12n
0888
(K12n
0888
)
A knot diagram
1
Linearized knot diagam
6 7 11 12 10 2 12 1 5 6 4 8
Solving Sequence
1,6
2 7
3,10
11 4 5 9 8 12
c
1
c
6
c
2
c
10
c
3
c
5
c
9
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
3
+ 2b + 2u + 1, a − 1, u
4
− u
3
− 2u
2
+ 3u + 1i
I
u
2
= hu
3
a − u
3
− 2u
2
+ 2b + a + 1, −u
2
a + 2u
3
+ a
2
− au + 3u
2
+ 2u − 2, u
4
+ u
3
− u + 1i
I
u
3
= h−9u
7
+ 18u
6
+ 4u
5
− 32u
4
+ 32u
3
− 7u
2
+ 14b − 57u + 81,
9u
7
− 27u
6
− 4u
5
+ 36u
4
− 28u
3
+ 12u
2
+ 77a + 32u − 111,
u
8
− 3u
7
+ 2u
6
+ 4u
5
− 8u
4
+ 5u
3
+ 6u
2
− 16u + 11i
I
u
4
= h2b − u − 1, 3a + u, u
2
− 3i
I
u
5
= h2b + a − 1, a
2
− 3, u − 1i
I
u
6
= hb − 1, −u
3
+ 2u
2
+ 2a − u + 2, u
4
− 2u
3
+ u
2
− 2i
I
u
7
= h2b − 3, a + 1, u
2
+ 2u + 1i
I
u
8
= h2b + 1, a + 2u + 3, u
2
+ 2u + 1i
I
u
9
= h−u
3
+ b + u + 2, −u
3
+ a + 2, u
4
+ u
3
− 2u − 1i
I
u
10
= h2u
3
+ u
2
+ b − 2, a − 1, u
4
+ u
3
− 2u − 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
= hb + 1, a, u − 1i
I
u
12
= ha + 1, u + 1i
I
v
1
= ha, b + 1, v + 1i
* 12 irreducible components of dim
C
= 0, with total 42 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
= h−u
3
+ 2b + 2u + 1, a − 1, u
4
− u
3
− 2u
2
+ 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
3
+ 3u + 1
a
10
=
1
1
2
u
3
− u −
1
2
a
11
=
1
1
2
u
3
+ u
2
− u −
1
2
a
4
=
−u
2
+ u + 1
1
2
u
3
+ u +
1
2
a
5
=
u
1
2
u
3
− u −
1
2
a
9
=
−u
2
+ 1
u
a
8
=
−u
2
+ u + 1
u
a
12
=
u
3
− u
2
− u + 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
3
− 20
3
(iv) u-Polynomials at the component
Crossings u-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
u
4
− u
3
− 2u
2
+ 3u + 1
4
(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
4
− 5y
3
+ 12y
2
− 13y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45873
a = 1.00000
b = −0.593286
−18.4021 −26.2080
u = 1.37348 + 0.70139I
a = 1.00000
b = −1.59149 + 1.11079I
−2.06772 − 13.64080I −18.8720 + 7.2487I
u = 1.37348 − 0.70139I
a = 1.00000
b = −1.59149 − 1.11079I
−2.06772 + 13.64080I −18.8720 − 7.2487I
u = −0.288231
a = 1.00000
b = −0.223742
−0.491481 −20.0480
6
II. I
u
2
=
hu
3
a−u
3
−2u
2
+2b+a+1, −u
2
a+2u
3
+a
2
−au+3u
2
+2u−2, u
4
+u
3
−u+1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
u
3
+ 2u
2
− u + 1
a
10
=
a
−
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
a −
1
2
a
11
=
a
−
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
a −
1
2
a
4
=
u
3
+ u
2
− 1
−
1
2
u
3
a −
1
2
u
3
+
1
2
a − u +
1
2
a
5
=
u
3
a + u
2
a − u
3
− 2u
2
+ 2
−
1
2
u
3
a +
1
2
u
3
+ ··· −
1
2
a −
1
2
a
9
=
−u
3
− u
2
− 2u
u
a
8
=
−u
3
− u
2
− u
u
a
12
=
u
2
+ u
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
3
+ 6u
2
+ 2u − 18
