12n
0549
(K12n
0549
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 12 2 6 5 6 8 9 10
Solving Sequence
2,6
7 3 8
4,10
11 1 9 12 5
c
6
c
2
c
7
c
3
c
10
c
1
c
9
c
12
c
5
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
3
− u
2
+ b, a − u, u
4
+ u
3
− 2u + 1i
I
u
2
= h−u
3
− u
2
+ b, a − u, u
4
+ u
3
+ 1i
I
u
3
= h−u
4
+ u
3
− u
2
+ b, a − u, u
6
− u
5
+ u
4
+ u
3
+ u
2
+ u + 1i
I
u
4
= h−u
5
+ 2u
4
− u
3
− u
2
+ b, −u
3
+ 2u
2
+ a − u, u
6
− u
5
+ u
4
+ u
3
+ u
2
+ u + 1i
I
u
5
= h−u
4
− u
2
+ 2b − u − 2, −3u
5
− u
4
− u
3
+ 10a − 9u − 8, u
6
+ 2u
5
+ 2u
4
+ 3u
2
+ 6u + 5i
I
u
6
= hb − u, −u
2
+ a + u, u
3
− u − 1i
I
u
7
= hb − u, u
2
+ a − u + 1, u
3
− u
2
+ 1i
I
u
8
= h−u
2
+ b + u, a − u, u
3
− u
2
+ 1i
I
u
9
= hb, a + 1, u + 1i
I
u
10
= hb − 1, a, u − 1i
I
u
11
= hb − 1, a − 1, u − 1i
I
v
1
= ha, b − 1, v + 1i
* 12 irreducible components of dim
C
= 0, with total 39 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
1
I. I
u
1
= h−u
3
− u
2
+ b, a − u, u
4
+ u
3
− 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
4
=
−4u
3
− u
2
+ 5u − 3
3u
3
− u
2
− 3u + 2
a
10
=
u
u
3
+ u
2
a
11
=
2u
3
+ u
2
− 2u + 1
−u
3
+ u
2
+ 2u − 1
a
1
=
u
3
2u
2
− 2u + 1
a
9
=
−u
3
− u
2
+ u
u
3
+ u
2
a
12
=
u
2
u
a
5
=
−u
3
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
3
+ 6u
2
− 12
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
4
+ u
3
+ 6u
2
+ 4u + 1
c
2
, c
5
, c
6
c
8
u
4
− u
3
+ 2u + 1
c
3
u
4
+ 8u
3
+ 66u
2
+ 56u + 13
c
4
, c
9
u
4
+ 6u
3
+ 12u
2
+ 9u + 3
c
10
, c
12
u
4
− 2u
3
+ 12u
2
+ 7u + 1
c
11
u
4
+ 4u
3
+ 6u
2
+ u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 11y
3
+ 30y
2
− 4y + 1
c
2
, c
5
, c
6
c
8
y
4
− y
3
+ 6y
2
− 4y + 1
c
3
y
4
+ 68y
3
+ 3486y
2
− 1420y + 169
c
4
, c
9
y
4
− 12y
3
+ 42y
2
− 9y + 9
c
10
, c
12
y
4
+ 20y
3
+ 174y
2
− 25y + 1
c
11
y
4
− 4y
3
+ 30y
2
+ 11y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621964 + 0.187730I
a = 0.621964 + 0.187730I
b = 0.526439 + 0.444772I
−1.130960 − 0.250238I −9.36589 + 2.03489I
u = 0.621964 − 0.187730I
a = 0.621964 − 0.187730I
b = 0.526439 − 0.444772I
−1.130960 + 0.250238I −9.36589 − 2.03489I
u = −1.12196 + 1.05376I
a = −1.12196 + 1.05376I
b = 2.47356 + 0.44477I
17.5803 + 11.9291I −4.13411 − 5.75934I
u = −1.12196 − 1.05376I
a = −1.12196 − 1.05376I
b = 2.47356 − 0.44477I
