11n
126
(K11n
126
)
A knot diagram
1
Linearized knot diagam
5 1 10 7 2 9 11 5 1 8 4
Solving Sequence
4,11 1,8
7 5 10 3 2 6 9
c
11
c
7
c
4
c
10
c
3
c
2
c
5
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hb + u, a − u − 1, u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 2u − 1i
I
u
2
= hb + u, a − u + 1, u
4
− u
3
+ u
2
+ u − 1i
I
u
3
= hb + u, u
5
+ u
3
+ u
2
+ a, u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
4
= h−u
5
− 3u
4
− 4u
3
− 3u
2
+ b − 3u − 1, u
5
+ 4u
4
+ 7u
3
+ 7u
2
+ 2a + 6u + 4,
u
6
+ 4u
5
+ 7u
4
+ 7u
3
+ 6u
2
+ 4u + 2i
I
u
5
= h−u
5
+ u
4
− 2u
3
+ u
2
+ b − 2u + 1, u
5
− u
4
+ 2u
3
− u
2
+ a + 2u − 2, u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
6
= hb − u + 1, a + u, u
2
+ 1i
I
u
7
= hb − u + 1, 2a + u − 2, u
2
− 2u + 2i
I
u
8
= hb + u, a − 2u − 1, u
2
+ 1i
* 8 irreducible components of dim
C
= 0, with total 33 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
= hb + u, a − u − 1, u
5
+ 2u
4
+ 4u
3
+ 2u
2
+ 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
u + 1
−u
a
7
=
1
−u
a
5
=
−u
u
2
+ u
a
10
=
u
2
+ u + 1
−u
2
a
3
=
−u
3
− u + 1
u
4
+ 3u
3
+ 2u
2
+ 3u − 1
a
2
=
−u
4
− u
3
− u
2
+ 1
−2u
3
− 2u + 1
a
6
=
2u
4
+ 2u
3
+ 2u
2
− 1
5u
3
+ 2u
2
+ 6u − 2
a
9
=
−u
4
− u
3
− u
2
+ u + 1
−2u
3
− u
2
− 3u + 1
a
9
=
−u
4
− u
3
− u
2
+ u + 1
−2u
3
− u
2
− 3u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
4
− 9u
3
− 12u
2
− 9u − 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
8
u
5
+ 4u
4
+ 3u
3
− 2u
2
+ u + 1
c
2
u
5
+ 10u
4
+ 27u
3
+ 6u
2
+ 5u + 1
c
4
, c
7
, c
10
c
11
u
5
− 2u
4
+ 4u
3
− 2u
2
+ 2u + 1
c
6
, c
9
u
5
− 6u
4
+ 12u
3
− 9u
2
+ 5u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
y
5
− 10y
4
+ 27y
3
− 6y
2
+ 5y −1
c
2
y
5
− 46y
4
+ 619y
3
+ 214y
2
+ 13y −1
c
4
, c
7
, c
10
c
11
y
5
+ 4y
4
+ 12y
3
+ 16y
2
+ 8y −1
c
6
, c
9
y
5
− 12y
4
+ 46y
3
+ 63y
2
+ 61y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.260956 + 1.064160I
a = 0.739044 + 1.064160I
b = 0.260956 − 1.064160I
4.11394 − 0.50358I −4.17139 + 2.42983I
u = −0.260956 − 1.064160I
a = 0.739044 − 1.064160I
b = 0.260956 + 1.064160I
4.11394 + 0.50358I −4.17139 − 2.42983I
u = −0.89902 + 1.33981I
a = 0.100977 + 1.339810I
b = 0.89902 − 1.33981I
−11.1448 + 10.7639I −11.61144 − 5.00628I
u = −0.89902 − 1.33981I
a = 0.100977 − 1.339810I
b = 0.89902 + 1.33981I
−11.1448 − 10.7639I −11.61144 + 5.00628I
u = 0.319959
a = 1.31996
b = −0.319959
