10
122
(K10a
89
)
A knot diagram
1
Linearized knot diagam
5 6 7 9 8 10 1 2 4 3
Solving Sequence
3,7 4,10
1 8 6 2 5 9
c
3
c
10
c
7
c
6
c
2
c
5
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
4
− u
3
− 4u
2
+ 6b + u + 3, a + 1, u
5
+ u
4
+ u
3
− u
2
+ 3u + 3i
I
u
2
= hu
9
− 3u
8
+ 2u
7
− u
6
− u
5
− 8u
4
+ u
3
− 5u
2
+ 4b − u + 3, a + 1, u
10
+ u
8
+ u
7
+ 4u
6
+ u
5
+ u
4
− 2u
3
+ 1i
I
u
3
= h1.44071 × 10
22
u
23
+ 2.00575 × 10
22
u
22
+ ··· + 8.55063 × 10
22
b + 4.63180 × 10
23
,
6.78118 × 10
27
u
23
+ 1.02960 × 10
28
u
22
+ ··· + 1.85674 × 10
28
a + 3.22471 × 10
29
, u
24
+ u
23
+ ··· − 26u + 67i
I
u
4
= h118u
11
− 136u
10
+ ··· + 209b − 456, −142u
11
− 116u
10
+ ··· + 209a − 90,
u
12
− u
11
+ 2u
10
+ u
9
+ 2u
8
− 9u
7
+ 3u
6
+ 3u
5
+ 2u
4
− 8u
3
+ 8u
2
− 4u + 1i
I
u
5
= hu
5
+ 2u
4
− 4u
3
+ u
2
+ 12b + 5u + 3, a + 1, u
6
− u
5
+ 2u
4
+ u
3
+ 2u
2
+ 3i
I
u
6
= hb + u + 1, a + 1, u
2
+ u + 1i
I
u
7
= hb − 1, −3u
5
− 4u
4
− 6u
3
+ 6u
2
+ a − 7u + 1, u
6
+ u
5
+ 2u
4
− 2u
3
+ 4u
2
− 2u + 1i
I
u
8
= hb, a + 1, u
3
− u
2
+ 1i
* 8 irreducible components of dim
C
= 0, with total 68 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
4
− u
3
− 4u
2
+ 6b + u + 3, a + 1, u
5
+ u
4
+ u
3
− u
2
+ 3u + 3i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
−1
1
6
u
4
+
1
6
u
3
+ ··· −
1
6
u −
1
2
a
1
=
−
1
6
u
4
−
1
6
u
3
+ ··· +
1
6
u −
1
2
1
6
u
4
+
1
6
u
3
+ ··· −
1
6
u −
1
2
a
8
=
1
3
u
4
+
1
3
u
3
+
1
3
u
2
+
2
3
u + 1
−
1
3
u
4
−
5
6
u
3
+ ··· +
1
3
u −
1
2
a
6
=
−u
1
2
u
3
−
1
2
a
2
=
1
2
u
4
−
1
2
u + 1
u
2
− 1
a
5
=
1
6
u
4
−
1
6
u
3
+ ··· +
1
2
u +
5
6
−
1
2
u
4
−
2
3
u
3
+ ··· −
7
6
u −
4
3
a
9
=
−
1
6
u
4
−
1
6
u
3
+ ··· +
1
6
u −
1
2
−
1
3
u
4
+
1
6
u
3
+ ··· −
2
3
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
17
9
u
4
−
7
9
u
3
−
28
9
u
2
−
35
9
u + 7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
5
− u
4
+ u
3
+ u
2
+ 3u − 3
c
2
, c
7
u
5
− 3u
3
+ 7u − 4
c
4
, c
9
3(3u
5
− 12u
4
+ 26u
3
− 36u
2
+ 28u − 8)
c
5
, c
10
3(3u
5
− 15u
4
+ 35u
3
− 41u
2
+ 23u − 1)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
5
+ y
4
+ 9y
3
− y
2
+ 15y −9
c
2
, c
7
y
5
− 6y
4
+ 23y
3
− 42y
2
+ 49y −16
c
4
, c
9
9(9y
5
+ 12y
4
− 20y
3
− 32y
2
+ 208y −64)
c
5
, c
10
9(9y
5
− 15y
4
+ 133y
3
− 101y
2
+ 447y −1)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.860145 + 0.891716I
a = −1.00000
b = −1.30783 + 1.05747I
−1.64634 + 10.42060I 0.48885 − 9.54868I
u = 0.860145 − 0.891716I
a = −1.00000
b = −1.30783 − 1.05747I
−1.64634 − 10.42060I 0.48885 + 9.54868I
u = −0.724026
a = −1.00000
b = −0.0473103
1.11365 8.99900
u = −0.99813 + 1.30502I
a = −1.00000
b = −1.16851 − 1.06085I
−7.9576 − 16.4108I −1.98837 + 8.68093I
u = −0.99813 − 1.30502I
a = −1.00000
b = −1.16851 + 1.06085I
−7.9576 + 16.4108I −1.98837 − 8.68093I
5
II.