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(u
4
+ u
3
− u + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
8
− 3u
7
+ 2u
6
+ 4u
5
− 8u
4
+ 5u
3
+ 6u
2
− 16u + 11
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y
4
− y
3
+ 4y
2
− y + 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
8
− 5y
7
+ 12y
6
− 6y
5
− 26y
4
+ 51y
3
+ 20y
2
− 124y + 121
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.566121 + 0.458821I
a = 1.69837 − 0.55270I
b = −1.27294 + 0.62687I
−3.95056 − 1.45022I −16.5601 + 4.7237I
u = 0.566121 + 0.458821I
a = −1.02228 + 1.53102I
b = 0.206818 + 0.237188I
−3.95056 − 1.45022I −16.5601 + 4.7237I
u = 0.566121 − 0.458821I
a = 1.69837 + 0.55270I
b = −1.27294 − 0.62687I
−3.95056 + 1.45022I −16.5601 − 4.7237I
u = 0.566121 − 0.458821I
a = −1.02228 − 1.53102I
b = 0.206818 − 0.237188I
−3.95056 + 1.45022I −16.5601 − 4.7237I
u = −1.066121 + 0.864054I
a = 0.424245 − 0.799184I
b = −0.903065 − 0.310360I
1.48316 + 6.78371I −15.4399 − 4.7237I
u = −1.066121 + 0.864054I
a = −1.100342 − 0.179134I
b = 1.46919 + 0.76918I
1.48316 + 6.78371I −15.4399 − 4.7237I
u = −1.066121 − 0.864054I
a = 0.424245 + 0.799184I
b = −0.903065 + 0.310360I
1.48316 − 6.78371I −15.4399 + 4.7237I
u = −1.066121 − 0.864054I
a = −1.100342 + 0.179134I
b = 1.46919 − 0.76918I
1.48316 − 6.78371I −15.4399 + 4.7237I
10
III. I
u
3
= h−9u
7
+ 18u
6
+ · · · + 14b + 81, 9u
7
− 27u
6
+ · · · + 77a − 111, u
8
−
3u
7
+ · · · − 16u + 11i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
−0.116883u
7
+ 0.350649u
6
+ ··· − 0.415584u + 1.44156
9
14
u
7
−
9
7
u
6
+ ··· +
57
14
u −
81
14
a
11
=
−0.116883u
7
+ 0.350649u
6
+ ··· − 0.415584u + 1.44156
13
14
u
7
−
9
7
u
6
+ ··· +
75
14
u −
81
14
a
4
=
0.0129870u
7
− 0.0389610u
6
+ ··· − 0.0649351u + 0.506494
−
3
14
u
7
+
1
7
u
6
+ ··· −
13
14
u +
9
14
a
5
=
0.0129870u
7
− 0.0389610u
6
+ ··· − 0.0649351u − 0.493506
−
1
14
u
7
+
1
7
u
6
+ ··· +
3
14
u +
9
14
a
9
=
−0.480519u
7
+ 0.870130u
6
+ ··· − 2.74026u + 2.68831
4
7
u
7
−
8
7
u
6
+ ··· +
23
7
u −
29
7
a
8
=
0.0909091u
7
− 0.272727u
6
+ ··· + 0.545455u − 1.45455
4
7
u
7
−
8
7
u
6
+ ··· +
23
7
u −
29
7
a
12
=
0.376623u
7
− 0.558442u
6
+ ··· + 2.25974u − 1.74026
4
7
u
7
−
9
7
u
6
+ ··· + 5u −
51
7
(ii) Obstruction class = −1
(iii) Cusp Shapes =
8
7
u
7
−
16
7
u
6
−
2
7
u
5
+
30
7
u
4
−
16
7
u
3
+
46
7
u −
170
7
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
u
8
− 3u
7
+ 2u
6
+ 4u
5
− 8u
4
+ 5u
3
+ 6u
2
− 16u + 11
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(u
4
+ u
3
− u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y
8
− 5y
7
+ 12y
6
− 6y
5
− 26y
4
+ 51y
3
+ 20y
2
− 124y + 121
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y