−0.742760 −13.4340
5
II. I
u
2
= hb + u, a − u + 1, u
4
− u
3
+ u
2
+ u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
u − 1
−u
a
7
=
−1
−u
a
5
=
−u
−u
2
+ u
a
10
=
u
2
− u + 1
−u
2
a
3
=
u
3
− 2u
2
+ 3u − 1
u
2
a
2
=
u
2u
2
− 2u + 1
a
6
=
−1
−u
3
+ 2u
2
− 4u + 2
a
9
=
0
−u
2
+ u − 1
a
9
=
0
−u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
3
+ 3u
2
− 18
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 3u
3
+ 2u
2
− 1
c
2
u
4
+ 5u
3
+ 2u
2
+ 4u + 1
c
3
, c
5
, c
8
u
4
− 3u
3
+ 2u
2
− 1
c
4
, c
7
, c
11
u
4
− u
3
+ u
2
+ u − 1
c
6
, c
9
u
4
− 2u
3
− 2u
2
+ u + 1
c
10
u
4
+ u
3
+ u
2
− u − 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
y
4
− 5y
3
+ 2y
2
− 4y + 1
c
2
y
4
− 21y
3
− 34y
2
− 12y + 1
c
4
, c
7
, c
10
c
11
y
4
+ y
3
+ y
2
− 3y + 1
c
6
, c
9
y
4
− 8y
3
+ 10y
2
− 5y + 1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.848375
a = −1.84837
b = 0.848375
−13.8089 −12.1770
u = 0.593691 + 1.196160I
a = −0.406309 + 1.196160I
b = −0.593691 − 1.196160I
3.04056 − 6.31855I −7.20042 + 6.94067I
u = 0.593691 − 1.196160I
a = −0.406309 − 1.196160I
b = −0.593691 + 1.196160I
3.04056 + 6.31855I −7.20042 − 6.94067I
u = 0.660993
a = −0.339007
b = −0.660993
−2.14179 −18.4220
9
III. I
u
3
= hb + u, u
5
+ u
3
+ u
2
+ a, u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−u
5
− u
3
− u
2
−u
a
7
=
−u
5
− u
3
− u
2
− u
−u
a
5
=
−u
5
+ u
4
− u
3
+ 1
1
a
10
=
−u
5
+ u
4
− 2u
3
+ 2u
2
− 2u + 2
−u
2
a
3
=
u
4
− 2u
3
+ 3u
2
− 2u + 2
−u
5
− u
2
+ u
a
2
=
−u
3
+ 2u
2
− 3u + 3
−u
5
+ u
4
− 2u
3
+ 2u
2
− u + 1
a
6
=
2u
5
− u
4
+ 2u
3
+ 3u
2
− 2u + 1
u
4
− 2u
3
+ 2u
2
a
9
=
−u
5
− 2u
3
+ u
2
− 3u + 2
−u
5
+ u
4
− 2u
3
+ u
2
− 2u + 1
a
9
=
−u
5
− 2u
3
+ u
2
− 3u + 2
−u
5
+ u
4
− 2u
3
+ u
2
− 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
5
− 2u
4
+ 2u
3
+ 2u − 14
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
8
u
6
− 3u
5
+ 3u
3
+ 2u
2
+ 1
c
2
u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 4u
2
− 4u + 1
c
3
u
6
+ 4u
5
+ u
4
− 9u
3
+ 16u + 10
c
4
u
6
− 4u
5
+ 7u
4
− 7u
3
+ 6u
2
− 4u + 2
c
6
u
6
+ 4u
5
+ u
4
− 2u
3
+ 13u
2
− 2u + 1
c
7
, c
10
, c
11
u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1
c
9
u
6
− 5u
5
+ 9u
4
− 7u
3
+ 8u
2
− 12u + 8
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
6
− 9y
5
+ 22y
4
− 7y
3
+ 4y
2
+ 4y + 1
c
2
y
6
− 37y
5
+ 366y
4
+ 201y
3
+ 116y
2
− 8y + 1
c
3
y
6
− 14y
5
+ 73y
4
− 189y
3
+ 308y
2
− 256y + 100