I
u
2
= hu
9
− 3u
8
+ · · · + 4b + 3, a + 1, u
10
+ u
8
+ u
7
+ 4u
6
+ u
5
+ u
4
− 2u
3
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
−1
−
1
4
u
9
+
3
4
u
8
+ ··· +
1
4
u −
3
4
a
1
=
1
4
u
9
−
3
4
u
8
+ ··· −
1
4
u −
1
4
−
1
4
u
9
+
3
4
u
8
+ ··· +
1
4
u −
3
4
a
8
=
3
4
u
9
−
3
4
u
8
+ ··· +
5
4
u +
3
4
−
3
2
u
9
+ u
8
+ ··· −
1
2
u − 1
a
6
=
−u
3
4
u
9
−
1
4
u
8
+ ··· +
1
4
u +
1
4
a
2
=
−
1
4
u
9
−
1
4
u
8
+ ··· +
1
4
u +
1
4
−
3
4
u
9
−
1
4
u
8
+ ··· +
3
4
u −
3
4
a
5
=
3
2
u
9
− u
8
+ ··· +
1
2
u + 1
−
5
4
u
9
+
3
4
u
8
+ ··· +
5
4
u −
7
4
a
9
=
1
4
u
9
−
3
4
u
8
+ ··· −
1
4
u −
1
4
−
1
2
u
9
+
1
2
u
8
+ ··· +
1
2
u −
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1
4
u
9
+
5
4
u
8
−
5
2
u
7
+
5
4
u
6
+
11
4
u
5
−
9
4
u
3
+
15
4
u
2
+
25
4
u +
7
4
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
10
+ u
8
− u
7
+ 4u
6
− u
5
+ u
4
+ 2u
3
+ 1
c
2
, c
7
(u
5
− u
4
+ 1)
2
c
4
, c
9
(u
5
− 4u
4
+ 9u
3
− 13u
2
+ 10u − 4)
2
c
5
, c
10
u
10
− 10u
9
+ ··· − 95u + 19
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
10
+ 2y
9
+ 9y
8
+ 9y
7
+ 16y
6
+ 13y
5
+ 7y
4
+ 4y
3
+ 2y
2
+ 1
c
2
, c
7
(y
5
− y
4
+ 2y
2
− 1)
2
c
4
, c
9
(y
5
+ 2y
4
− 3y
3
− 21y
2
− 4y −16)
2
c
5
, c
10
y
10
− 4y
9
+ ··· + 361y + 361
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.186488 + 0.884166I
a = −1.00000
b = −1.29181 + 1.28122I
−7.58413 − 7.68015I −6.00758 + 6.55636I
u = −0.186488 − 0.884166I
a = −1.00000
b = −1.29181 − 1.28122I
−7.58413 + 7.68015I −6.00758 − 6.55636I
u = −0.583652 + 0.627090I
a = −1.00000
b = −1.68130 − 0.73200I
−1.88219 −6 − 1.264578 + 0.10I
u = −0.583652 − 0.627090I
a = −1.00000
b = −1.68130 + 0.73200I
−1.88219 −6 − 1.264578 + 0.10I
u = −0.837561 + 0.788016I
a = −1.00000
b = −0.560268 − 0.657796I
1.94548 − 2.30273I 6.63987 + 2.99878I
u = −0.837561 − 0.788016I
a = −1.00000
b = −0.560268 + 0.657796I
1.94548 + 2.30273I 6.63987 − 2.99878I
u = 0.656329 + 0.295939I
a = −1.00000
b = −0.297621 + 1.050690I
1.94548 − 2.30273I 6.63987 + 2.99878I
u = 0.656329 − 0.295939I
a = −1.00000
b = −0.297621 − 1.050690I
1.94548 + 2.30273I 6.63987 − 2.99878I
u = 0.95137 + 1.23664I
a = −1.00000
b = −1.169000 + 0.742016I
−7.58413 + 7.68015I −6.00758 − 6.55636I
u = 0.95137 − 1.23664I
a = −1.00000
b = −1.169000 − 0.742016I
−7.58413 − 7.68015I −6.00758 + 6.55636I
9
III. I
u
3
=
h1.44×10
22
u
23
+2.01×10
22
u
22
+· · ·+8.55×10
22
b+4.63×10
23
, 6.78×10
27
u
23
+
1.03 × 10
28
u
22
+ · · · + 1.86 × 10
28
a + 3.22 × 10
29
, u
24
+ u
23
