10
103
(K10a
105
)
A knot diagram
1
Linearized knot diagam
5 9 6 1 8 10 4 3 2 7
Solving Sequence
2,9 3,6
4 10 7 8 5 1
c
2
c
3
c
9
c
6
c
8
c
5
c
1
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
14
− 7u
13
+ ··· + 2b + 6, −3u
14
− 17u
13
+ ··· + 4a + 24, u
15
+ 5u
14
+ ··· − 22u − 4i
I
u
2
= h−a
3
u − a
3
+ a
2
u + 2u
2
a + 2a
2
+ 2au − 3u
2
+ 4b + a − u − 7,
− a
3
u
2
+ a
4
+ a
3
u + a
2
u
2
− 2a
3
+ 6u
2
a − 2a
2
− 3au + 7u
2
+ 11a − 3u + 17, u
3
+ 2u + 1i
I
u
3
= h−u
6
+ 2u
5
− 4u
4
+ 4u
3
− 3u
2
+ b + u, u
4
− 2u
3
+ 3u
2
+ a − 3u + 1, u
7
− u
6
+ 4u
5
− 3u
4
+ 4u
3
− 3u
2
− 1i
I
u
4
= h−u
3
a + u
2
a − u
3
− 2au + u
2
+ b + a − u + 1, u
3
a + u
2
a − 2u
3
+ a
2
+ u
2
− u, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
5
= hb − u, a, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
6
= hu
3
− 2u
2
+ b + 2u − 1, −u
2
+ a + 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
7
= hb + 1, a, u + 1i
* 7 irreducible components of dim
C
= 0, with total 51 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
=
h−u
14
−7u
13
+· · ·+2b+6, −3u
14
−17u
13
+· · ·+4a+24, u
15
+5u
14
+· · ·−22u−4i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
3
4
u
14
+
17
4
u
13
+ ··· −
107
4
u − 6
1
2
u
14
+
7
2
u
13
+ ··· −
25
2
u − 3
a
4
=
1
2
u
13
+
3
2
u
12
+ ··· +
13
2
u +
5
2
1
2
u
14
+
5
2
u
13
+ ··· −
33
2
u
2
−
7
2
u
a
10
=
u
u
a
7
=
−
1
4
u
14
−
3
4
u
13
+ ··· −
67
4
u − 4
−
1
2
u
14
−
3
2
u
13
+ ··· −
5
2
u − 1
a
8
=
−u
u
3
+ u
a
5
=
3
4
u
14
+
13
4
u
13
+ ··· −
59
4
u − 4
1
2
u
14
+
3
2
u
13
+ ··· −
5
2
u − 1
a
1
=
−
1
2
u
13
−
5
2
u
12
+ ··· +
19
2
u +
5
2
−
1
2
u
14
−
5
2
u
13
+ ··· +
23
2
u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
14
− 17u
13
− 63u
12
− 150u
11
− 301u
10
− 461u
9
− 582u
8
−
556u
7
− 394u
6
− 135u
5
+ 61u
4
+ 145u
3
+ 106u
2
+ 46u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
15
− 5u
13
+ 12u
11
+ u
10
− 13u
9
− u
8
+ 7u
7
− 2u
6
− 2u
5
+ 6u
4
+ 4u
3
− 1
c
2
, c
8
, c
9
u
15
+ 5u
14
+ ··· − 22u − 4
c
3
, c
5
u
15
− u
14
+ ··· + 7u − 1
c
7
u
15
+ 12u
14
+ ··· − 352u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
15
− 10y
14
+ ··· + 12y
2
− 1
c
2
, c
8
, c
9
y
15
+ 15y
14
+ ··· + 12y −16
c
3
, c
5
y
15
− 7y
14
+ ··· + 39y −1
c
7
y
15
+ 4y
14
+ ··· + 15360y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.887920 + 0.390096I
a = −0.456559 + 0.349463I
b = 1.021850 + 0.430810I
5.98098 − 9.46445I 7.81439 + 7.21994I
u = −0.887920 − 0.390096I
