11n
78
(K11n
78
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 9 10 4 7 1 6
Solving Sequence
1,4 2,8
9
3,6
11 5 10 7
c
1
c
8
c
3
c
11
c
5
c
10
c
7
c
2
, c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
10
− u
9
+ 6u
8
+ 5u
7
− 12u
6
− 5u
5
+ 10u
4
− 4u
3
− 6u
2
+ 2d + u + 1,
u
8
+ u
7
− 6u
6
− 4u
5
+ 12u
4
+ u
3
− 8u
2
+ 2c + 8u − 1,
− u
10
− 2u
9
+ 5u
8
+ 12u
7
− 8u
6
− 23u
5
+ 9u
4
+ 16u
3
− 15u
2
+ 4b − 3u + 2,
− u
10
− 2u
9
+ 6u
8
+ 12u
7
− 14u
6
− 21u
5
+ 21u
4
+ 5u
3
− 22u
2
+ 2a + 10u,
u
11
+ 2u
10
− 6u
9
− 12u
8
+ 13u
7
+ 21u
6
− 17u
5
− 7u
4
+ 18u
3
− 3u
2
− u − 1i
I
u
2
= h−u
7
− 3u
6
+ u
5
+ 3u
4
− 5u
3
+ 6u
2
+ 4d + 7u − 2, u
7
+ 7u
6
+ 7u
5
− 7u
4
+ u
3
+ 2u
2
+ 8c − 23u − 14,
u
7
+ 3u
6
− u
5
− 3u
4
+ 5u
3
− 2u
2
+ 4b − 7u − 2, 3u
7
+ 7u
6
− u
5
− 3u
4
+ 5u
3
− 8u
2
+ 4a − 13u − 8,
u
8
+ u
7
− 3u
6
− u
5
+ 3u
4
− 4u
3
− 3u
2
+ 4u + 4i
I
u
3
= hd + u − 1, c + 1, au + 2b − 1, a
2
− 2au − 4a − u, u
2
+ u − 1i
I
u
4
= h−u
3
+ u
2
+ d − u, u
3
+ c + 1, b − u, a, u
4
− u
3
+ 2u − 1i
I
u
5
= hd + u − 1, c + 1, b − u, a, u
2
+ u − 1i
I
u
6
= hd + 1, c, b, a + 1, u − 1i
I
u
7
= hd − 1, c, b − 1, a, u − 1i
I
u
8
= hda − 1, c, b − 1, u − 1i
I
v
1
= ha, d, c − 1, b + 1, v − 1i
* 8 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).
1
* 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
10
− u
9
+ · · · + 2d + 1, u
8
+ u
7
+ · · · + 2c − 1, −u
10
− 2u
9
+ · · · +
4b + 2, −u
10
− 2u
9
+ · · · + 2a + 10u, u
11
+ 2u
10
+ · · · − u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
−
1
2
u
8
−
1
2
u
7
+ ··· − 4u +
1
2
1
2
u
10
+
1
2
u
9
+ ··· −
1
2
u −
1
2
a
9
=
−
1
2
u
8
−
1
2
u
7
+ ··· − 4u +
1
2
−
1
2
u
7
+ 2u
5
+ ··· −
1
2
u −
1
2
a
3
=
−u
2
+ 1
u
2
a
6
=
1
2
u
10
+ u
9
+ ··· + 11u
2
− 5u
1
4
u
10
+
1
2
u
9
+ ··· +
3
4
u −
1
2
a
11
=
−
1
2
u
10
−
3
4
u
9
+ ··· +
19
4
u +
3
4
−
1
4
u
9
+
5
4
u
7
+ ··· +
1
4
u +
3
4
a
5
=
−u
−u
3
+ u
a
10
=
−
1
2
u
10
−
1
2
u
9
+ ··· − 7u
2
+
9
2
u
−
1
4
u
9
+
5
4
u
7
+ ··· +
1
4
u +
3
4
a
7
=
1
2
u
10
+
1
2
u
9
+ ··· + 7u
2
−
9
2
u
1
4
u
10
+
1
2
u
9
+ ··· +
1
4
u −
1
2
a
7
=
1
2
u
10
+
1
2
u
9
+ ··· + 7u
2
−
9
2
u
1
4
u
10
+
1
2
u
9
+ ··· +
1
4
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −u
10
−
7
2
u
9
+ 4u
8
+
45
2
u
7
− u
6
− 47u
5
−
3
2
u
4
+
71
2
u
3
− 20u
2
−
23
2
u −
1
2
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
9
u
11
− 2u
10
+ ··· − u + 1
c
2
u
11
+ 16u
10
+ ··· − 5u + 1
c
3
, c
8
u
11
− 2u
10
− u
9
+ 8u
8
− 11u
7
+ 46u
5
− 76u
4
+ 32u
3
+ 12u
2
− 16u + 8
c
5
, c
11
u
11
+ 2u
10
+ u
9
− 2u
8
+ 5u
6
+ 7u
5
− 6u
4
− 13u
3
− 3u
2
+ 8u + 4
c
10
u
11
− 2u
10
+ ··· + 88u − 16
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
9
y
11
− 16y
10
+ ··· − 5y − 1
c
2
y
11
− 36y
10
+ ··· − 93y − 1
c
3
, c
8
y
11
− 6y
10
+ ··· + 64y − 64
c
5
, c
11
y
11
− 2y
10
+ ··· + 88y − 16
c
10
y
11
+ 14y
10
+ ··· + 2336y − 256
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552760 + 0.641799I