17.5803 − 11.9291I −4.13411 + 5.75934I
5
II. I
u
2
= h−u
3
− u
2
+ b, a − u, u
4
+ u
3
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
4
=
u
2
− u − 1
−u
3
− u
2
+ u
a
10
=
u
u
3
+ u
2
a
11
=
−u
2
− 1
u
3
+ u
2
+ 1
a
1
=
u
3
1
a
9
=
−u
3
− u
2
+ u
u
3
+ u
2
a
12
=
2u
3
+ u
2
−u
a
5
=
−u
3
− 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
3
+ 6u
2
+ 6u − 6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ 2u
2
+ 1
c
2
, c
5
, c
8
u
4
− u
3
+ 1
c
3
(u + 1)
4
c
4
, c
9
u
4
+ u + 1
c
6
u
4
+ u
3
+ 1
c
7
u
4
+ u
3
+ 2u
2
+ 1
c
10
, c
12
u
4
+ 2u
2
− u + 1
c
11
u
4
− 4u
3
+ 8u
2
− 9u + 5
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
2
, c
5
, c
6
c
8
y
4
− y
3
+ 2y
2
+ 1
c
3
(y −1)
4
c
4
, c
9
y
4
+ 2y
2
− y + 1
c
10
, c
12
y
4
+ 4y
3
+ 6y
2
+ 3y + 1
c
11
y
4
+ 2y
2
− y + 25
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518913 + 0.666610I
a = 0.518913 + 0.666610I
b = −0.727136 + 0.934099I
1.43949 − 4.22398I −2.28100 + 7.42378I
u = 0.518913 − 0.666610I
a = 0.518913 − 0.666610I
b = −0.727136 − 0.934099I
1.43949 + 4.22398I −2.28100 − 7.42378I
u = −1.018910 + 0.602565I
a = −1.018910 + 0.602565I
b = 0.727136 + 0.430014I
0.20545 + 7.54387I −8.21900 − 8.72596I
u = −1.018910 − 0.602565I
a = −1.018910 − 0.602565I
b = 0.727136 − 0.430014I
0.20545 − 7.54387I −8.21900 + 8.72596I
9
III. I
u
3
= h−u
4
+ u
3
− u
2
+ b, a − u, u
6
− u
5
+ u
4
+ u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
4
=
−2u
5
− 2u
4
− 2u
2
− 4u − 1
u
5
+ 2u
4
+ 2u
2
+ 3u + 1
a
10
=
u
u
4
− u
3
+ u
2
a
11
=
u
3
− 2u
2
− u − 2
−u
3
+ u
2
+ u + 1
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
−u
4
+ u
3
− u
2
+ u
u
4
− u
3
+ u
2
a
12
=
−u
4
+ u
3
− u
2
− 2u − 1
u
a
5
=
u
5
− u
4
+ u
3
+ 2u
2
+ u + 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5u
5
+ 10u
4
− 11u
3
+ u
2
− 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− u
5
+ 5u
4
− 5u
3
+ u
2
− u + 1
c
2
, c
5
, c
6
u
6
+ u
5
+ u
4
− u
3
+ u
2
− u + 1
c
3
u
6
− 3u
5
+ 45u
4
+ u
3
+ 155u
2
− 155u + 37
c
4
u
6
+ 3u
5
− 4u
4
− 17u
3
+ 2u
2
+ 32u + 24
c
8
u
6
− 2u
5
+ 2u
4
+ 3u
2
− 6u + 5
c
9
u
6
− 5u
5
+ 8u
4
− 9u
3
+ 12u
2
− 2u + 3
c
10
u
6
+ u
5
+ 14u
4
+ 19u
3
+ 60u
2
+ 44u + 61
c
11
u
6
− 2u
5
− u
4
+ 7u
3
− 4u
2
− 4u + 8
c
12
u
6
− 7u
5
+ 28u
4
− 65u
3
+ 78u
2
− 32u + 5
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