a = −0.456559 − 0.349463I
b = 1.021850 − 0.430810I
5.98098 + 9.46445I 7.81439 − 7.21994I
u = −0.744334 + 0.885606I
a = 0.126989 + 0.717975I
b = −0.257749 − 0.301552I
4.59236 + 3.90754I 6.20530 − 5.11964I
u = −0.744334 − 0.885606I
a = 0.126989 − 0.717975I
b = −0.257749 + 0.301552I
4.59236 − 3.90754I 6.20530 + 5.11964I
u = 0.666897
a = −0.432662
b = 0.365528
1.03900 11.4360
u = −0.12237 + 1.42140I
a = 1.69571 − 0.09050I
b = 2.22357 − 0.39328I
−6.94441 − 2.69912I −1.74572 + 0.84288I
u = −0.12237 − 1.42140I
a = 1.69571 + 0.09050I
b = 2.22357 + 0.39328I
−6.94441 + 2.69912I −1.74572 − 0.84288I
u = −0.41800 + 1.40303I
a = 1.190560 − 0.502109I
b = 1.52895 + 0.14725I
−2.92891 − 5.10870I 4.27958 + 4.78875I
u = −0.41800 − 1.40303I
a = 1.190560 + 0.502109I
b = 1.52895 − 0.14725I
−2.92891 + 5.10870I 4.27958 − 4.78875I
u = 0.00988 + 1.50056I
a = −0.858298 + 0.099548I
b = −1.290570 + 0.574441I
−4.75856 + 2.25763I 0.39685 − 3.44983I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00988 − 1.50056I
a = −0.858298 − 0.099548I
b = −1.290570 − 0.574441I
−4.75856 − 2.25763I 0.39685 + 3.44983I
u = −0.33501 + 1.48524I
a = −1.82710 − 0.08509I
b = −2.42017 − 0.90791I
−0.04257 − 13.87480I 4.10212 + 7.41823I
u = −0.33501 − 1.48524I
a = −1.82710 + 0.08509I
b = −2.42017 + 0.90791I
−0.04257 + 13.87480I 4.10212 − 7.41823I
u = −0.335695 + 0.310740I
a = 0.095018 − 1.380210I
b = −0.488639 − 0.337278I
−1.35319 − 0.99888I −2.77065 + 2.25299I
u = −0.335695 − 0.310740I
a = 0.095018 + 1.380210I
b = −0.488639 + 0.337278I
−1.35319 + 0.99888I −2.77065 − 2.25299I
6
II.
I
u
2
= h2u
2
a − 3u
2
+ · · · + a − 7, −a
3
u
2
+ a
2
u
2
+ · · · + 11a + 17, u
3
+ 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
a
−
1
2
u
2
a +
3
4
u
2
+ ··· −
1
4
a +
7
4
a
4
=
1
4
a
2
u
2
− u
2
+ ··· +
1
2
a −
3
2
−
1
2
a
3
u +
1
2
u
2
a + ··· + a + 2
a
10
=
u
u
a
7
=
1
4
a
3
u
2
−
1
2
a
2
u
2
+ ··· +
3
2
a −
1
4
1
4
a
3
u
2
−
1
2
a
2
u
2
+ ··· +
1
4
a +
3
2
a
8
=
−u
−u − 1
a
5
=
1
4
a
3
u
2
−
1
2
a
2
u
2
+ ··· +
3
2
a −
1
4
1
2
a
3
u
2
−
3
4
a
2
u
2
+ ··· −
1
4
a +
3
4
a
1
=
−
1
4
a
3
u
2
−
1
2
a
2
u
2
+ ··· +
5
4
a − 1
1
4
a
3
u
2
−
3
4
a
2
u
2
+ ··· +
5
4
a +
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3a
3
u + a
2
u
2
+ a
3
− 4a
2
u − u
2
a − a
2
− 7au + 4u
2
− 4a + 2u + 12
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
12
− 3u
10
+ ··· + 14u + 4
c
2
, c
8
, c
9
(u
3
+ 2u + 1)
4
c
3
, c
5
u
12
− 2u
11
+ ··· − 6u + 4
c
7