+ · · · − 26u + 67i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
−0.365219u
23
− 0.554519u
22
+ ··· − 56.6942u − 17.3675
−0.168492u
23
− 0.234573u
22
+ ··· − 18.0977u − 5.41691
a
1
=
−0.196727u
23
− 0.319946u
22
+ ··· − 38.5965u − 11.9506
−0.168492u
23
− 0.234573u
22
+ ··· − 18.0977u − 5.41691
a
8
=
0.378827u
23
+ 0.547263u
22
+ ··· + 70.2497u + 31.8889
0.0711438u
23
+ 0.0997089u
22
+ ··· + 6.43136u + 6.60068
a
6
=
0.413307u
23
+ 0.527233u
22
+ ··· + 69.0401u + 33.4117
−0.0366636u
23
− 0.119739u
22
+ ··· − 5.64098u − 5.07784
a
2
=
−0.531591u
23
− 1.06310u
22
+ ··· − 46.4641u − 72.9977
−0.0738408u
23
− 0.0393684u
22
+ ··· − 4.06916u + 5.13154
a
5
=
0.163715u
23
+ 0.0132091u
22
+ ··· + 44.8521u − 33.5831
0.0580226u
23
− 0.0407545u
22
+ ··· + 14.5495u − 11.8038
a
9
=
−0.318510u
23
− 0.571602u
22
+ ··· − 58.1444u − 24.6338
−0.0998054u
23
− 0.191253u
22
+ ··· − 13.3096u − 9.69092
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
49507502818400620336471888
55425173492754441021594851
u
23
−
25666816923514324973679840
55425173492754441021594851
u
22
+
··· −
8454714591899753146209998108
55425173492754441021594851
u +
3209287438838954049727512794
55425173492754441021594851
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
24
− u
23
+ ··· + 26u + 67
c
2
, c
7
(u
12
− u
11
+ ··· − 24u + 19)
2
c
4
, c
9
(u
3
+ u
2
+ 2u + 1)
8
c
5
, c
10
(u
4
+ u
3
− 2u + 1)
6
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
24
+ 9y
23
+ ··· + 68200y + 4489
c
2
, c
7
(y
12
− 13y
11
+ ··· − 2096y + 361)
2
c
4
, c
9
(y
3
+ 3y
2
+ 2y −1)
8
c
5
, c
10
(y
4
− y
3
+ 6y
2
− 4y + 1)
6
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.690412 + 0.835611I
a = 0.969409 + 0.292352I
b = 1.12196 − 1.05376I
−2.17641 + 4.05977I −2.98049 − 6.92820I
u = 0.690412 − 0.835611I
a = 0.969409 − 0.292352I
b = 1.12196 + 1.05376I
−2.17641 − 4.05977I −2.98049 + 6.92820I
u = −0.611027 + 0.676812I
a = −0.37068 + 1.40297I
b = −0.621964 − 0.187730I
−2.17641 − 4.05977I −2.98049 + 6.92820I
u = −0.611027 − 0.676812I
a = −0.37068 − 1.40297I
b = −0.621964 + 0.187730I
−2.17641 + 4.05977I −2.98049 − 6.92820I
u = −0.424999 + 1.011890I
a = 0.945558 + 0.285159I
b = 1.12196 + 1.05376I
−2.17641 − 4.05977I −2.98049 + 6.92820I
u = −0.424999 − 1.011890I
a = 0.945558 − 0.285159I
b = 1.12196 − 1.05376I
−2.17641 + 4.05977I −2.98049 − 6.92820I
u = 0.211529 + 0.854823I
a = −1.85383 + 1.20187I
b = −0.621964 + 0.187730I
−6.31400 + 1.23164I −9.50976 − 3.94876I
u = 0.211529 − 0.854823I
a = −1.85383 − 1.20187I