4
− y
3
+ 4y
2
− y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238242 + 1.218598I
a = 0.518207 + 0.976187I
b = −0.903065 − 0.310360I
1.48316 + 6.78371I −15.4399 − 4.7237I
u = 0.238242 − 1.218598I
a = 0.518207 − 0.976187I
b = −0.903065 + 0.310360I
1.48316 − 6.78371I −15.4399 + 4.7237I
u = 1.215075 + 0.466358I
a = 0.532414 + 0.173262I
b = −1.27294 + 0.62687I
−3.95056 − 1.45022I −16.5601 + 4.7237I
u = 1.215075 − 0.466358I
a = 0.532414 − 0.173262I
b = −1.27294 − 0.62687I
−3.95056 + 1.45022I −16.5601 − 4.7237I
u = −1.281196 + 0.397697I
a = −0.301641 − 0.451752I
b = 0.206818 + 0.237188I
−3.95056 − 1.45022I −16.5601 + 4.7237I
u = −1.281196 − 0.397697I
a = −0.301641 + 0.451752I
b = 0.206818 − 0.237188I
−3.95056 + 1.45022I −16.5601 − 4.7237I
u = 1.32788 + 0.75978I
a = −0.885344 − 0.144133I
b = 1.46919 − 0.76918I
1.48316 − 6.78371I −15.4399 + 4.7237I
u = 1.32788 − 0.75978I
a = −0.885344 + 0.144133I
b = 1.46919 + 0.76918I
1.48316 + 6.78371I −15.4399 − 4.7237I
14
IV. I
u
4
= h2b − u − 1, 3a + u, u
2
− 3i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
3
a
7
=
−u
−2u
a
3
=
−2
−3
a
10
=
−
1
3
u
1
2
u +
1
2
a
11
=
−
1
3
u
−
1
2
u +
1
2
a
4
=
1
3
u − 2
1
2
u −
7
2
a
5
=
1
3
u
1
2
u −
1
2
a
9
=
0
u
a
8
=
u
u
a
12
=
−2
−3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
u
2
− 3
c
3
, c
4
, c
9
c
10
(u + 1)
2
c
5
, c
11
(u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y −3)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73205
a = −0.577350
b = 1.36603
−16.4493 −24.0000
u = −1.73205
a = 0.577350
b = −0.366025
−16.4493 −24.0000
18
V. I
u
5
= h2b + a − 1, a
2
− 3, u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
1
a
2
=
1
1
a
7
=
−1
0
a
3
=
0
1
a
10
=
a
−
1
2
a +
1
2
a
11
=
a
1
2
a +
1
2
a
4
=
−3
−
1
2
a −
1
2
a
5
=
3
1
2
a −
1
2
a
9
=
−2a
−1
a
8
=
−2a − 1
−1
a
12
=
−2a
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(u − 1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
2
− 3
c
6
, c
12
(u + 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
(y −1)
2
c
3
, c
4
, c
5
c
9
, c
10
, c
11
(y −3)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.73205
b = −0.366025
−16.4493 −24.0000
u = 1.00000
a = −1.73205
b = 1.36603
−16.4493 −24.0000
22
VI. I
u
6
= hb − 1, −u
3
+ 2u
2
+ 2a − u + 2, u
4
− 2u
3
+ u
2
− 2i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−2u
3
+ 3u
2
− 2
a
10
=
1
2
u
3
− u
2
+
1
2
u − 1
1
a
11
=
1
2
u
3
− u
2
+
1
2
u − 1
−u
2
+ u + 1
a
4
=
1
2
u
3
− 2u
2
+
3
2
u − 1
−u
3
+ u
2
− 1
a
5
=
1
2
u
3
− u
2
+
3
2
u − 2
1
a
9
=
u
2
− 3u + 2
u
a
8
=
u
2
− 2u + 2
u
a
12
=
−u
3
+ 2u
2
− 2u + 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-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