+ 9y
5
+ 17y
4
− 15y
3
+ y
2
+ y + 1
c
2
, c
5
, c
6
y
6
+ y
5
+ 5y
4
+ 5y
3
+ y
2
+ y + 1
c
3
y
6
+ 81y
5
+ 2341y
4
+ 13093y
3
+ 27665y
2
− 12555y + 1369
c
4
y
6
− 17y
5
+ 122y
4
− 449y
3
+ 900y
2
− 928y + 576
c
8
y
6
+ 10y
4
− 2y
3
+ 29y
2
− 6y + 25
c
9
y
6
− 9y
5
− 2y
4
+ 97y
3
+ 156y
2
+ 68y + 9
c
10
y
6
+ 27y
5
+ 278y
4
+ 1353y
3
+ 3636y
2
+ 5384y + 3721
c
11
y
6
− 6y
5
+ 21y
4
− 41y
3
+ 56y
2
− 80y + 64
c
12
y
6
+ 7y
5
+ 30y
4
− 295y
3
+ 2204y
2
− 244y + 25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.102788 + 0.875092I
a = 0.102788 + 0.875092I
b = 0.017830 + 0.550569I
2.61732 − 2.66854I −0.25508 + 2.31468I
u = 0.102788 − 0.875092I
a = 0.102788 − 0.875092I
b = 0.017830 − 0.550569I
2.61732 + 2.66854I −0.25508 − 2.31468I
u = −0.650074 + 0.404455I
a = −0.650074 + 0.404455I
b = 0.005272 − 1.244860I
0.04312 + 4.55341I −9.55430 − 8.62438I
u = −0.650074 − 0.404455I
a = −0.650074 − 0.404455I
b = 0.005272 + 1.244860I
0.04312 − 4.55341I −9.55430 + 8.62438I
u = 1.04729 + 1.04909I
a = 1.04729 + 1.04909I
b = −2.52310 − 0.11659I
17.9012 − 3.8563I −3.69061 + 2.17548I
u = 1.04729 − 1.04909I
a = 1.04729 − 1.04909I
b = −2.52310 + 0.11659I
17.9012 + 3.8563I −3.69061 − 2.17548I
13
IV.
I
u
4
= h−u
5
+2u
4
−u
3
−u
2
+b, −u
3
+2u
2
+a −u, u
6
−u
5
+u
4
+u
3
+u
2
+u +1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
4
=
−2u
5
− 2u
4
− 2u
2
− 4u − 1
u
5
+ 2u
4
+ 2u
2
+ 3u + 1
a
10
=
u
3
− 2u
2
+ u
u
5
− 2u
4
+ u
3
+ u
2
a
11
=
−2u
5
+ u
4
− 5u
2
+ 1
2u
5
− 2u
4
+ 2u
3
+ 3u
2
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
−u
5
+ 2u
4
− 3u
2
+ u
u
5
− 2u
4
+ u
3
+ u
2
a
12
=
2u
5
− 3u
4
+ 3u
3
+ 2u + 2
u
2
− u
a
5
=
−u
5
+ 2u
4
− 3u
3
− u
2
+ u − 2
−u
4
+ 2u
3
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5u
5
+ 10u
4
− 11u
3
+ u
2
− 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
− u
5
+ 5u
4
− 5u
3
+ u
2
− u + 1
c
2
, c
6
, c
8
u
6
+ u
5
+ u
4
− u
3
+ u
2
− u + 1
c
3
u
6
− 3u
5
+ 45u
4
+ u
3
+ 155u
2
− 155u + 37
c
4
u
6
− 5u
5
+ 8u
4
− 9u
3
+ 12u
2
− 2u + 3
c
5
u
6
− 2u
5
+ 2u
4
+ 3u
2
− 6u + 5
c
9
u
6
+ 3u
5
− 4u
4
− 17u
3
+ 2u
2
+ 32u + 24
c
10
u
6
− 7u
5
+ 28u
4
− 65u
3
+ 78u
2
− 32u + 5
c
11
u
6
− 2u
5
− u
4
+ 7u
3
− 4u
2
− 4u + 8
c
12
u
6
+ u
5
+ 14u
4
+ 19u
3
+ 60u
2
+ 44u + 61
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