b = −0.621964 − 0.187730I
−6.31400 − 1.23164I −9.50976 + 3.94876I
u = −0.211301 + 1.222120I
a = 0.610648 − 0.042788I
b = 1.12196 − 1.05376I
−6.31400 + 1.23164I −9.50976 − 3.94876I
u = −0.211301 − 1.222120I
a = 0.610648 + 0.042788I
b = 1.12196 + 1.05376I
−6.31400 − 1.23164I −9.50976 + 3.94876I
13
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.076739 + 0.755326I
a = 1.62960 − 0.11419I
b = 1.12196 + 1.05376I
−6.31400 − 1.23164I −9.50976 + 3.94876I
u = 0.076739 − 0.755326I
a = 1.62960 + 0.11419I
b = 1.12196 − 1.05376I
−6.31400 + 1.23164I −9.50976 − 3.94876I
u = 0.723053 + 1.108140I
a = −0.176034 − 0.666262I
b = −0.621964 − 0.187730I
−2.17641 − 4.05977I −2.98049 + 6.92820I
u = 0.723053 − 1.108140I
a = −0.176034 + 0.666262I
b = −0.621964 + 0.187730I
−2.17641 + 4.05977I −2.98049 − 6.92820I
u = 0.011192 + 0.596382I
a = −2.23288 − 3.23226I
b = −0.621964 + 0.187730I
−6.31400 + 6.88789I −9.50976 − 9.90765I
u = 0.011192 − 0.596382I
a = −2.23288 + 3.23226I
b = −0.621964 − 0.187730I
−6.31400 − 6.88789I −9.50976 + 9.90765I
u = 0.67325 + 1.26988I
a = 1.192260 − 0.277988I
b = 1.12196 − 1.05376I
−6.31400 + 6.88789I −9.50976 − 9.90765I
u = 0.67325 − 1.26988I
a = 1.192260 + 0.277988I
b = 1.12196 + 1.05376I
−6.31400 − 6.88789I −9.50976 + 9.90765I
u = −1.15569 + 1.32686I
a = 0.795498 − 0.185479I
b = 1.12196 + 1.05376I
−6.31400 − 6.88789I −9.50976 + 9.90765I
u = −1.15569 − 1.32686I
a = 0.795498 + 0.185479I
b = 1.12196 − 1.05376I
−6.31400 + 6.88789I −9.50976 − 9.90765I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41952 + 1.33047I
a = −0.379792 − 0.246225I
b = −0.621964 + 0.187730I
−6.31400 + 1.23164I −9.50976 − 3.94876I
u = 1.41952 − 1.33047I
a = −0.379792 + 0.246225I
b = −0.621964 − 0.187730I
−6.31400 − 1.23164I −9.50976 + 3.94876I
u = −1.90267 + 1.36783I
a = −0.144680 + 0.209435I
b = −0.621964 + 0.187730I
−6.31400 + 6.88789I 0
u = −1.90267 − 1.36783I
a = −0.144680 − 0.209435I
b = −0.621964 − 0.187730I
−6.31400 − 6.88789I 0
15
IV. I
u
4
= h118u
11
− 136u
10
+ · · · + 209b − 456, −142u
11
− 116u
10
+ · · · +
209a − 90, u
12
− u
11
+ · · · − 4u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
0.679426u
11
+ 0.555024u
10
+ ··· + 1.19139u + 0.430622
−0.564593u
11
+ 0.650718u
10
+ ··· − 4.52153u + 2.18182
a
1
=
1.24402u
11
− 0.0956938u
10
+ ··· + 5.71292u − 1.75120
−0.564593u
11
+ 0.650718u
10
+ ··· − 4.52153u + 2.18182
a
8
=
−4.11005u
11
+ 2.44976u
10
+ ··· − 15.3349u + 4.11483
0.210526u
11
− 0.578947u
10
+ ··· + 1.84211u − 0.473684
a
6
=
−3.77512u
11
+ 1.07177u
