12n
0642
(K12n
0642
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 12 2 4 3 5 7 6
Solving Sequence
7,11 3,12
2 8
1,5
4 6 10 9
c
11
c
2
c
7
c
1
c
4
c
6
c
10
c
9
c
3
, c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hd − u, u
2
+ 2c + 1, u
2
+ 2b − 2u + 1, a − 1, u
3
+ u
2
+ 3u − 1i
I
u
2
= hd − u, u
3
− u
2
+ 2c + 3u − 1, −u
3
+ u
2
+ 2b − 3u − 1, a − 1, u
4
+ 4u
2
+ 2u + 1i
I
u
3
= hd − u, u
3
− u
2
+ 2c + 3u − 1, u
3
− u
2
+ 2b + u − 1, −u
3
+ u
2
+ 2a − 5u + 3, u
4
+ 4u
2
+ 2u + 1i
I
u
4
= hu
3
− u
2
+ 2d + 5u + 1, u
3
+ c + 4u + 2, −u
3
+ u
2
+ 2b − 3u − 1, a − 1, u
4
+ 4u
2
+ 2u + 1i
I
u
5
= hu
3
+ u
2
+ 2d + 2u + 2, u
3
+ 3u
2
+ 4c + 4u + 4, u
3
+ u
2
+ b + u + 1, −u
3
− u
2
+ 4a − 2u,
u
4
+ 3u
3
+ 4u
2
+ 4u + 4i
I
u
6
= hd − u, c − u + 2, b + 1, 2a + u + 1, u
2
− u + 2i
I
u
7
= hd + u − 1, 2c + u − 1, b + 1, 2a + u + 1, u
2
− u + 2i
I
u
8
= hd + u − 1, 2c + u − 1, b + 2u, a − 1, u
2
− u + 2i
I
u
9
= hd, c + u, b + u, a + 1, u
2
+ 1i
I
u
10
= hd + u, c + u + 1, b − 1, a, u
2
+ 1i
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
= hd + u, c + u + 1, b + u, a + 1, u
2
+ 1i
I
u
12
= hd + u, cb + bu − u − 1, a + 1, u
2
+ 1i
I
v
1
= ha, d − v, −av + c − v + 1, b −1, v
2
+ 1i
* 12 irreducible components of dim
C
= 0, with total 33 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
= hd − u, u
2
+ 2c + 1, u
2
+ 2b − 2u + 1, a − 1, u
3
+ u
2
+ 3u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
1
−
1
2
u
2
+ u −
1
2
a
12
=
1
−u
2
a
2
=
1
1
2
u
2
+ u −
1
2
a
8
=
u
1
2
u
2
− u +
1
2
a
1
=
u
2
+ 1
−4u + 1
a
5
=
−
1
2
u
2
−
1
2
u
a
4
=
−
1
2
u
2
− u −
1
2
u
a
6
=
−u
−u
2
− 2u + 1
a
10
=
1
2
u
2
+ u +
1
2
u
2
a
9
=
1
2
u
2
+
1
2
−
1
2
u
2
− u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
2
+ 8u + 18
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ 5u
2
+ 11u − 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
3
+ u
2
+ 3u − 1
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
− 3y
2
+ 131y −1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
3
+ 5y
2
+ 11y −1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295598
a = 1.00000
b = −0.248091
c = −0.543689
d = 0.295598
0.476945 20.7140
u = −0.64780 + 1.72143I
a = 1.00000
b = 0.12405 + 2.83658I
c = 0.771845 + 1.115140I
d = −0.64780 + 1.72143I
12.0985 − 12.7092I 2.64285 + 4.85033I
u = −0.64780 − 1.72143I
a = 1.00000
b = 0.12405 − 2.83658I
c = 0.771845 − 1.115140I
d = −0.64780 − 1.72143I
12.0985 + 12.7092I 2.64285 − 4.85033I
6
II.