c
4
y
6
− 2y
5
+ 5y
4
+ 7y
3
+ 8y
2
+ 8y + 4
c
6
y
6
− 14y
5
+ 43y
4
+ 40y
3
+ 163y
2
+ 22y + 1
c
7
, c
10
, c
11
y
6
+ 3y
5
+ 6y
4
+ 5y
3
+ 4y
2
+ 1
c
9
y
6
− 7y
5
+ 27y
4
− 9y
3
+ 40y
2
− 16y + 64
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.601492 + 0.919611I
a = −0.43524 + 2.43997I
b = 0.601492 − 0.919611I
−13.38990 + 2.37783I −11.38532 − 2.96944I
u = −0.601492 − 0.919611I
a = −0.43524 − 2.43997I
b = 0.601492 + 0.919611I
−13.38990 − 2.37783I −11.38532 + 2.96944I
u = 0.560586 + 0.395699I
a = 0.081238 − 0.765128I
b = −0.560586 − 0.395699I
−0.389538 − 0.233200I −13.01274 + 1.15455I
u = 0.560586 − 0.395699I
a = 0.081238 + 0.765128I
b = −0.560586 + 0.395699I
−0.389538 + 0.233200I −13.01274 − 1.15455I
u = 0.540906 + 1.210940I
a = −0.14600 + 1.47596I
b = −0.540906 − 1.210940I
2.26485 − 4.47692I −9.60193 + 3.00061I
u = 0.540906 − 1.210940I
a = −0.14600 − 1.47596I
b = −0.540906 + 1.210940I
2.26485 + 4.47692I −9.60193 − 3.00061I
13
IV. I
u
4
= h−u
5
− 3u
4
− 4u
3
− 3u
2
+ b − 3u − 1, u
5
+ 4u
4
+ 7u
3
+ 7u
2
+ 2a +
6u + 4, u
6
+ 4u
5
+ 7u
4
+ 7u
3
+ 6u
2
+ 4u + 2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−
1
2
u
5
− 2u
4
−
7
2
u
3
−
7
2
u
2
− 3u − 2
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 3u + 1
a
7
=
1
2
u
5
+ u
4
+
1
2
u
3
−
1
2
u
2
− 1
u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 3u + 1
a
5
=
−
3
2
u
5
− 5u
4
−
13
2
u
3
−
9
2
u
2
− 4u − 2
−u
5
− 4u
4
− 6u
3
− 5u
2
− 3u − 3
a
10
=
1
2
u
5
+ u
4
+
1
2
u
3
−
1
2
u
2
u
5
+ 4u
4
+ 6u
3
+ 5u
2
+ 4u + 3
a
3
=
−
1
2
u
5
− u
4
−
3
2
u
3
−
3
2
u
2
− u
−u
5
− 3u
4
− 3u
3
− 2u
2
− u − 1
a
2
=
1
2
u
5
+ u
4
+
1
2
u
3
+
1
2
u
2
+ u + 1
2u
5
+ 6u
4
+ 7u
3
+ 7u
2
+ 5u + 3
a
6
=
−u
4
− 2u
3
− u
2
− 2u − 1
3u
5
+ 7u
4
+ 5u
3
+ 5u
2
+ 4u + 2
a
9
=
1
2
u
5
+ 2u
4
+
5
2
u
3
+
1
2
u
2
+ u + 1
−u
5
− 2u
4
+ 1
a
9
=
1
2
u
5
+ 2u
4
+
5
2
u
3
+
1
2
u
2
+ u + 1
−u
5
− 2u
4
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
5
− 6u
4
− 6u
3
− 4u
2
− 6u − 14
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
6
− 3u
5
+ 3u
3
+ 2u
2
+ 1
c
2
u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 4u
2
− 4u + 1
c
4
, c
7
, c
10
u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1
c
6
u
6
− 5u
5
+ 9u
4
− 7u
3
+ 8u
2
− 12u + 8
c
8
u
6
+ 4u
5
+ u
4
− 9u
3
+ 16u + 10
c
9
u
6
+ 4u
5
+ u
4
− 2u
3
+ 13u
2
− 2u + 1
c
11
u
6
− 4u
5
+ 7u
4
− 7u
3
+ 6u
2
− 4u + 2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