a = −0.712390 − 0.815288I
b = 0.792159 − 0.569904I
c = 0.940583 − 0.816704I
d = −0.608897 + 0.153639I
−0.79689 − 3.53286I −6.46290 + 7.08687I
u = 0.552760 − 0.641799I
a = −0.712390 + 0.815288I
b = 0.792159 + 0.569904I
c = 0.940583 + 0.816704I
d = −0.608897 − 0.153639I
−0.79689 + 3.53286I −6.46290 − 7.08687I
u = 0.590824
a = −0.0396568
b = 0.563771
c = −1.04963
d = 0.389828
−0.987118 −9.97440
u = 1.64391 + 0.11631I
a = −0.234439 + 1.284060I
b = −0.962808 + 0.959946I
c = 0.077846 − 1.022100I
d = −0.065433 + 0.634970I
−10.83450 − 3.51232I −10.06687 + 2.29315I
u = 1.64391 − 0.11631I
a = −0.234439 − 1.284060I
b = −0.962808 − 0.959946I
c = 0.077846 + 1.022100I
d = −0.065433 − 0.634970I
−10.83450 + 3.51232I −10.06687 − 2.29315I
u = −1.60901 + 0.41639I
a = −0.194428 + 1.371430I
b = 1.29448 + 0.81734I
c = −1.048640 + 0.270416I
d = 2.42888 + 0.22926I
−14.9243 + 12.3125I −9.62929 − 5.75829I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60901 − 0.41639I
a = −0.194428 − 1.371430I
b = 1.29448 − 0.81734I
c = −1.048640 − 0.270416I
d = 2.42888 − 0.22926I
−14.9243 − 12.3125I −9.62929 + 5.75829I
u = −0.162723 + 0.277330I
a = 0.22673 − 2.50982I
b = −0.937916 − 0.171871I
c = 0.96637 − 1.53134I
d = −0.472206 − 0.461294I
1.66390 + 0.61823I 3.63835 − 1.22407I
u = −0.162723 − 0.277330I
a = 0.22673 + 2.50982I
b = −0.937916 + 0.171871I
c = 0.96637 + 1.53134I
d = −0.472206 + 0.461294I
1.66390 − 0.61823I 3.63835 + 1.22407I
u = −1.72035 + 0.28600I
a = 0.434360 − 0.920646I
b = 0.532201 − 1.268140I
c = 1.088660 − 0.174544I
d = −2.47725 − 0.13447I
−17.3830 + 4.9116I −11.49209 − 1.65700I
u = −1.72035 − 0.28600I
a = 0.434360 + 0.920646I
b = 0.532201 + 1.268140I
c = 1.088660 + 0.174544I
d = −2.47725 + 0.13447I
−17.3830 − 4.9116I −11.49209 + 1.65700I
7
II. I
u
2
= h−u
7
− 3u
6
+ · · · + 4d − 2, u
7
+ 7u
6
+ · · · + 8c − 14, u
7
+ 3u
6
+
· · · + 4b − 2, 3u
7
+ 7u
6
+ · · · + 4a − 8, u
8
+ u
7
+ · · · + 4u + 4i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
−
1
8
u
7
−
7
8
u
6
+ ··· +
23
8
u +
7
4
1
4
u
7
+
3
4
u
6
+ ··· −
7
4
u +
1
2
a
9
=
−
1
8
u
7
−
7
8
u
6
+ ··· +
23
8
u +
7
4
−
1
4
u
7
−
3
4
u
6
+ ··· +
7
4
u +
7
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−
3
4
u
7
−
7
4
u
6
+ ··· +
13
4
u + 2
−
1
4
u
7
−
3
4
u
6
+ ··· +
7
4
u +
1
2
a
11
=
7
8
u
7
+
13
8
u
6
+ ··· −
33
8
u −
7
4
1
2
u
7
+
1
2
u
6
+ ··· − 2u
2
−
3
2
u
a
5
=
−u
−u
3
+ u
a
10
=
3
8
u
7
+
9
8
u
6
+ ··· −
21
8
u −
7
4
1
2
u
7
+
1
2
u
6
+ ··· − 2u
2
−
3
2
u
a
7
=
−
3
8
u
7
−
9
8
u
6
+ ··· +
21
8
u +
7
4
1
2
u
7
+
1
2
u
6
+ ··· −
1
2
u + 2
a
7
=
−
3
8
u
7
−
9
8
u
6
+ ··· +
21
8
u +
7
4
1
2
u
7
+
1
2
u
6
+ ··· −
1
2
u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 6u
6
+ 4u
5
− 6u
3
+ 14u
2
+ 14u − 4
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
9
u
8
− u
7
− 3u
6
+ u
5
+ 3u
4
+ 4u
3
− 3u
2
− 4u + 4
c
2
u
8
+ 7u
7
+ 17u
6
+ 17u
5
+ 19u
4
+ 50u
3
+ 65u
2
+ 40u + 16
c
3
, c
8
(u
4