10
+ ··· − 12.5742u + 2.60287
0.124402u
11
− 0.799043u
10
+ ··· + 2.91866u − 1.03828
a
2
=
−1.77990u
11
− 0.0574163u
10
+ ··· − 4.54067u + 0.717703
2.27751u
11
− 1.03349u
10
+ ··· + 9.68900u − 3.50239
a
5
=
−1.03349u
11
+ 1.56938u
10
+ ··· − 10.1340u + 2.96172
−1.32057u
11
− 0.392344u
10
+ ··· − 1.07177u + 0.114833
a
9
=
−0.162679u
11
+ 0.344498u
10
+ ··· + 1.45455u − 0.516746
0.172249u
11
+ 0.440191u
10
+ ··· − 1.15311u + 1.12919
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1120
209
u
11
+
1572
209
u
10
−
1784
209
u
9
−
296
209
u
8
−
144
209
u
7
+
13308
209
u
6
−
3548
209
u
5
−
7224
209
u
4
−
268
19
u
3
+
10060
209
u
2
−
9100
209
u +
4462
209
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
12
+ u
11
+ ··· + 4u + 1
c
2
, c
7
u
12
+ 3u
11
+ ··· + 30u + 7
c
4
, c
9
(u
3
+ u
2
+ 2u + 1)
4
c
5
, c
10
(u
2
+ u + 1)
6
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
12
+ 3y
11
+ ··· + 4y
2
+ 1
c
2
, c
7
y
12
+ 7y
11
+ ··· − 228y + 49
c
4
, c
9
(y
3
+ 3y
2
+ 2y −1)
4
c
5
, c
10
(y
2
+ y + 1)
6
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.861381 + 0.168036I
a = −0.127543 + 0.669764I
b = 0.500000 + 0.866025I
−3.02413 − 1.23164I 2.49024 + 3.94876I
u = 0.861381 − 0.168036I
a = −0.127543 − 0.669764I
b = 0.500000 − 0.866025I
−3.02413 + 1.23164I 2.49024 − 3.94876I
u = −0.982330 + 0.603340I
a = 1.36153 − 0.93064I
b = 0.500000 + 0.866025I
−3.02413 − 6.88789I 2.49024 + 9.90765I
u = −0.982330 − 0.603340I
a = 1.36153 + 0.93064I
b = 0.500000 − 0.866025I
−3.02413 + 6.88789I 2.49024 − 9.90765I
u = 0.514136 + 0.376971I
a = 2.08379 + 0.47689I
b = 0.500000 − 0.866025I
1.11345 + 4.05977I 9.01951 − 6.92820I
u = 0.514136 − 0.376971I
a = 2.08379 − 0.47689I
b = 0.500000 + 0.866025I
1.11345 − 4.05977I 9.01951 + 6.92820I
u = −0.891575 + 1.030720I
a = 0.456012 + 0.104362I
b = 0.500000 + 0.866025I
1.11345 − 4.05977I 9.01951 + 6.92820I
u = −0.891575 − 1.030720I
a = 0.456012 − 0.104362I
b = 0.500000 − 0.866025I
1.11345 + 4.05977I 9.01951 − 6.92820I
u = 0.222408 + 0.555490I
a = −0.27437 + 1.44082I
b = 0.500000 − 0.866025I
−3.02413 + 1.23164I 2.49024 − 3.94876I
u = 0.222408 − 0.555490I
a = −0.27437 − 1.44082I
b = 0.500000 + 0.866025I
−3.02413 − 1.23164I 2.49024 + 3.94876I
19
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.77598 + 1.73565I
a = 0.500591 − 0.342166I
b = 0.500000 − 0.866025I
−3.02413 + 6.88789I 2.49024 − 9.90765I
u = 0.77598 − 1.73565I
a = 0.500591 + 0.342166I
b = 0.500000 + 0.866025I
−3.02413 − 6.88789I 2.49024 + 9.90765I
20
V.