+ 9y
5
+ 17y
4
− 15y
3
+ y
2
+ y + 1
c
2
, c
6
, c
8
y
6
+ y
5
+ 5y
4
+ 5y
3
+ y
2
+ y + 1
c
3
y
6
+ 81y
5
+ 2341y
4
+ 13093y
3
+ 27665y
2
− 12555y + 1369
c
4
y
6
− 9y
5
− 2y
4
+ 97y
3
+ 156y
2
+ 68y + 9
c
5
y
6
+ 10y
4
− 2y
3
+ 29y
2
− 6y + 25
c
9
y
6
− 17y
5
+ 122y
4
− 449y
3
+ 900y
2
− 928y + 576
c
10
y
6
+ 7y
5
+ 30y
4
− 295y
3
+ 2204y
2
− 244y + 25
c
11
y
6
− 6y
5
+ 21y
4
− 41y
3
+ 56y
2
− 80y + 64
c
12
y
6
+ 27y
5
+ 278y
4
+ 1353y
3
+ 3636y
2
+ 5384y + 3721
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.102788 + 0.875092I
a = 1.378180 − 0.127101I
b = −1.77318 + 0.52382I
2.61732 − 2.66854I −0.25508 + 2.31468I
u = 0.102788 − 0.875092I
a = 1.378180 + 0.127101I
b = −1.77318 − 0.52382I
2.61732 + 2.66854I −0.25508 − 2.31468I
u = −0.650074 + 0.404455I
a = −1.12379 + 1.90276I
b = 0.968507 + 0.557933I
0.04312 + 4.55341I −9.55430 − 8.62438I
u = −0.650074 − 0.404455I
a = −1.12379 − 1.90276I
b = 0.968507 − 0.557933I
0.04312 − 4.55341I −9.55430 + 8.62438I
u = 1.04729 + 1.04909I
a = −1.25438 − 1.04838I
b = 2.30468 − 0.55501I
17.9012 − 3.8563I −3.69061 + 2.17548I
u = 1.04729 − 1.04909I
a = −1.25438 + 1.04838I
b = 2.30468 + 0.55501I
17.9012 + 3.8563I −3.69061 − 2.17548I
17
V. I
u
5
=
h−u
4
−u
2
+2b−u−2, −3u
5
−u
4
−u
3
+10a−9u−8, u
6
+2u
5
+2u
4
+3u
2
+6u+5i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
4
=
4u
4
− u
3
+ 5u + 10
−u
5
− 4u
4
+ u
3
− 6u − 10
a
10
=
3
10
u
5
+
1
10
u
4
+ ··· +
9
10
u +
4
5
1
2
u
4
+
1
2
u
2
+
1
2
u + 1
a
11
=
3
10
u
5
+
13
5
u
4
+ ··· +
12
5
u +
24
5
−
1
2
u
5
− 2u
4
−
1
2
u
3
−
1
2
u
2
− 3u − 4
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
3
10
u
5
−
2
5
u
4
+ ··· +
2
5
u −
1
5
1
2
u
4
+
1
2
u
2
+
1
2
u + 1
a
12
=
4
5
u
5
+
11
10
u
4
+ ··· +
29
10
u +
14
5
−
1
2
u
5
−
1
2
u
4
− 2u −
3
2
a
5
=
−
3
10
u
5
−
1
10
u
4
+ ··· −
2
5
u −
3
10
1
2
u
5
+
1
2
u
4
+ u +
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1
2
u
5
+
3
2
u
4
+
5
2
u
3
+ 3u
2
−
3
2
u − 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
6
+ 10u
4
+ 2u
3
+ 29u
2
+ 6u + 25
c
2
, c
6
u
6
− 2u
5
+ 2u
4
+ 3u
2
− 6u + 5
c
3
u
6
+ 2u
5
+ 92u
4
+ 48u
3
+ 977u
2
+ 228u + 785
c
4
, c
9
u
6
− 5u
5
+ 8u
4
− 9u
3
+ 12u
2
− 2u + 3
c
5
, c
8
u
6
+ u
5
+ u
4
− u
3
+ u
2
− u + 1
c
10
, c
12
u
6
+ 4u
5
+ 18u
4
+ 66u
3
+ 77u
2
− 18u + 1
c
11
u
6
+ 9u
5
+ 35u