(u
2
− u + 1)
6
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
12
− 6y
11
+ ··· − 108y + 16
c
2
, c
8
, c
9
(y
3
+ 4y
2
+ 4y − 1)
4
c
3
, c
5
y
12
− 2y
11
+ ··· + 36y + 16
c
7
(y
2
+ y + 1)
6
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = −1.269590 − 0.163681I
b = −1.85587 + 0.33973I
−4.50593 + 3.10806I 2.68207 + 0.25508I
u = 0.22670 + 1.46771I
a = −1.47391 − 0.21481I
b = −2.37427 − 0.36871I
−4.50593 + 7.16782I 2.68207 − 6.67312I
u = 0.22670 + 1.46771I
a = 0.410077 + 0.047895I
b = 0.496356 + 0.410508I
−4.50593 + 3.10806I 2.68207 + 0.25508I
u = 0.22670 + 1.46771I
a = 2.00394 − 0.47166I
b = 2.40430 − 1.18378I
−4.50593 + 7.16782I 2.68207 − 6.67312I
u = 0.22670 − 1.46771I
a = −1.269590 + 0.163681I
b = −1.85587 − 0.33973I
−4.50593 − 3.10806I 2.68207 − 0.25508I
u = 0.22670 − 1.46771I
a = −1.47391 + 0.21481I
b = −2.37427 + 0.36871I
−4.50593 − 7.16782I 2.68207 + 6.67312I
u = 0.22670 − 1.46771I
a = 0.410077 − 0.047895I
b = 0.496356 − 0.410508I
−4.50593 − 3.10806I 2.68207 − 0.25508I
u = 0.22670 − 1.46771I
a = 2.00394 + 0.47166I
b = 2.40430 + 1.18378I
−4.50593 − 7.16782I 2.68207 + 6.67312I
u = −0.453398
a = −1.28266 + 0.65754I
b = 1.42257 + 0.97392I
5.72200 + 2.02988I 14.6359 − 3.4641I
u = −0.453398
a = −1.28266 − 0.65754I
b = 1.42257 − 0.97392I
5.72200 − 2.02988I 14.6359 + 3.4641I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.453398
a = 2.61214 + 1.64520I
b = −0.593090 + 0.462783I
5.72200 + 2.02988I 14.6359 − 3.4641I
u = −0.453398
a = 2.61214 − 1.64520I
b = −0.593090 − 0.462783I
5.72200 − 2.02988I 14.6359 + 3.4641I
11
III. I
u
3
= h−u
6
+ 2u
5
− 4u
4
+ 4u
3
− 3u
2
+ b + u, u
4
− 2u
3
+ 3u
2
+ a − 3u +
1, u
7
− u
6
+ 4u
5
− 3u
4
+ 4u
3
− 3u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
−u
4
+ 2u
3
− 3u
2
+ 3u − 1
u
6
− 2u
5
+ 4u
4
− 4u
3
+ 3u
2
− u
a
4
=
−u
6
− 2u
4
− u
3
+ u
2
+ 3
−u
6
+ u
5
− 3u
4
+ 2u
3
− 2u
2
+ 2u
a
10
=
u
u
a
7
=
u
5
− 2u
4
+ 5u
3
− 5u
2
+ 4u − 2
u
6
− u
5
+ 3u
4
− u
3
+ u
2
− 1
a
8
=
−u
u
3
+ u
a
5
=
u
5
− 2u
4
+ 4u
3
− 4u
2
+ 3u − 1
u
6
− u
5
+ 3u
4
− 2u
3
+ u
2
− u − 1
a
1
=
u
6
− u
5
+ 3u
4
− 3u
3
+ 3u
2
− 4u + 2
−u
4
+ u
3
− 2u
2
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
6
− u
5
− 4u
4
− 3u
3
− u
2
− 2u + 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
7
− u
6
− 3u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1
c
2
u
7
− u
6
+ 4u
5
− 3u
4
+ 4u
3
− 3u
2
− 1
c
3
, c
5
u
7
− 2u
4
+ 2u
3
+ u − 1
c
4
, c
10
u
7
+ u
6