I
u
2
= hd−u, u
3
−u
2
+2c+3u−1, −u
3
+u
2
+2b−3u−1, a−1, u
4
+4u
2
+2u+1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
1
1
2
u
3
−
1
2
u
2
+
3
2
u +
1
2
a
12
=
1
−u
2
a
2
=
1
1
2
u
3
+
1
2
u
2
+
3
2
u +
1
2
a
8
=
u
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
a
1
=
u
2
+ 1
2u
2
+ 2u + 1
a
5
=
−
1
2
u
3
+
1
2
u
2
−
3
2
u +
1
2
u
a
4
=
−
1
2
u
3
+
1
2
u
2
−
5
2
u +
1
2
u
a
6
=
−u
u
3
+ u
a
10
=
1
2
u
3
+
1
2
u
2
+
3
2
u +
3
2
u
2
a
9
=
u
3
+ 4u + 2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 14u + 12
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 8u
3
+ 18u
2
+ 4u + 1
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
u
4
+ 4u
2
+ 2u + 1
c
3
, c
8
, c
9
u
4
+ 3u
3
+ 4u
2
+ 4u + 4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 28y
3
+ 262y
2
+ 20y + 1
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
3
, c
8
, c
9
y
4
− y
3
+ 16y + 16
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264316 + 0.422125I
a = 1.00000
b = 0.219104 + 0.751390I
c = 0.780896 − 0.751390I
d = −0.264316 + 0.422125I
−2.86313 − 1.17563I 8.79089 + 5.96277I
u = −0.264316 − 0.422125I
a = 1.00000
b = 0.219104 − 0.751390I
c = 0.780896 + 0.751390I
d = −0.264316 − 0.422125I
−2.86313 + 1.17563I 8.79089 − 5.96277I
u = 0.26432 + 1.99036I
a = 1.00000
b = 1.28090 − 1.27441I
c = −0.280896 + 1.274410I
d = 0.26432 + 1.99036I
19.3125 + 4.7517I 3.20911 − 2.00586I
u = 0.26432 − 1.99036I
a = 1.00000
b = 1.28090 + 1.27441I
c = −0.280896 − 1.274410I
d = 0.26432 − 1.99036I
19.3125 − 4.7517I 3.20911 + 2.00586I
10
III. I
u
3
= hd − u, u
3
− u
2
+ 2c + 3u − 1, u
3
− u
2
+ 2b + u − 1, −u
3
+ u
2
+
2a − 5u + 3, u
4
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
1
2
u
3
−
1
2
u
2
+
5
2
u −
3
2
−
1
2
u
3
+
1
2
u
2
−
1
2
u +
1
2
a
12
=
1
−u
2
a
2
=
1
2
u
3
−
1
2
u
2
+
5
2
u −
3
2
1
a
8
=
3
2
u
3
−
1
2
u
2
+
11
2
u +
5
2
−
1
2
u
3
+
1
2
u
2
−
3
2
u −
1
2
a
1
=
u
2
+ 1
2u
2
+ 2u + 1
a
5
=
−
1
2
u
3
+
1
2
u
2
−
3
2
u +
1
2
u
a
4
=
−
1
2
u
3
+
1
2
u
2
−
5
2
u +
1
2
u
a
6
=
−u
u
3
+ u
a
10
=
1
2
u
3
+
1
2
u
2
+
3
2
u +
3
2
u
2
a
9
=
u
3
+ 4u + 2
−
1
2
u
3
−
1
2
u
2
−
3
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 14u + 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ 16u + 16
c
2
, c
7
u
4
+ 3u
3
+ 4u
2
+ 4u + 4
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
u
4
+ 4u
2
+ 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− y
3
+ 64y
2
− 256y + 256
c
2
, c
7
y
4
− y
3
+ 16y + 16
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264316 + 0.422125I
a = −2.04521 + 1.17351I
b = 0.516580 − 0.329264I
c = 0.780896 − 0.751390I
d = −0.264316 + 0.422125I
−2.86313 − 1.17563I 8.79089 + 5.96277I
u = −0.264316 − 0.422125I
a = −2.04521 − 1.17351I
b = 0.516580 + 0.329264I
c = 0.780896 + 0.751390I
d = −0.264316 − 0.422125I
−2.86313 + 1.17563I 8.79089 − 5.96277I
u = 0.26432 + 1.99036I
a = −0.454787 + 0.715953I
b = −0.01658 + 3.26477I
c = −0.280896 + 1.274410I
d = 0.26432 + 1.99036I
19.3125 + 4.7517I 3.20911 − 2.00586I
u = 0.26432 − 1.99036I
a = −0.454787 − 0.715953I
b = −0.01658 − 3.26477I
c = −0.280896 − 1.274410I
d = 0.26432 − 1.99036I
19.3125 − 4.7517I 3.20911 + 2.00586I
14
IV. I
u
4
= hu
3
