=
1
0
a
11
=
1
0
a
12
=
1
−1
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
11
c
12
u − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
u
c
5
, c
6
u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
, c
12
y − 1
c
3
, c
4
, c
7
c
8
, c
9
, c
10
y
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
0 0
40
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
11
(u + 1)
· (u
9
+ 6u
8
+ 15u
7
+ 17u
6
+ 3u
5
− 12u
4
− 9u
3
+ u
2
+ 2u + 1)
· (u
31
+ 49u
30
+ ··· − 15231u + 529)
c
2
u(u − 1)
6
(u + 1)
6
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
· (u
31
+ 3u
30
+ ··· + 77u − 23)
c
3
, c
9
u(u − 1)
2
(u + 1)
2
(u
3
+ u
2
− 1)
3
(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
31
− 2u
30
+ ··· + 4u − 2)
c
4
u
10
(u − 1)
2
(u + 1)
2
(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
31
+ 7u
30
+ ··· + 69324u − 24982)
c
5
u(u − 1)
7
(u + 1)
5
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
· (u
31
+ 3u
30
+ ··· + 77u − 23)
c
6
u(u − 1)
6
(u + 1)
6
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
· (u
31
− 3u
30
+ ··· + 9u − 9)
c
7
u(u − 1)
2
(u + 1)
2
(u
3
− u
2
+ 2u − 1)
3
(u
4
+ 1)(u
4
− u
2
+ 2)
· (u
31
+ 2u
30
+ ··· − 1028u − 3866)
c
8
u(u − 1)
2
(u + 1)
2
(u
2
+ 1)
2
(u
2
+ u + 2)
2
(u
3
− u
2
+ 2u − 1)
3
· (u
31
− 8u
30
+ ··· + 76u
2
− 4)
c
10
u(u − 1)
4
(u
2
+ 1)
2
(u
2
− u + 2)
2
(u
3
− u
2
+ 2u − 1)
3
· (u
31
− 8u
30
+ ··· + 76u
2
− 4)
c
11
u(u − 1)
5
(u + 1)
7
(u
9
− 3u
7
+ u
6
+ 3u
5
− 2u
4
+ u
3
+ u
2
− 2u + 1)
· (u
31
− 3u
30
+ ··· + 9u − 9)
c
12
u(u − 1)
12
(u
9
− 6u
8
+ ··· + 2u − 1)
· (u
31
− u
30
+ ··· − 783u − 81)
41
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y − 1)
12
· (y
9
− 6y
8
+ 27y
7
− 73y
6
+ 139y
5
− 184y
4
+ 83y
3
− 13y
2
+ 2y − 1)
· (y
31
− 121y
30
+ ··· + 137554745y − 279841)
c
2
, c
5
y(y − 1)
12
(y
9
− 6y
8
+ ··· + 2y − 1)
· (y
31
− 49y
30
+ ··· − 15231y − 529)
c
3
, c
9
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
3
− y
2
+ 2y − 1)
3
· (y
31
− 8y
30
+ ··· + 76y
2
− 4)
c
4
y
10
(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
· (y
31
+ 61y
30
+ ··· + 2635081032y − 624100324)
c
6
, c
11
y(y − 1)
12
(y
9
− 6y
8
+ ··· + 2y − 1)
· (y
31
− y
30
+ ··· − 783y − 81)
c
7
y(y − 1)
4
(y
2
+ 1)
2
(y
2
− y + 2)
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
31
+ 16y
30
+ ··· + 26974448y − 14945956)
c
8
, c
10
y(y − 1)
4
(y + 1)
4
(y
2
+ 3y + 4)
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
31
+ 28y
30
+ ··· + 608y − 16)
c
12
y(y − 1)
12
· (y
9
− 6y
8
+ 27y
7
− 73y
6
+ 139y
5
− 184y
4
+ 83y
3
− 13y
2
+ 2y − 1)
· (y
31
+ 71y
30
+ ··· + 24057y − 6561)
42