− 3u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1
c
7
u
7
+ u
6
+ 2u
4
+ 2u
3
+ 1
c
8
, c
9
u
7
+ u
6
+ 4u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
7
− 7y
6
+ 21y
5
− 33y
4
+ 29y
3
− 15y
2
+ 6y − 1
c
2
, c
8
, c
9
y
7
+ 7y
6
+ 18y
5
+ 17y
4
− 4y
3
− 15y
2
− 6y − 1
c
3
, c
5
y
7
+ 4y
5
− 2y
4
+ 4y
3
+ y − 1
c
7
y
7
− y
6
− 4y
4
+ 2y
3
− 4y
2
− 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.918562
a = 0.0625775
b = 0.653034
0.366890 −3.70900
u = −0.067922 + 1.289750I
a = 1.72899 − 0.44162I
b = 2.07818 + 0.63907I
1.60291 − 2.64701I 5.65301 + 1.06537I
u = −0.067922 − 1.289750I
a = 1.72899 + 0.44162I
b = 2.07818 − 0.63907I
1.60291 + 2.64701I 5.65301 − 1.06537I
u = −0.187854 + 0.509305I
a = −0.62575 + 1.85982I
b = −0.882406 − 0.430998I
4.59137 + 1.74054I 6.14623 − 0.88292I
u = −0.187854 − 0.509305I
a = −0.62575 − 1.85982I
b = −0.882406 + 0.430998I
4.59137 − 1.74054I 6.14623 + 0.88292I
u = 0.29650 + 1.45837I
a = −1.134520 − 0.126961I
b = −1.52229 + 0.18408I
−4.73279 + 4.40574I 1.05528 − 5.72803I
u = 0.29650 − 1.45837I
a = −1.134520 + 0.126961I
b = −1.52229 − 0.18408I
−4.73279 − 4.40574I 1.05528 + 5.72803I
15
IV. I
u
4
= h−u
3
a + u
2
a − u
3
− 2au + u
2
+ b + a − u + 1, u
3
a + u
2
a − 2u
3
+
a
2
+ u
2
− u, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
a
u
3
a − u
2
a + u
3
+ 2au − u
2
− a + u − 1
a
4
=
u
2
a − au − u
2
+ a + 2u − 1
−2u
3
− au − 2u + 1
a
10
=
u
u
a
7
=
−u
3
− au + u
2
+ a − u
u
3
a − u
2
a + au − a − 1
a
8
=
−u
u
3
+ u
a
5
=
u
3
a − u
3
+ au + u
2
− u
u
3
+ a + u − 1
a
1
=
−u
3
a + u
3
− au + 1
u
3
a − u
2
a + u
3
+ 2au − u
2
− 2a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8u
3
− 8u + 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
8
+ 2u
7
− u
6
− 6u
5
− 4u
4
+ 2u
2
+ 8u + 7
c
2
, c
8
, c
9
(u
4
− u
3
+ 2u
2
− 2u + 1)
2
c
3
, c
5
u
8
− u
7
+ 4u
6
+ 2u
5
+ 6u
4
− 5u
3
+ 4u
2
+ 4u + 1
c
7
(u
2
− u + 1)
4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
8
− 6y
7
+ 17y
6
− 24y
5
− 6y
4
+ 66y
3
− 52y
2
− 36y + 49
c
2
, c
8
, c
9
(y
4
+ 3y
3
+ 2y
2
+ 1)
2
c
3
, c
5
y
8
+ 7y
7
+ 32y
6
+ 42y
5
+ 98y
4
+ 15y
3
+ 68y
2
− 8y + 1
c
7
(y
2
+ y + 1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −0.639419 − 1.130600I
b = 0.210602 − 0.087079I
1.64493 + 4.05977I 6.00000 − 6.92820I
u = 0.621744 + 0.440597I
a = 0.568723 + 0.157295I
b = −0.851993 + 0.738544I
1.64493 + 4.05977I 6.00000 − 6.92820I
u = 0.621744 − 0.440597I
a = −0.639419 + 1.130600I