+ 3u
3
+ 3u
2
+ 2u + 2)
2
c
5
, c
11
(u
4
+ u
3
− u + 1)
2
c
10
(u
4
− u
3
+ 4u
2
− u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
9
y
8
− 7y
7
+ 17y
6
− 17y
5
+ 19y
4
− 50y
3
+ 65y
2
− 40y + 16
c
2
y
8
− 15y
7
+ 89y
6
− 213y
5
+ 343y
4
− 846y
3
+ 833y
2
+ 480y + 256
c
3
, c
8
(y
4
− 3y
3
+ y
2
+ 8y + 4)
2
c
5
, c
11
(y
4
− y
3
+ 4y
2
− y + 1)
2
c
10
(y
4
+ 7y
3
+ 16y
2
+ 7y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.695289 + 0.428533I
a = 0.542307 − 0.680462I
b = −0.566121 − 0.458821I
c = −0.623998 + 0.858133I
d = 1.26633 + 1.05473I
−2.62917 + 1.45022I −7.43990 − 4.72374I
u = −0.695289 − 0.428533I
a = 0.542307 + 0.680462I
b = −0.566121 + 0.458821I
c = −0.623998 − 0.858133I
d = 1.26633 − 1.05473I
−2.62917 − 1.45022I −7.43990 + 4.72374I
u = 0.529919 + 1.081980I
a = −0.865083 − 0.577452I
b = 1.066120 − 0.864054I
c = −0.913781 + 0.999915I
d = 0.823753 − 0.282672I
−8.06290 − 6.78371I −8.56010 + 4.72374I
u = 0.529919 − 1.081980I
a = −0.865083 + 0.577452I
b = 1.066120 + 0.864054I
c = −0.913781 − 0.999915I
d = 0.823753 + 0.282672I
−8.06290 + 6.78371I −8.56010 − 4.72374I
u = 1.261410 + 0.030288I
a = −1.29231 − 1.30385I
b = −0.566121 − 0.458821I
c = 0.035950 − 0.685854I
d = −0.024117 + 0.382409I
−2.62917 + 1.45022I −7.43990 − 4.72374I
u = 1.261410 − 0.030288I
a = −1.29231 + 1.30385I
b = −0.566121 + 0.458821I
c = 0.035950 + 0.685854I
d = −0.024117 − 0.382409I
−2.62917 − 1.45022I −7.43990 + 4.72374I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.59604 + 0.21793I
a = 0.115083 + 1.406860I
b = 1.066120 + 0.864054I
c = 1.001830 − 0.150682I
d = −2.56597 − 0.16841I
−8.06290 + 6.78371I −8.56010 − 4.72374I
u = −1.59604 − 0.21793I
a = 0.115083 − 1.406860I
b = 1.066120 − 0.864054I
c = 1.001830 + 0.150682I
d = −2.56597 + 0.16841I
−8.06290 − 6.78371I −8.56010 + 4.72374I
12
III. I
u
3
= hd + u − 1, c + 1, au + 2b − 1, a
2
− 2au − 4a − u, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
8
=
−1
−u + 1
a
9
=
−1
0
a
3
=
u
−u + 1
a
6
=
a
−
1
2
au +
1
2
a
11
=
−au −
1
2
a +
1
2
u +
1
2
−
1
2
au +
1
2
a +
1
2
u
a
5
=
−u
−u + 1
a
10
=
−
1
2
au − a +
1
2
−
1
2
au +
1
2
a +
1
2
u
a
7
=
1
2
au + a −
1
2
−
1
2
au +
1
2
a
7
=
1
2
au + a −
1
2
−
1
2
au +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
(u
2
− u − 1)
2
c
2
(u
2
+ 3u + 1)
2
c
5
, c
6
, c
7
c
9
, c
11
u
4
+ u
3
− 2u − 1
c
10
u
4
− u
3
+ 2u
2
− 4u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
(y
2
− 3y + 1)
2
c
2
(y
2
− 7y + 1)
2
c
5
, c
6
, c
7
c
9
, c
11
y
4
− y
3
+ 2y
2
− 4y + 1
c
10
y
4
+ 3y
3
− 2y
2
− 12y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.115487
b = 0.535687
c = −1.00000
d = 0.381966
−0.986960 −10.0000
u = 0.618034
a = 5.35155
b = −1.15372
c = −1.00000
d = 0.381966
−0.986960 −10.0000
u = −1.61803
a = 0.381966 + 1.213320I
b = 0.809017 + 0.981593I
c = −1.00000
d = 2.61803
−8.88264 −10.0000
u = −1.61803
a = 0.381966 − 1.213320I
b = 0.809017 − 0.981593I
c = −1.00000