4
+ 71u
3
+ 75u
2
+ 33u + 5
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
+ 20y
5
+ 158y
4
+ 626y
3
+ 1317y
2
+ 1414y + 625
c
2
, c
6
y
6
+ 10y
4
− 2y
3
+ 29y
2
− 6y + 25
c
3
y
6
+ 180y
5
+ ··· + 1481906y + 616225
c
4
, c
9
y
6
− 9y
5
− 2y
4
+ 97y
3
+ 156y
2
+ 68y + 9
c
5
, c
8
y
6
+ y
5
+ 5y
4
+ 5y
3
+ y
2
+ y + 1
c
10
, c
12
y
6
+ 20y
5
− 50y
4
− 1438y
3
+ 8341y
2
− 170y + 1
c
11
y
6
− 11y
5
+ 97y
4
− 375y
3
+ 1289y
2
− 339y + 25
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.858009 + 0.695194I
a = 0.428810 + 0.557108I
b = 0.017830 − 0.550569I
2.61732 + 2.66854I −0.25508 − 2.31468I
u = −0.858009 − 0.695194I
a = 0.428810 − 0.557108I
b = 0.017830 + 0.550569I
2.61732 − 2.66854I −0.25508 + 2.31468I
u = 0.909086 + 0.930307I
a = 0.428314 + 0.140128I
b = 0.005272 + 1.244860I
0.04312 − 4.55341I −9.55430 + 8.62438I
u = 0.909086 − 0.930307I
a = 0.428314 − 0.140128I
b = 0.005272 − 1.244860I
0.04312 + 4.55341I −9.55430 − 8.62438I
u = −1.05108 + 1.14831I
a = 1.042880 − 0.951271I
b = −2.52310 − 0.11659I
17.9012 − 3.8563I −3.69061 + 2.17548I
u = −1.05108 − 1.14831I
a = 1.042880 + 0.951271I
b = −2.52310 + 0.11659I
17.9012 + 3.8563I −3.69061 − 2.17548I
21
VI. I
u
6
= hb − u, −u
2
+ a + u, u
3
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−1
a
8
=
−u
2
+ 1
u
2
a
4
=
1
−u
2
− 2u − 2
a
10
=
u
2
− u
u
a
11
=
u
2
− 2u
u
2
+ 2u
a
1
=
u + 1
u
2
+ u
a
9
=
u
2
− 2u
u
a
12
=
−u
2
+ u + 2
u
2
− 1
a
5
=
−2u
2
+ u + 2
u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
− 2u − 5
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
, c
12
u
3
− 2u
2
+ u − 1
c
2
, c
4
, c
9
u
3
− u + 1
c
3
u
3
+ 2u
2
− 3u + 1
c
5
, c
8
u
3
+ u
2
− 1
c
6
u
3
− u − 1
c
7
u
3
+ 2u
2
+ u + 1
c
11
u
3
− 5u
2
+ 8u − 5
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
c
12
y
3
− 2y
2
− 3y −1
c
2
, c
4
, c
6
c
9
y
3
− 2y
2
+ y −1
c
3
y
3
− 10y
2
+ 5y −1
c
5
, c
8
y
3
− y
2
+ 2y −1
c
11
y
3
− 9y
2
+ 14y −25
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662359 + 0.562280I
a = 0.78492 − 1.30714I
b = −0.662359 + 0.562280I
1.37919 − 2.82812I −4.28809 + 2.59975I
u = −0.662359 − 0.562280I
a = 0.78492 + 1.30714I
b = −0.662359 − 0.562280I
1.37919 + 2.82812I −4.28809 − 2.59975I
u = 1.32472
a = 0.430160
b = 1.32472
−2.75839 −16.4240
25
VII. I
u
7
= hb − u, u
2