b = 0.210602 + 0.087079I
1.64493 − 4.05977I 6.00000 + 6.92820I
u = 0.621744 − 0.440597I
a = 0.568723 − 0.157295I
b = −0.851993 − 0.738544I
1.64493 − 4.05977I 6.00000 + 6.92820I
u = −0.121744 + 1.306620I
a = −0.81180 + 1.76022I
b = −1.012310 + 0.720834I
1.64493 − 4.05977I 6.00000 + 6.92820I
u = −0.121744 + 1.306620I
a = 1.88250 + 0.73058I
b = 2.65370 + 1.66268I
1.64493 − 4.05977I 6.00000 + 6.92820I
u = −0.121744 − 1.306620I
a = −0.81180 − 1.76022I
b = −1.012310 − 0.720834I
1.64493 + 4.05977I 6.00000 − 6.92820I
u = −0.121744 − 1.306620I
a = 1.88250 − 0.73058I
b = 2.65370 − 1.66268I
1.64493 + 4.05977I 6.00000 − 6.92820I
19
V. I
u
5
= hb − u, a, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
0
u
a
4
=
1
0
a
10
=
u
u
a
7
=
u
3
u
3
+ u
a
8
=
−u
u
3
+ u
a
5
=
u
3
1
a
1
=
u
3
+ 1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)
4
c
2
, c
3
, c
8
c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
5
u
4
− 3u
3
+ 2u
2
+ 1
c
6
, c
10
u
4
+ 3u
3
+ 2u
2
+ 1
c
7
(u
2
− u + 1)
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y − 1)
4
c
2
, c
3
, c
8
c
9
y
4
+ 3y
3
+ 2y
2
+ 1
c
5
, c
6
, c
10
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
7
(y
2
+ y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 0
b = 0.621744 + 0.440597I
1.64493 6.00000
u = 0.621744 − 0.440597I
a = 0
b = 0.621744 − 0.440597I
1.64493 6.00000
u = −0.121744 + 1.306620I
a = 0
b = −0.121744 + 1.306620I
1.64493 6.00000
u = −0.121744 − 1.306620I
a = 0
b = −0.121744 − 1.306620I
1.64493 6.00000
23
VI. I
u
6
= hu
3
− 2u
2
+ b + 2u − 1, −u
2
+ a + 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
6
=
u
2
− 1
−u
3
+ 2u
2
− 2u + 1
a
4
=
−u
3
+ 3u
2
− 2u + 2
−u
3
+ 2u
2
− 3u + 1
a
10
=
u
u
a
7
=
u
2
+ u − 1
−u
3
+ 2u
2
− u + 1
a
8
=
−u
u
3
+ u
a
5
=
−1
u
2
a
1
=
−u
2
+ 1
u
3
− 2u
2
+ 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
+ 3u
3
+ 2u
2
+ 1
c
2
, c
5
, c
8
c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
3
u
4
− 3u
3
+ 2u
2
+ 1
c
6
, c
10
(u − 1)
4
c
7
(u
2
− u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
2
, c
5
, c
8
c
9
y
4
+ 3y
3
+ 2y
2
+ 1
c
6
, c
10
(y − 1)
4
c
7
(y
2
+ y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = −0.807560 + 0.547877I
b = 0.263136 − 0.210868I
1.64493 6.00000
u = 0.621744 − 0.440597I
a = −0.807560 − 0.547877I
b = 0.263136 + 0.210868I
1.64493 6.00000
u = −0.121744 + 1.306620I
a = −2.69244 − 0.31815I
b = −2.76314 − 1.07689I
1.64493 6.00000