y
6
− 9y
5
+ 22y
4
− 7y
3
+ 4y
2
+ 4y + 1
c
2
y
6
− 37y
5
+ 366y
4
+ 201y
3
+ 116y
2
− 8y + 1
c
4
, c
7
, c
10
y
6
+ 3y
5
+ 6y
4
+ 5y
3
+ 4y
2
+ 1
c
6
y
6
− 7y
5
+ 27y
4
− 9y
3
+ 40y
2
− 16y + 64
c
8
y
6
− 14y
5
+ 73y
4
− 189y
3
+ 308y
2
− 256y + 100
c
9
y
6
− 14y
5
+ 43y
4
+ 40y
3
+ 163y
2
+ 22y + 1
c
11
y
6
− 2y
5
+ 5y
4
+ 7y
3
+ 8y
2
+ 8y + 4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.692483 + 0.688444I
a = −0.726263 − 0.722027I
b = −0.540906 + 1.210940I
2.26485 + 4.47692I −9.60193 − 3.00061I
u = −0.692483 − 0.688444I
a = −0.726263 + 0.722027I
b = −0.540906 − 1.210940I
2.26485 − 4.47692I −9.60193 + 3.00061I
u = 0.190623 + 0.840421I
a = 0.256681 − 1.131660I
b = −0.560586 + 0.395699I
−0.389538 + 0.233200I −13.01274 − 1.15455I
u = 0.190623 − 0.840421I
a = 0.256681 + 1.131660I
b = −0.560586 − 0.395699I
−0.389538 − 0.233200I −13.01274 + 1.15455I
u = −1.49814 + 0.76160I
a = −0.530418 − 0.269644I
b = 0.601492 + 0.919611I
−13.38990 − 2.37783I −11.38532 + 2.96944I
u = −1.49814 − 0.76160I
a = −0.530418 + 0.269644I
b = 0.601492 − 0.919611I
−13.38990 + 2.37783I −11.38532 − 2.96944I
17
V. I
u
5
= h−u
5
+ u
4
− 2u
3
+ u
2
+ b − 2u + 1, u
5
− u
4
+ 2u
3
− u
2
+ a + 2u −
2, u
6
− u
5
+ 2u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
u
2
a
8
=
−u
5
+ u
4
− 2u
3
+ u
2
− 2u + 2
u
5
− u
4
+ 2u
3
− u
2
+ 2u − 1
a
7
=
1
u
5
− u
4
+ 2u
3
− u
2
+ 2u − 1
a
5
=
−u
1
a
10
=
−u
5
− u
3
− u
2
− u + 1
u
4
− u
3
+ 2u
2
− u + 1
a
3
=
−u
5
+ u
4
− 3u
3
+ 2u
2
− 3u + 1
−u
4
+ 2u
3
− 3u
2
+ 3u
a
2
=
−u
4
− u + 1
u
3
+ u
2
+ 1
a
6
=
−u
5
+ u
4
− 2u
3
+ u − 2
−2u
5
+ 2u
4
− 3u
3
+ u
2
− 2u + 1
a
9
=
−u
5
+ u
4
− 2u
3
− u + 1
u
a
9
=
−u
5
+ u
4
− 2u
3
− u + 1
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
5
− 2u
4
+ 2u
3
+ 2u − 14
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
6
+ 4u
5
+ u
4
− 9u
3
+ 16u + 10
c
2
u
6
+ 14u
5
+ 73u
4
+ 189u
3
+ 308u
2
+ 256u + 100
c
3
, c
8
u
6
− 3u
5
+ 3u
3
+ 2u
2
+ 1
c
4
, c
11
u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1
c
6
, c
9
u
6
+ 4u
5
+ u
4
− 2u
3
+ 13u
2
− 2u + 1
c
7
, c
10
u
6
− 4u
5
+ 7u
4
− 7u
3
+ 6u
2
− 4u + 2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
− 14y
5
+ 73y
4
− 189y
3
+ 308y
2
− 256y + 100
c
2
y
6
− 50y
5
+ 653y
4
+ 2279y
3
+ 12696y
2
− 3936y + 10000
c
3
, c
8
y
6
− 9y
5
+ 22y
4
− 7y
3
+ 4y
2
+ 4y + 1
c
4
, c
11
y
6
+ 3y
5
+ 6y
4
+ 5y
3
+ 4y
2
+ 1
c
6
, c
9
y
6
− 14y
5
+ 43y