− u
2
+ 2d + 5u + 1, u
3
+ c + 4u + 2, −u
3
+ u
2
+ 2b − 3u −
1, a − 1, u
4
+ 4u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
1
1
2
u
3
−
1
2
u
2
+
3
2
u +
1
2
a
12
=
1
−u
2
a
2
=
1
1
2
u
3
+
1
2
u
2
+
3
2
u +
1
2
a
8
=
u
1
2
u
3
−
1
2
u
2
+
1
2
u −
1
2
a
1
=
u
2
+ 1
2u
2
+ 2u + 1
a
5
=
−u
3
− 4u − 2
−
1
2
u
3
+
1
2
u
2
−
5
2
u −
1
2
a
4
=
−
1
2
u
3
−
1
2
u
2
−
3
2
u −
3
2
−
1
2
u
3
+
1
2
u
2
−
5
2
u −
1
2
a
6
=
−u
u
3
+ u
a
10
=
1
2
u
3
−
1
2
u
2
+
5
2
u −
1
2
−
1
2
u
3
−
1
2
u
2
−
1
2
u −
3
2
a
9
=
1
2
u
3
−
1
2
u
2
+
3
2
u −
1
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
3
+ 14u + 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 8u
3
+ 18u
2
+ 4u + 1
c
2
, c
3
, c
6
c
7
, c
8
, c
9
c
11
, c
12
u
4
+ 4u
2
+ 2u + 1
c
4
, c
5
, c
10
u
4
+ 3u
3
+ 4u
2
+ 4u + 4
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 28y
3
+ 262y
2
+ 20y + 1
c
2
, c
3
, c
6
c
7
, c
8
, c
9
c
11
, c
12
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
4
, c
5
, c
10
y
4
− y
3
+ 16y + 16
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.264316 + 0.422125I
a = 1.00000
b = 0.219104 + 0.751390I
c = −1.06556 − 1.70176I
d = 0.045213 − 1.173520I
−2.86313 − 1.17563I 8.79089 + 5.96277I
u = −0.264316 − 0.422125I
a = 1.00000
b = 0.219104 − 0.751390I
c = −1.06556 + 1.70176I
d = 0.045213 + 1.173520I
−2.86313 + 1.17563I 8.79089 − 5.96277I
u = 0.26432 + 1.99036I
a = 1.00000
b = 1.28090 − 1.27441I
c = 0.065564 − 0.493715I
d = −1.54521 − 0.71595I
19.3125 + 4.7517I 3.20911 − 2.00586I
u = 0.26432 − 1.99036I
a = 1.00000
b = 1.28090 + 1.27441I
c = 0.065564 + 0.493715I
d = −1.54521 + 0.71595I
19.3125 − 4.7517I 3.20911 + 2.00586I
18
V. I
u
5
= hu
3
+ u
2
+ 2d + 2u + 2, u
3
+ 3u
2
+ 4c + 4u + 4, u
3
+ u
2
+ b + u +
1, −u
3
− u
2
+ 4a − 2u, u
4
+ 3u
3
+ 4u
2
+ 4u + 4i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
1
4
u
3
+
1
4
u
2
+
1
2
u
−u
3
− u
2
− u − 1
a
12
=
1
−u
2
a
2
=
1
4
u
3
+
1
4
u
2
+
1
2
u
1
a
8
=
3
4
u
3
+
5
4
u
2
+ u + 2
−
1
2
u
3
−
1
2
u
2
− 1
a
1
=
u
2
+ 1
3u
3
+ 2u
2
+ 4u + 4
a
5
=
−
1
4
u
3
−
3
4
u
2
− u − 1
−
1
2
u
3
−
1
2
u
2
− u − 1
a
4
=
1
4
u
3
−
1
4
u
2
−
1
2
u
3
−
1
2
u
2
− u − 1
a
6
=
−u
u
3
+ u
a
10
=
1
4
u
3
+
1
4
u
2
+
1
2
u + 1
−u
3
− 2u
2
− u − 3
a
9
=
−
1
2
u
3
− u
2
−
1
2
u − 1
1
2
u
3
+
3
2
u
2
+ u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
3
− 5u
2
− 6u + 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 8u
3
+ 18u
2
+ 4u + 1
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
u
4
+ 4u
2
+ 2u + 1
c
6
, c
11
, c
12
u
4
+ 3u
3
+ 4u
2
+ 4u + 4
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 28y
3
+ 262y
2
+ 20y + 1
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
y
4
+ 8y
3
+ 18y
2
+ 4y + 1
c
6
, c
11
, c
12
y
4
− y
3
+ 16y + 16
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.045213 + 1.173520I
a = −0.367842 + 0.211063I
b = 0.516580 + 0.329264I
c = 0.032782 − 0.850878I
d = −0.264316 − 0.422125I
−2.86313 + 1.17563I 8.79089 − 5.96277I
u = 0.045213 − 1.173520I
a = −0.367842 − 0.211063I
b = 0.516580 − 0.329264I
c = 0.032782 + 0.850878I
d = −0.264316 + 0.422125I
−2.86313 − 1.17563I 8.79089 + 5.96277I
u = −1.54521 + 0.71595I
a = −0.632158 + 0.995180I