+ a − u + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
8
=
−u
2
+ 1
u
2
a
4
=
1
0
a
10
=
−u
2
+ u − 1
u
a
11
=
u − 2
−u
2
+ u
a
1
=
u
2
− 1
−u
2
a
9
=
−u
2
− 1
u
a
12
=
u − 2
−u
2
+ u
a
5
=
−2u
2
+ 2u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
+ 7u − 10
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
, c
8
, c
9
u
3
+ u
2
− 1
c
4
, c
5
u
3
− u + 1
c
6
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
10
, c
12
(u + 1)
3
c
11
u
3
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
6
, c
8
c
9
y
3
− y
2
+ 2y −1
c
4
, c
5
y
3
− 2y
2
+ y −1
c
10
, c
12
(y −1)
3
c
11
y
3
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.337641 − 0.562280I
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −4.28809 + 2.59975I
u = 0.877439 − 0.744862I
a = −0.337641 + 0.562280I
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −4.28809 − 2.59975I
u = −0.754878
a = −2.32472
b = −0.754878
−2.75839 −16.4240
29
VIII. I
u
8
= h−u
2
+ b + u, a − u, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
8
=
−u
2
+ 1
u
2
a
4
=
1
0
a
10
=
u
u
2
− u
a
11
=
u
2
+ u − 1
−u
a
1
=
u
2
− 1
−u
2
a
9
=
−u
2
+ 2u
u
2
− u
a
12
=
u
2
+ u − 1
−u
a
5
=
2u
2
− u
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
+ 7u − 10
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
, c
4
, c
5
u
3
+ u
2
− 1
c
6
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
u
3
− u + 1
c
10
, c
12
(u + 1)
3
c
11
u
3
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
4
, c
5
c
6
y
3
− y
2
+ 2y −1
c
8
, c
9
y
3
− 2y
2
+ y −1
c
10
, c
12
(y −1)
3
c
11
y
3
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.877439 + 0.744862I
b = −0.662359 + 0.562280I
1.37919 − 2.82812I −4.28809 + 2.59975I
u = 0.877439 − 0.744862I
a = 0.877439 − 0.744862I
b = −0.662359 − 0.562280I
1.37919 + 2.82812I −4.28809 − 2.59975I
u = −0.754878
a = −0.754878
b = 1.32472
−2.75839 −16.4240
33
IX. I
u
9
= 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
8
=
0
1
a
4
=
1
1
a
10
=
−1
0
a
11
=
−1
−1
a
1
=
−1
−1
a
9
=
−1
0
a
12
=
−2
−1
a
5
=
−1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
c
11
, c
12
u + 1
c
2
, c
3
, c
5
c
6
, c
8
u − 1
c
4
, c
9
u
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y −1
c
4
, c
9
y
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
9
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−4.93480 −18.0000