u
4
− 2u
3
+ u
2
− 2
24
(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
4
− 2y
3
− 3y
2
− 4y + 4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 1.078987I
a = −0.646447 − 0.762959I
b = 1.00000
4.11234 −12.0000
u = 0.500000 − 1.078987I
a = −0.646447 + 0.762959I
b = 1.00000
4.11234 −12.0000
u = −0.790044
a = −2.26575
b = 1.00000
−15.6269 −12.0000
u = 1.79004
a = −0.441355
b = 1.00000
−15.6269 −12.0000
26
VII. I
u
7
= h2b − 3, a + 1, u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−2u − 1
a
7
=
−u
−2u − 2
a
3
=
2u + 2
1
a
10
=
−1
1.5
a
11
=
−1
2u +
5
2
a
4
=
u
5
2
u + 4
a
5
=
u
−
1
2
u
a
9
=
−2u − 2
u + 2
a
8
=
−u
u + 2
a
12
=
0
−2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
11
(u + 1)
2
c
3
, c
4
, c
6
c
9
, c
10
, c
12
(u − 1)
2
28
(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)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 1.50000
−6.57974 −24.0000
u = −1.00000
a = −1.00000
b = 1.50000
−6.57974 −24.0000
30
VIII. I
u
8
= h2b + 1, a + 2u + 3, u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−2u − 1
a
7
=
−u
−2u − 2
a
3
=
2u + 2
1
a
10
=
−2u − 3
−0.5
a
11
=
−2u − 3
−1.5
a
4
=
u
3
2
u + 1
a
5
=
−3u − 4
1
2
u − 1
a
9
=
2u + 2
u + 2
a
8
=
3u + 4
u + 2
a
12
=
−4u − 4
−2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
31
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
11
(u + 1)
2
c
3
, c
4
, c
6
c
9
, c
10
, c
12
(u − 1)
2
32
(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)
2
33
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −0.500000
−6.57974 −24.0000
u = −1.00000
a = −1.00000
b = −0.500000
−6.57974 −24.0000
34
IX. I
u
9
= h−u
3
+ b + u + 2, −u
3
+ a + 2, u
4
+ u
3
− 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
u
3
+ 2u
2
− 2u − 1
a
10
=
u
3
− 2
u
3
− u − 2
a
11
=
u
3
− 2
2u
3
− 2u − 3
a
4
=
−u
3
− u
2
+ 2
−u
3
− u + 1
a
5
=
2u
3
+ u
2
− u − 3
u
3
+ u
2
+ u − 2
a
9
=
−u
2
+ 1
−u
3
+ 1
a
8
=
−u
3
− u
2
+ 2
−u
3
+ 1
a
12
=
u
3
− 1
u
3
+ u
2
− u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14
35
(iv) u-Polynomials at the component
Crossings u-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
u
4
+ u
3
− 2u − 1
36
(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
4
− y
3
+ 2y
2
− 4y + 1
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = 1.15372
a = −0.464313
b = −1.61803
−5.59278 −14.0000
u = −0.809017 + 0.981593I
a = −0.190983 + 0.981593I
b = 0.618034
2.30291 −14.0000
u = −0.809017 − 0.981593I
a = −0.190983 − 0.981593I
b = 0.618034
2.30291 −14.0000
u = −0.535687
a = −2.15372
b = −1.61803
−5.59278 −14.0000
38
X. I
u
10
= h2u
3
+ u
2
+ b − 2, a − 1, u
4
+ u
3