I
u
5
= hu
5
+ 2u
4
− 4u
3
+ u
2
+ 12b + 5u + 3, a + 1, u
6
− u
5
+ 2u
4
+ u
3
+ 2u
2
+ 3i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
−1
−
1
12
u
5
−
1
6
u
4
+ ··· −
5
12
u −
1
4
a
1
=
1
12
u
5
+
1
6
u
4
+ ··· +
5
12
u −
3
4
−
1
12
u
5
−
1
6
u
4
+ ··· −
5
12
u −
1
4
a
8
=
1
12
u
5
−
1
3
u
4
+ ··· −
7
12
u +
3
4
1
6
u
5
−
1
6
u
4
+ ··· +
5
6
u − 1
a
6
=
−u
−
1
4
u
5
+
1
2
u
4
+ ··· +
3
4
u +
1
4
a
2
=
1
4
u
5
+
1
2
u
4
+ ··· +
1
4
u +
7
4
−
1
4
u
5
+
1
2
u
3
+ ··· +
3
4
u −
1
4
a
5
=
−
1
6
u
5
−
1
6
u
4
+ ··· −
1
6
u −
2
3
−
5
12
u
5
+
1
2
u
4
+ ··· −
3
4
u +
5
12
a
9
=
1
12
u
5
+
1
6
u
4
+ ··· +
5
12
u −
3
4
1
6
u
5
−
2
3
u
4
+ ··· −
1
6
u +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3
4
u
5
− u
4
−
1
2
u
3
+
5
4
u
2
−
9
4
u −
17
4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
6
− u
5
+ 2u
4
+ u
3
+ 2u
2
+ 3
c
2
, c
7
(u
3
+ 2u
2
+ u − 1)
2
c
4
, c
9
3(3u
6
+ 14u
4
+ 23u
2
+ 13)
c
5
, c
10
3(3u
6
− 9u
5
+ 11u
4
− 3u
3
− 3u
2
+ u + 1)
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
6
+ 3y
5
+ 10y
4
+ 13y
3
+ 16y
2
+ 12y + 9
c
2
, c
7
(y
3
− 2y
2
+ 5y −1)
2
c
4
, c
9
9(3y
3
+ 14y
2
+ 23y + 13)
2
c
5
, c
10
9(9y
6
− 15y
5
+ 49y
4
− 51y
3
+ 37y
2
− 7y + 1)
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783974 + 0.693760I
a = −1.00000
b = 0.383600 + 0.213445I
−5.55560 + 6.33267I −0.64281 − 3.53920I
u = −0.783974 − 0.693760I
a = −1.00000
b = 0.383600 − 0.213445I
−5.55560 − 6.33267I −0.64281 + 3.53920I
u = 0.391622 + 0.997262I
a = −1.00000
b = −0.841164 − 0.404475I
−5.33814 −4.71439 + 0.I
u = 0.391622 − 0.997262I
a = −1.00000
b = −0.841164 + 0.404475I
−5.33814 −4.71439 + 0.I
u = 0.89235 + 1.26033I
a = −1.00000
b = −1.042440 + 0.948097I
−5.55560 + 6.33267I −0.64281 − 3.53920I
u = 0.89235 − 1.26033I
a = −1.00000
b = −1.042440 − 0.948097I
−5.55560 − 6.33267I −0.64281 + 3.53920I
24
VI. I
u
6
= hb + u + 1, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u + 1
a
10
=
−1
−u − 1
a
1
=
u
−u − 1
a
8
=
−1
0
a
6
=
−u
u + 1
a
2
=
0
−u
a
5
=
1
u + 1
a
9
=
−1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u + 4
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
2
+ u + 1
c
2
, c
5
, c
7
c
10
u
2
− u + 1
c
4
, c
9
u
2
26
(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
y
2
+ y + 1
c
4
, c
9
y
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = −0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = −0.500000 − 0.866025I
a = −1.00000
b = −0.500000 + 0.866025I
4.05977I 0. − 6.92820I
28
VII.