37
X. I
u
10
= hb − 1, a, u − 1i
(i) Arc colorings
a
2
=
0
1
a
6
=
1
0
a
7
=
1
1
a
3
=
−1
0
a
8
=
0
1
a
4
=
−1
−1
a
10
=
0
1
a
11
=
0
1
a
1
=
1
1
a
9
=
−1
1
a
12
=
1
0
a
5
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
u + 1
c
5
, c
10
u
c
11
, c
12
u − 1
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
9
, c
11
c
12
y −1
c
5
, c
10
y
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
10
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
41
XI. I
u
11
= hb − 1, a − 1, u − 1i
(i) Arc colorings
a
2
=
0
1
a
6
=
1
0
a
7
=
1
1
a
3
=
−1
0
a
8
=
0
1
a
4
=
−1
−1
a
10
=
1
1
a
11
=
1
2
a
1
=
1
1
a
9
=
0
1
a
12
=
1
1
a
5
=
0
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
42
(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
9
u + 1
c
8
, c
12
u
c
10
, c
11
u − 1
43
(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
9
, c
10
c
11
y −1
c
8
, c
12
y
44
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
11
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.00000
−1.64493 −6.00000
45
XII. 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
8
=
1
0
a
4
=
−1
0
a
10
=
0
1
a
11
=
−1
1
a
1
=
−1
0
a
9
=
−1
1
a
12
=
−1
1
a
5
=
2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
46
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
11
u
c
4
, c
5
, c
8
c
9
, c
10
, c
12
u + 1
47
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
11
y
c
4
, c
5
, c
8
c
9
, c
10
, c
12
y −1
48
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−1.64493 −6.00000
49
XIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u + 1)
3
(u
3
− 2u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
4
− u
3
+ 2u
2
+ 1)
· (u
4
+ u
3
+ 6u
2
+ 4u + 1)(u
6
+ 10u
4
+ 2u
3
+ 29u
2
+ 6u + 25)
· (u
6
− u
5
+ 5u
4
− 5u
3
+ u
2
− u + 1)
2
c
2
, c
5
, c
8
u(u − 1)(u + 1)
2
(u
3
− u + 1)(u
3
+ u
2
− 1)
2
(u
4
− u
3
+ 1)(u
4
− u
3
+ 2u + 1)
· (u
6
− 2u
5
+ 2u
4
+ 3u
2
− 6u + 5)(u
6
+ u
5
+ u
4
− u
3
+ u
2
− u + 1)
2
c
3
u(u − 1)(u + 1)
6
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ 2u
2
− 3u + 1)
· (u
4
+ 8u
3
+ 66u
2
+ 56u + 13)
· (u
6
− 3u
5
+ 45u
4
+ u
3
+ 155u
2
− 155u + 37)
2
· (u
6
+ 2u
5
+ 92u
4
+ 48u
3
+ 977u
2
+ 228u + 785)
c
4
, c
9
u(u + 1)
3
(u
3
− u + 1)
2
(u
3
+ u
2
− 1)(u
4
+ u + 1)(u
4
+ 6u
3
+ ··· + 9u + 3)
· (u
6
− 5u
5
+ 8u
4
− 9u
3
+ 12u
2