− 2u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
u
3
+ 2u
2
− 2u − 1
a
10
=
1
−2u
3
− u
2
+ 2
a
11
=
1
−2u
3
+ 2
a
4
=
−u
3
− u
2
+ 2
−u
3
+ 3
a
5
=
u
u
3
− u − 2
a
9
=
−u
2
+ 1
−u
3
+ 1
a
8
=
−u
3
− u
2
+ 2
−u
3
+ 1
a
12
=
u
3
− 1
u
3
+ u
2
− u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14
39
(iv) u-Polynomials at the component
Crossings u-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
u
4
+ u
3
− 2u − 1
40
(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
4
− y
3
+ 2y
2
− 4y + 1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 1.15372
a = 1.00000
b = −2.40245
−5.59278 −14.0000
u = −0.809017 + 0.981593I
a = 1.00000
b = −1.309017 − 0.374935I
2.30291 −14.0000
u = −0.809017 − 0.981593I
a = 1.00000
b = −1.309017 + 0.374935I
2.30291 −14.0000
u = −0.535687
a = 1.00000
b = 2.02048
−5.59278 −14.0000
42
XI. I
u
11
= hb + 1, a, u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
1
a
2
=
1
1
a
7
=
−1
0
a
3
=
0
1
a
10
=
0
−1
a
11
=
0
−1
a
4
=
0
1
a
5
=
0
1
a
9
=
0
−1
a
8
=
−1
−1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
12
u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
46
XII. I
u
12
= ha + 1, u + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
−1
a
2
=
1
1
a
7
=
1
0
a
3
=
0
1
a
10
=
−1
b
a
11
=
−1
b − 1
a
4
=
−1
b
a
5
=
−1
b − 1
a
9
=
0
1
a
8
=
1
1
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −24
(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 = ···
−6.57974 −24.0000
48
XIII. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
−1
0
a
2
=
1
0
a
7
=
−1
0
a
3
=
1
0
a
10
=
0
−1
a
11
=
1
−1
a
4
=
0
1
a
5
=
−1
1
a
9
=
−1
0
a
8
=
−1
0
a
12
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
49
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
u
c
3
, c
4
, c
9
c
10
u + 1
c
5
, c
11
u − 1
50
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y −1
51
(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
52
XIV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
11
u(u − 1)
3
(u + 1)
4
(u
2
− 3)(u
4
− 2u
3
+ u
2
− 2)(u
4
− u
3
+ ··· + 3u + 1)
· (u
4
+ u
3
− 2u − 1)
2
(u
4
+ u
3
− u + 1)
2
· (u
8
− 3u
7
+ 2u
6
+ 4u
5
− 8u
4
+ 5u
3
+ 6u
2
− 16u + 11)
c
3
, c
4
, c
6
c
9
, c
10
, c
12
u(u − 1)
4
(u + 1)
3
(u
2
− 3)(u
4
− 2u
3
+ u
2
− 2)(u
4
− u
3
+ ··· + 3u + 1)
· (u
4
+ u
3
− 2u − 1)
2
(u
4
+ u
3
− u + 1)
2
· (u
8
− 3u
7
+ 2u
6
+ 4u
5
− 8u
4
+ 5u
3
+ 6u
2
− 16u + 11)
53
XV. Riley Polynomials
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(y − 3)
2
(y −1)
7
(y
4
− 5y
3
+ ··· − 13y + 1)(y
4
− 2y
3
+ ··· − 4y + 4)
· (y
4
− y
3
+ 2y
2
− 4y + 1)
2
(y
4
− y
3
+ 4y
2
− y + 1)
2
· (y
8
− 5y
7
+ 12y
6
− 6y
5
− 26y
4
+ 51y
3
+ 20y
2
− 124y + 121)
54