b = −0.01658 − 3.26477I
c = −0.532782 − 0.246857I
d = 0.26432 − 1.99036I
19.3125 − 4.7517I 3.20911 + 2.00586I
u = −1.54521 − 0.71595I
a = −0.632158 − 0.995180I
b = −0.01658 + 3.26477I
c = −0.532782 + 0.246857I
d = 0.26432 + 1.99036I
19.3125 + 4.7517I 3.20911 − 2.00586I
22
VI. I
u
6
= hd − u, c − u + 2, b + 1, 2a + u + 1, u
2
− u + 2i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
−
1
2
u −
1
2
−1
a
12
=
1
−u + 2
a
2
=
−
1
2
u −
1
2
1
a
8
=
1
2
u −
3
2
1
a
1
=
u − 1
u + 2
a
5
=
u − 2
u
a
4
=
−2
u
a
6
=
−u
−2
a
10
=
−u − 1
u − 2
a
9
=
−
3
2
u +
1
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 3u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
− u + 2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
2
+ 3y + 4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = −0.750000 − 0.661438I
b = −1.00000
c = −1.50000 + 1.32288I
d = 0.50000 + 1.32288I
−8.22467 2.00000
u = 0.50000 − 1.32288I
a = −0.750000 + 0.661438I
b = −1.00000
c = −1.50000 − 1.32288I
d = 0.50000 − 1.32288I
−8.22467 2.00000
26
VII. I
u
7
= hd + u − 1, 2c + u − 1, b + 1, 2a + u + 1, u
2
− u + 2i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
−
1
2
u −
1
2
−1
a
12
=
1
−u + 2
a
2
=
−
1
2
u −
1
2
1
a
8
=
1
2
u −
3
2
1
a
1
=
u − 1
u + 2
a
5
=
−
1
2
u +
1
2
−u + 1
a
4
=
1
2
u −
1
2
−u + 1
a
6
=
−u
−2
a
10
=
−
1
2
u +
1
2
−u − 1
a
9
=
1
2
u −
1
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 3u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
− u + 2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
2
+ 3y + 4
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = −0.750000 − 0.661438I
b = −1.00000
c = 0.250000 − 0.661438I
d = 0.50000 − 1.32288I
−8.22467 2.00000
u = 0.50000 − 1.32288I
a = −0.750000 + 0.661438I
b = −1.00000
c = 0.250000 + 0.661438I
d = 0.50000 + 1.32288I
−8.22467 2.00000
30
VIII. I
u
8
= hd + u − 1, 2c + u − 1, b + 2u, a − 1, u
2
− u + 2i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
1
−2u
a
12
=
1
−u + 2
a
2
=
1
−u − 2
a
8
=
u
−2u + 2
a
1
=
u − 1
u + 2
a
5
=
−
1
2
u +
1
2
−u + 1
a
4
=
1
2
u −
1
2
−u + 1
a
6
=
−u
−2
a
10
=
−
1
2
u +
1
2
−u − 1
a
9
=
1
2
u −
1
2
−u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
+ 3u + 4
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
− u + 2
32
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− y + 16
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
2
+ 3y + 4
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.50000 + 1.32288I
a = 1.00000
b = −1.00000 − 2.64575I
c = 0.250000 − 0.661438I
d = 0.50000 − 1.32288I
−8.22467 2.00000
u = 0.50000 − 1.32288I
a = 1.00000
b = −1.00000 + 2.64575I
c = 0.250000 + 0.661438I
d = 0.50000 + 1.32288I
−8.22467 2.00000
34
IX. I
u
9
= hd, c + u, b + u, a + 1, u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
−1
−u
a
12
=
1
1
a
2
=
−1
−u + 1
a
8
=
u
−1
a
1
=
0
1
a
5
=
−u
0
a
4
=
−u
0
a
6
=
−u
0
a
10
=
1
0
a
9
=
u + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
3
, c
6
c
7
, c
8
, c
9
c
11
, c
12
u
2
+ 1
c
4
, c
5
, c
10
u
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
3
, c
6
c
7
, c
8
, c
9
c
11
, c
12
(y + 1)
2
c
4
, c
5
, c
10
y
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = − 1.000000I