4
+ 40y
3
+ 163y
2
+ 22y + 1
c
7
, c
10
y
6
− 2y
5
+ 5y
4
+ 7y
3
+ 8y
2
+ 8y + 4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.601492 + 0.919611I
a = −0.498140 − 0.761597I
b = 1.49814 + 0.76160I
−13.38990 + 2.37783I −11.38532 − 2.96944I
u = −0.601492 − 0.919611I
a = −0.498140 + 0.761597I
b = 1.49814 − 0.76160I
−13.38990 − 2.37783I −11.38532 + 2.96944I
u = 0.560586 + 0.395699I
a = 1.19062 − 0.84042I
b = −0.190623 + 0.840421I
−0.389538 − 0.233200I −13.01274 + 1.15455I
u = 0.560586 − 0.395699I
a = 1.19062 + 0.84042I
b = −0.190623 − 0.840421I
−0.389538 + 0.233200I −13.01274 − 1.15455I
u = 0.540906 + 1.210940I
a = 0.307517 − 0.688444I
b = 0.692483 + 0.688444I
2.26485 − 4.47692I −9.60193 + 3.00061I
u = 0.540906 − 1.210940I
a = 0.307517 + 0.688444I
b = 0.692483 − 0.688444I
2.26485 + 4.47692I −9.60193 − 3.00061I
21
VI. I
u
6
= hb − u + 1, a + u, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
−1
a
8
=
−u
u − 1
a
7
=
−1
u − 1
a
5
=
−u
−1
a
10
=
−u
2u
a
3
=
−u
3u
a
2
=
u
u
a
6
=
−1
u − 2
a
9
=
0
u
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
2
+ 2u + 2
c
2
u
2
+ 4
c
3
, c
8
(u + 1)
2
c
4
, c
6
, c
9
c
11
u
2
+ 1
c
5
, c
7
u
2
− 2u + 2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
10
y
2
+ 4
c
2
(y + 4)
2
c
3
, c
8
(y −1)
2
c
4
, c
6
, c
9
c
11
(y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = − 1.000000I
b = −1.00000 + 1.00000I
1.64493 −8.00000
u = − 1.000000I
a = 1.000000I
b = −1.00000 − 1.00000I
1.64493 −8.00000
25
VII. I
u
7
= hb − u + 1, 2a + u − 2, u
2
− 2u + 2i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
2u − 2
a
8
=
−
1
2
u + 1
u − 1
a
7
=
1
2
u
u − 1
a
5
=
−
1
2
u + 1
u + 1
a
10
=
−
1
2
u + 1
1
a
3
=
−
1
2
u + 1
u + 1
a
2
=
−
1
2
u + 2
3u − 1
a
6
=
−1
−2u + 2
a
9
=
−
3
2
u + 2
3
a
9
=
−
3
2
u + 2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
3
, c
5
(u + 1)
2
c
4
, c
6
, c
7
c
9
, c
10
u
2
+ 1
c
8
, c
11
u
2
− 2u + 2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y −1)
2
c
4
, c
6
, c
7
c
9
, c
10
(y + 1)
2
c
8
, c
11
y
2
+ 4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000 + 1.00000I
a = 0.500000 − 0.500000I
b = 1.000000I
1.64493 −8.00000
u = 1.00000 − 1.00000I
a = 0.500000 + 0.500000I
b = − 1.000000I
1.64493 −8.00000
29
VIII. I
u
8
= hb + u, a − 2u − 1, u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
1
=
1
−1
a
8
=
2u + 1
−u
a
7
=
u + 1
−u
a
5
=
2
−1
a
10
=
u − 1
1
a
3
=
2
−1
a
2
=
3
−2
a
6