− 2u + 3)
2
· (u
6
+ 3u
5
− 4u
4
− 17u
3
+ 2u
2
+ 32u + 24)
c
6
u(u − 1)(u + 1)
2
(u
3
− u − 1)(u
3
− u
2
+ 1)
2
(u
4
− u
3
+ 2u + 1)(u
4
+ u
3
+ 1)
· (u
6
− 2u
5
+ 2u
4
+ 3u
2
− 6u + 5)(u
6
+ u
5
+ u
4
− u
3
+ u
2
− u + 1)
2
c
7
u(u + 1)
3
(u
3
+ u
2
+ 2u + 1)
2
(u
3
+ 2u
2
+ u + 1)(u
4
+ u
3
+ 2u
2
+ 1)
· (u
4
+ u
3
+ 6u
2
+ 4u + 1)(u
6
+ 10u
4
+ 2u
3
+ 29u
2
+ 6u + 25)
· (u
6
− u
5
+ 5u
4
− 5u
3
+ u
2
− u + 1)
2
c
10
, c
12
u(u − 1)(u + 1)
8
(u
3
− 2u
2
+ u − 1)(u
4
+ 2u
2
− u + 1)
· (u
4
− 2u
3
+ 12u
2
+ 7u + 1)(u
6
− 7u
5
+ ··· − 32u + 5)
· (u
6
+ u
5
+ 14u
4
+ 19u
3
+ 60u
2
+ 44u + 61)
· (u
6
+ 4u
5
+ 18u
4
+ 66u
3
+ 77u
2
− 18u + 1)
c
11
u
7
(u − 1)
2
(u + 1)(u
3
− 5u
2
+ 8u − 5)(u
4
− 4u
3
+ 8u
2
− 9u + 5)
· (u
4
+ 4u
3
+ 6u
2
+ u + 1)(u
6
− 2u
5
− u
4
+ 7u
3
− 4u
2
− 4u + 8)
2
· (u
6
+ 9u
5
+ 35u
4
+ 71u
3
+ 75u
2
+ 33u + 5)
50
XIV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y(y −1)
3
(y
3
− 2y
2
− 3y −1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
4
+ 3y
3
+ 6y
2
+ 4y + 1)(y
4
+ 11y
3
+ 30y
2
− 4y + 1)
· (y
6
+ 9y
5
+ 17y
4
− 15y
3
+ y
2
+ y + 1)
2
· (y
6
+ 20y
5
+ 158y
4
+ 626y
3
+ 1317y
2
+ 1414y + 625)
c
2
, c
5
, c
6
c
8
y(y −1)
3
(y
3
− 2y
2
+ y −1)(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 1)
· (y
4
− y
3
+ 6y
2
− 4y + 1)(y
6
+ 10y
4
− 2y
3
+ 29y
2
− 6y + 25)
· (y
6
+ y
5
+ 5y
4
+ 5y
3
+ y
2
+ y + 1)
2
c
3
y(y −1)
7
(y
3
− 10y
2
+ 5y −1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
4
+ 68y
3
+ 3486y
2
− 1420y + 169)
· (y
6
+ 81y
5
+ 2341y
4
+ 13093y
3
+ 27665y
2
− 12555y + 1369)
2
· (y
6
+ 180y
5
+ ··· + 1481906y + 616225)
c
4
, c
9
y(y −1)
3
(y
3
− 2y
2
+ y −1)
2
(y
3
− y
2
+ 2y −1)(y
4
+ 2y
2
− y + 1)
· (y
4
− 12y
3
+ 42y
2
− 9y + 9)
· (y
6
− 17y
5
+ 122y
4
− 449y
3
+ 900y
2
− 928y + 576)
· (y
6
− 9y
5
− 2y
4
+ 97y
3
+ 156y
2
+ 68y + 9)
2
c
10
, c
12
y(y −1)
9
(y
3
− 2y
2
− 3y −1)(y
4
+ 4y
3
+ 6y
2
+ 3y + 1)
· (y
4
+ 20y
3
+ 174y
2
− 25y + 1)
· (y
6
+ 7y
5
+ 30y
4
− 295y
3
+ 2204y
2
− 244y + 25)
· (y
6
+ 20y
5
− 50y
4
− 1438y
3
+ 8341y
2
− 170y + 1)
· (y
6
+ 27y
5
+ 278y
4
+ 1353y
3
+ 3636y
2
+ 5384y + 3721)
c
11
y
7
(y −1)
3
(y
3
− 9y
2
+ 14y −25)(y
4
+ 2y
2
− y + 25)
· (y
4
− 4y
3
+ 30y
2
+ 11y + 1)
· (y
6
− 11y
5
+ 97y
4
− 375y
3
+ 1289y
2
− 339y + 25)
· (y
6
− 6y
5
+ 21y
4
− 41y
3
+ 56y
2
− 80y + 64)
2
51