u = −0.121744 − 1.306620I
a = −2.69244 + 0.31815I
b = −2.76314 + 1.07689I
1.64493 6.00000
27
VII. I
u
7
= hb + 1, a, u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
−1
a
3
=
1
−1
a
6
=
0
−1
a
4
=
1
0
a
10
=
−1
−1
a
7
=
−1
−2
a
8
=
1
−2
a
5
=
−1
1
a
1
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u − 1
c
2
, c
3
, c
5
c
8
, c
9
u + 1
c
7
u + 2
29
(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
8
, c
9
, c
10
y − 1
c
7
y − 4
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0
b = −1.00000
1.64493 6.00000
31
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u − 1)
5
(u
4
+ 3u
3
+ 2u
2
+ 1)(u
7
− u
6
− 3u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1)
· (u
8
+ 2u
7
+ ··· + 8u + 7)(u
12
− 3u
10
+ ··· + 14u + 4)
· (u
15
− 5u
13
+ 12u
11
+ u
10
− 13u
9
− u
8
+ 7u
7
− 2u
6
− 2u
5
+ 6u
4
+ 4u
3
− 1)
c
2
(u + 1)(u
3
+ 2u + 1)
4
(u
4
− u
3
+ 2u
2
− 2u + 1)
4
· (u
7
− u
6
+ ··· − 3u
2
− 1)(u
15
+ 5u
14
+ ··· − 22u − 4)
c
3
, c
5
(u + 1)(u
4
− 3u
3
+ 2u
2
+ 1)(u
4
− u
3
+ ··· − 2u + 1)(u
7
− 2u
4
+ ··· + u − 1)
· (u
8
− u
7
+ 4u
6
+ 2u
5
+ 6u
4
− 5u
3
+ 4u
2
+ 4u + 1)
· (u
12
− 2u
11
+ ··· − 6u + 4)(u
15
− u
14
+ ··· + 7u − 1)
c
4
, c
10
(u − 1)
5
(u
4
+ 3u
3
+ 2u
2
+ 1)(u
7
+ u
6
− 3u
5
− 3u
4
+ 3u
3
+ 3u
2
− 1)
· (u
8
+ 2u
7
+ ··· + 8u + 7)(u
12
− 3u
10
+ ··· + 14u + 4)
· (u
15
− 5u
13
+ 12u
11
+ u
10
− 13u
9
− u
8
+ 7u
7
− 2u
6
− 2u
5
+ 6u
4
+ 4u
3
− 1)
c
7
(u + 2)(u
2
− u + 1)
14
(u
7
+ u
6
+ 2u
4
+ 2u
3
+ 1)
· (u
15
+ 12u
14
+ ··· − 352u − 64)
c
8
, c
9
(u + 1)(u
3
+ 2u + 1)
4
(u
4
− u
3
+ 2u
2
− 2u + 1)
4
· (u
7
+ u
6
+ ··· + 3u
2
+ 1)(u
15
+ 5u
14
+ ··· − 22u − 4)
32
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
(y − 1)
5
(y
4
− 5y
3
+ 6y
2
+ 4y + 1)
· (y
7
− 7y
6
+ 21y
5
− 33y
4
+ 29y
3
− 15y
2
+ 6y − 1)
· (y
8
− 6y
7
+ 17y
6
− 24y
5
− 6y
4
+ 66y
3
− 52y
2
− 36y + 49)
· (y
12
− 6y
11
+ ··· − 108y + 16)(y
15
− 10y
14
+ ··· + 12y
2
− 1)
c
2
, c
8
, c
9
(y − 1)(y
3
+ 4y
2
+ 4y − 1)
4
(y
4
+ 3y
3
+ 2y
2
+ 1)
4
· (y
7
+ 7y
6
+ 18y
5
+ 17y
4
− 4y
3
− 15y
2
− 6y − 1)
· (y
15
+ 15y
14
+ ··· + 12y − 16)
c
3
, c
5
(y − 1)(y
4
− 5y
3
+ 6y
2
+ 4y + 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
7
+ 4y
5
− 2y
4
+ 4y
3
+ y − 1)
· (y
8
+ 7y
7
+ 32y
6
+ 42y
5
+ 98y
4
+ 15y
3
+ 68y
2
− 8y + 1)
· (y
12
− 2y
11
+ ··· + 36y + 16)(y
15
− 7y
14
+ ··· + 39y − 1)
c
7
(y − 4)(y
2
+ y + 1)
14
(y
7
− y
6
− 4y
4
+ 2y
3
− 4y
2
− 1)
· (y
15
+ 4y
14
+ ··· + 15360y − 4096)
33