=
−1
1
a
9
=
2u − 1
−u + 1
a
9
=
2u − 1
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
5
, c
8
(u + 1)
2
c
3
, c
4
u
2
− 2u + 2
c
6
, c
7
, c
9
c
10
, c
11
u
2
+ 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
(y −1)
2
c
3
, c
4
y
2
+ 4
c
6
, c
7
, c
9
c
10
, c
11
(y + 1)
2
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000 + 2.00000I
b = − 1.000000I
1.64493 −8.00000
u = − 1.000000I
a = 1.00000 − 2.00000I
b = 1.000000I
1.64493 −8.00000
33
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
2
+ 2u + 2)(u
4
+ 3u
3
+ 2u
2
− 1)(u
5
+ 4u
4
+ ··· + u + 1)
· (u
6
− 3u
5
+ 3u
3
+ 2u
2
+ 1)
2
(u
6
+ 4u
5
+ u
4
− 9u
3
+ 16u + 10)
c
2
(u + 1)
4
(u
2
+ 4)(u
4
+ 5u
3
+ 2u
2
+ 4u + 1)
· (u
5
+ 10u
4
+ 27u
3
+ 6u
2
+ 5u + 1)
· (u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 4u
2
− 4u + 1)
2
· (u
6
+ 14u
5
+ 73u
4
+ 189u
3
+ 308u
2
+ 256u + 100)
c
3
, c
5
, c
8
((u + 1)
4
)(u
2
− 2u + 2)(u
4
− 3u
3
+ 2u
2
− 1)(u
5
+ 4u
4
+ ··· + u + 1)
· (u
6
− 3u
5
+ 3u
3
+ 2u
2
+ 1)
2
(u
6
+ 4u
5
+ u
4
− 9u
3
+ 16u + 10)
c
4
, c
7
, c
11
(u
2
+ 1)
2
(u
2
− 2u + 2)(u
4
− u
3
+ u
2
+ u − 1)
· (u
5
− 2u
4
+ 4u
3
− 2u
2
+ 2u + 1)(u
6
− 4u
5
+ ··· − 4u + 2)
· (u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1)
2
c
6
, c
9
(u
2
+ 1)
3
(u
4
− 2u
3
− 2u
2
+ u + 1)(u
5
− 6u
4
+ 12u
3
− 9u
2
+ 5u + 2)
· (u
6
− 5u
5
+ 9u
4
− 7u
3
+ 8u
2
− 12u + 8)
· (u
6
+ 4u
5
+ u
4
− 2u
3
+ 13u
2
− 2u + 1)
2
c
10
(u
2
+ 1)
2
(u
2
+ 2u + 2)(u
4
+ u
3
+ u
2
− u − 1)
· (u
5
− 2u
4
+ 4u
3
− 2u
2
+ 2u + 1)(u
6
− 4u
5
+ ··· − 4u + 2)
· (u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1)
2
34
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
(y −1)
4
(y
2
+ 4)(y
4
− 5y
3
+ 2y
2
− 4y + 1)
· (y
5
− 10y
4
+ 27y
3
− 6y
2
+ 5y −1)
· (y
6
− 14y
5
+ 73y
4
− 189y
3
+ 308y
2
− 256y + 100)
· (y
6
− 9y
5
+ 22y
4
− 7y
3
+ 4y
2
+ 4y + 1)
2
c
2
(y −1)
4
(y + 4)
2
(y
4
− 21y
3
− 34y
2
− 12y + 1)
· (y
5
− 46y
4
+ 619y
3
+ 214y
2
+ 13y −1)
· (y
6
− 50y
5
+ 653y
4
+ 2279y
3
+ 12696y
2
− 3936y + 10000)
· (y
6
− 37y
5
+ 366y
4
+ 201y
3
+ 116y
2
− 8y + 1)
2
c
4
, c
7
, c
10
c
11
((y + 1)
4
)(y
2
+ 4)(y
4
+ y
3
+ ··· − 3y + 1)(y
5
+ 4y
4
+ ··· + 8y −1)
· (y
6
− 2y
5
+ ··· + 8y + 4)(y
6
+ 3y
5
+ 6y
4
+ 5y
3
+ 4y
2
+ 1)
2
c
6
, c
9
((y + 1)
6
)(y
4
− 8y
3
+ ··· − 5y + 1)(y
5
− 12y
4
+ ··· + 61y −4)
· (y
6
− 14y
5
+ 43y
4
+ 40y
3
+ 163y
2
+ 22y + 1)
2
· (y
6
− 7y
5
+ 27y
4
− 9y
3
+ 40y
2
− 16y + 64)
35