c = − 1.000000I
d = 0
−4.93480 4.00000
u = − 1.000000I
a = −1.00000
b = 1.000000I
c = 1.000000I
d = 0
−4.93480 4.00000
38
X. I
u
10
= hd + u, c + u + 1, b − 1, a, u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
0
1
a
12
=
1
1
a
2
=
0
1
a
8
=
0
u
a
1
=
0
1
a
5
=
−u − 1
−u
a
4
=
−1
−u
a
6
=
−u
0
a
10
=
u
−1
a
9
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
u
2
+ 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
2
c
3
, c
4
, c
5
c
6
, c
8
, c
9
c
10
, c
11
, c
12
(y + 1)
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0
b = 1.00000
c = −1.00000 − 1.00000I
d = − 1.000000I
−4.93480 4.00000
u = − 1.000000I
a = 0
b = 1.00000
c = −1.00000 + 1.00000I
d = 1.000000I
−4.93480 4.00000
42
XI. I
u
11
= hd + u, c + u + 1, b + u, a + 1, u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
−1
−u
a
12
=
1
1
a
2
=
−1
−u + 1
a
8
=
u
−1
a
1
=
0
1
a
5
=
−u − 1
−u
a
4
=
−1
−u
a
6
=
−u
0
a
10
=
u
−1
a
9
=
u
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
u
2
+ 1
c
3
, c
8
, c
9
u
2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
(y + 1)
2
c
3
, c
8
, c
9
y
2
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −1.00000
b = − 1.000000I
c = −1.00000 − 1.00000I
d = − 1.000000I
−4.93480 4.00000
u = − 1.000000I
a = −1.00000
b = 1.000000I
c = −1.00000 + 1.00000I
d = 1.000000I
−4.93480 4.00000
46
XII. I
u
12
= hd + u, cb + bu − u − 1, a + 1, u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
3
=
−1
b
a
12
=
1
1
a
2
=
−1
b + 1
a
8
=
u
−bu
a
1
=
0
1
a
5
=
c
−u
a
4
=
c + u
−u
a
6
=
−u
0
a
10
=
−cu + 1
−1
a
9
=
−cu + u + 1
−bu − 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.
47
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
12
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
−6.57974 −2.00000
48
XIII. I
v
1
= ha, d − v, −av + c − v + 1, b − 1, v
2
+ 1i
(i) Arc colorings
a
7
=
v
0
a
11
=
1
0
a
3
=
0
1
a
12
=
1
0
a
2
=
1
1
a
8
=
0
−v
a
1
=
1
0
a
5
=
v −1
v
a
4
=
−1
v
a
6
=
v
0
a
10
=
−v
−1
a
9
=
−v
−v −1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4
49
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
u
2
+ 1
c
6
, c
11
, c
12
u
2
50
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
2
c
2
, c
3
, c
4
c
5
, c
7
, c
8
c
9
, c
10
(y + 1)
2
c
6
, c
11
, c
12
y
2
51
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.000000I
a = 0
b = 1.00000
c = −1.00000 + 1.00000I
d = 1.000000I
−4.93480 4.00000
v = − 1.000000I
a = 0
b = 1.00000
c = −1.00000 − 1.00000I
d = − 1.000000I
−4.93480 4.00000
52
XIV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
6
(u
2
+ 3u + 4)
3
(u
3
+ 5u
2
+ 11u − 1)(u
4
− u
3
+ 16u + 16)
· (u
4
+ 8u
3
+ 18u
2
+ 4u + 1)
3
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
(u
2
+ 1)
3
(u
2
− u + 2)
3
(u
3
+ u
2
+ 3u − 1)(u
4
+ 4u
2
+ 2u + 1)
3
· (u
4
+ 3u
3
+ 4u
2
+ 4u + 4)
53
XV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y −1)
6
(y
2
− y + 16)
3
(y
3
− 3y
2
+ 131y −1)
· (y
4
− 28y
3
+ 262y
2
+ 20y + 1)
3
(y
4
− y
3
+ 64y
2
− 256y + 256)
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
y
2
(y + 1)
6
(y
2
+ 3y + 4)
3
(y
3
+ 5y
2
+ 11y −1)(y
4
− y
3
+ 16y + 16)
· (y
4
+ 8y
3
+ 18y
2
+ 4y + 1)
3
54