d = 2.61803
−8.88264 −10.0000
16
IV. I
u
4
= h−u
3
+ u
2
+ d − u, u
3
+ c + 1, b − u, a, u
4
− u
3
+ 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
−u
3
− 1
u
3
− u
2
+ u
a
9
=
−u
3
− 1
2u − 1
a
3
=
−u
2
+ 1
u
2
a
6
=
0
u
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
10
=
−u
2
+ 1
u
2
a
7
=
u
2
− 1
u
3
− 2u
2
+ 1
a
7
=
u
2
− 1
u
3
− 2u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
11
u
4
+ u
3
− 2u − 1
c
2
u
4
+ u
3
+ 2u
2
+ 4u + 1
c
3
, c
6
, c
7
c
8
, c
9
(u
2
− u − 1)
2
c
10
u
4
− u
3
+ 2u
2
− 4u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
4
− y
3
+ 2y
2
− 4y + 1
c
2
, c
10
y
4
+ 3y
3
− 2y
2
− 12y + 1
c
3
, c
6
, c
7
c
8
, c
9
(y
2
− 3y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15372
a = 0
b = −1.15372
c = 0.535687
d = −4.02048
−0.986960 −10.0000
u = 0.809017 + 0.981593I
a = 0
b = 0.809017 + 0.981593I
c = 0.809017 − 0.981593I
d = −0.690983 + 0.374935I
−8.88264 −10.0000
u = 0.809017 − 0.981593I
a = 0
b = 0.809017 − 0.981593I
c = 0.809017 + 0.981593I
d = −0.690983 − 0.374935I
−8.88264 −10.0000
u = 0.535687
a = 0
b = 0.535687
c = −1.15372
d = 0.402448
−0.986960 −10.0000
20
V. I
u
5
= hd + u − 1, c + 1, b − u, a, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
8
=
−1
−u + 1
a
9
=
−1
0
a
3
=
u
−u + 1
a
6
=
0
u
a
11
=
1
−u + 1
a
5
=
−u
−u + 1
a
10
=
u
−u + 1
a
7
=
−u
u
a
7
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
u
2
− u − 1
c
2
u
2
+ 3u + 1
c
10
u
2
− 3u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
y
2
− 3y + 1
c
2
, c
10
y
2
− 7y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = 0.618034
c = −1.00000
d = 0.381966
−0.986960 −10.0000
u = −1.61803
a = 0
b = −1.61803
c = −1.00000
d = 2.61803
−8.88264 −10.0000
24
VI. I
u
6
= hd + 1, c, b, a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
8
=
0
−1
a
9
=
0
−1
a
3
=
0
1
a
6
=
−1
0
a
11
=
1
0
a
5
=
−1
0
a
10
=
1
0
a
7
=
−1
−1
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
6
, c
7
u − 1
c
2
, c
4
, c
9
u + 1
c
3
, c
5
, c
8
c
10
, c
11
u
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
9
y − 1
c
3
, c
5
, c
8
c
10
, c
11
y
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
c = 0
d = −1.00000
−3.28987 −12.0000
28
VII. I
u
7
= hd − 1, c, b − 1, a, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
8
=
0
1
a
9
=
0
1
a
3
=
0
1
a
6
=
0
1
a
11
=
1
1
a
5
=
−1
0
a
10
=
0
1
a
7
=
0
1
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u − 1
c
2
, c
4
, c
5
c
10
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
, c
11
y − 1
c
3
, c
6
, c
7
c
8
, c
9
y
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
c = 0
d = 1.00000
0 0
32
VIII. I
u
8
= hda − 1, c, b − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
8
=
0
d
a
9
=
0
d
a
3
=
0
1
a
6
=
a
1
a
11
=
a + 1
1
a
5
=
−1
0
a
10
=
a
1
a
7
=
a
d + 1
a
7
=
a
d + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ a
2
− 8
(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.
33
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
−1.64493 −5.90156 − 0.11931I
34
IX. I
v
1
= ha, d, c − 1, b + 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
1
0
a
2
=
1
0
a
8
=
1
0
a
9
=
1
0
a
3
=
1
0
a
6
=
0
−1
a
11
=
1
1
a
5
=
1
0
a
10
=
0
1
a
7
=
1
−1
a
7
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
c
5
, c
6
, c
7
u − 1
c
9
, c
10
, c
11
u + 1
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y − 1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
c = 1.00000
d = 0
0 0
38
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u(u − 1)
2
(u
2
− u − 1)
3
(u
4
+ u
3
− 2u − 1)
· (u
8
− u
7
+ ··· − 4u + 4)(u
11
− 2u
10
+ ··· − u + 1)
c
2
u(u + 1)
2
(u
2
+ 3u + 1)
3
(u
4
+ u
3
+ 2u
2
+ 4u + 1)
· (u
8
+ 7u
7
+ 17u
6
+ 17u
5
+ 19u
4
+ 50u
3
+ 65u
2
+ 40u + 16)
· (u
11
+ 16u
10
+ ··· − 5u + 1)
c
3
, c
8
u
3
(u
2
− u − 1)
5
(u
4
+ 3u
3
+ 3u
2
+ 2u + 2)
2
· (u
11
− 2u
10
− u
9
+ 8u
8
− 11u
7
+ 46u
5
− 76u
4
+ 32u
3
+ 12u
2
− 16u + 8)
c
4
, c
9
u(u + 1)
2
(u
2
− u − 1)
3
(u
4
+ u
3
− 2u − 1)
· (u
8
− u
7
+ ··· − 4u + 4)(u
11
− 2u
10
+ ··· − u + 1)
c
5
, c
11
u(u − 1)(u + 1)(u
2
− u − 1)(u
4
+ u
3
− 2u − 1)
2
(u
4
+ u
3
− u + 1)
2
· (u
11
+ 2u
10
+ u
9
− 2u
8
+ 5u
6
+ 7u
5
− 6u
4
− 13u
3
− 3u
2
+ 8u + 4)
c
10
u(u + 1)
2
(u
2
− 3u + 1)(u
4
− u
3
+ 2u
2
− 4u + 1)
2
· ((u
4
− u
3
+ 4u
2
− u + 1)
2
)(u
11
− 2u
10
+ ··· + 88u − 16)
39
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
7
, c
9
y(y − 1)
2
(y
2
− 3y + 1)
3
(y
4
− y
3
+ 2y
2
− 4y + 1)
· (y
8
− 7y
7
+ 17y
6
− 17y
5
+ 19y
4
− 50y
3
+ 65y
2
− 40y + 16)
· (y
11
− 16y
10
+ ··· − 5y − 1)
c
2
y(y − 1)
2
(y
2
− 7y + 1)
3
(y
4
+ 3y
3
− 2y
2
− 12y + 1)
· (y
8
− 15y
7
+ 89y
6
− 213y
5
+ 343y
4
− 846y
3
+ 833y
2
+ 480y + 256)
· (y
11
− 36y
10
+ ··· − 93y − 1)
c
3
, c
8
y
3
(y
2
− 3y + 1)
5
(y
4
− 3y
3
+ y
2
+ 8y + 4)
2
· (y
11
− 6y
10
+ ··· + 64y − 64)
c
5
, c
11
y(y − 1)
2
(y
2
− 3y + 1)(y
4
− y
3
+ 2y
2
− 4y + 1)
2
· ((y
4
− y
3
+ 4y
2
− y + 1)
2
)(y
11
− 2y
10
+ ··· + 88y − 16)
c
10
y(y − 1)
2
(y
2
− 7y + 1)(y
4
+ 3y
3
− 2y
2
− 12y + 1)
2
· ((y
4
+ 7y
3
+ 16y
2
+ 7y + 1)
2
)(y
11
+ 14y
10
+ ··· + 2336y − 256)
40