I
u
7
= hb−1, −3u
5
−4u
4
−6u
3
+6u
2
+a−7u+1, u
6
+u
5
+2u
4
−2u
3
+4u
2
−2u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
3u
5
+ 4u
4
+ 6u
3
− 6u
2
+ 7u − 1
1
a
1
=
3u
5
+ 4u
4
+ 6u
3
− 6u
2
+ 7u − 2
1
a
8
=
u
4
+ 2u
3
+ 3u
2
− u + 1
−u
5
+ 5u
2
− 3u + 3
a
6
=
−2u
5
+ u
4
+ 2u
3
+ 13u
2
− 10u + 7
−u
5
+ 5u
2
− 4u + 3
a
2
=
2u
5
+ 6u
4
+ 9u
3
+ 3u
2
− 2u + 5
u
5
+ 2u
4
+ 3u
3
− u
2
+ u
a
5
=
−2u
5
+ 10u
2
− 9u + 6
−u
a
9
=
4u
5
+ 6u
4
+ 9u
3
− 7u
2
+ 8u − 1
u
4
+ u
3
+ 2u
2
− u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
5
+ 20u
2
− 16u + 6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
u
6
− u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ 2u + 1
c
2
, c
7
(u
3
− u
2
+ 1)
2
c
4
, c
9
(u
3
+ u
2
+ 2u + 1)
2
c
5
, c
10
(u + 1)
6
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
y
6
+ 3y
5
+ 16y
4
+ 18y
3
+ 12y
2
+ 4y + 1
c
2
, c
7
(y
3
− y
2
+ 2y −1)
2
c
4
, c
9
(y
3
+ 3y
2
+ 2y −1)
2
c
5
, c
10
(y −1)
6
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.288915 + 0.750335I
a = 2.25666 − 0.68552I
b = 1.00000
−6.31400 + 2.82812I −9.50976 − 2.97945I
u = 0.288915 − 0.750335I
a = 2.25666 + 0.68552I
b = 1.00000
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = 0.377439 + 0.536376I
a = 0.337641 + 0.941275I
b = 1.00000
−2.17641 −2.98049 + 0.I
u = 0.377439 − 0.536376I
a = 0.337641 − 0.941275I
b = 1.00000
−2.17641 −2.98049 + 0.I
u = −1.16635 + 1.49520I
a = 0.405695 − 0.123240I
b = 1.00000
−6.31400 − 2.82812I −9.50976 + 2.97945I
u = −1.16635 − 1.49520I
a = 0.405695 + 0.123240I
b = 1.00000
−6.31400 + 2.82812I −9.50976 − 2.97945I
32
VIII. I
u
8
= hb, a + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
10
=
−1
0
a
1
=
−1
0
a
8
=
−u
u
a
6
=
−u
u
a
2
=
u
2
+ 1
−u
2
a
5
=
−u
u
a
9
=
u
2
− 1
−u
2
+ u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u + 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
u
3
+ u
2
− 1
c
4
, c
9
u
3
− u
2
+ 2u − 1
c
5
, c
10
u
3
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
8
y
3
− y
2
+ 2y −1
c
4
, c
9
y
3
+ 3y
2
+ 2y −1
c
5
, c
10
y
3
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −1.00000
b = 0
−3.02413 + 2.82812I 2.49024 − 2.97945I
u = 0.877439 − 0.744862I
a = −1.00000
b = 0
−3.02413 − 2.82812I 2.49024 + 2.97945I
u = −0.754878
a = −1.00000
b = 0
1.11345 9.01950
36
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
8
(u
2
+ u + 1)(u
3
+ u
2
− 1)(u
5
− u
4
+ u
3
+ u
2
+ 3u − 3)
· (u
6
− u
5
+ 2u
4
+ u
3
+ 2u
2
+ 3)(u
6
− u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ 2u + 1)
· (u
10
+ u
8
+ ··· + 2u
3
+ 1)(u
12
+ u
11
+ ··· + 4u + 1)
· (u
24
− u
23
+ ··· + 26u + 67)
c
2
, c
7
(u
2
− u + 1)(u
3
− u
2
+ 1)
2
(u
3
+ u
2
− 1)(u
3
+ 2u
2
+ u − 1)
2
· (u
5
− 3u
3
+ 7u − 4)(u
5
− u
4
+ 1)
2
(u
12
− u
11
+ ··· − 24u + 19)
2
· (u
12
+ 3u
11
+ ··· + 30u + 7)
c
4
, c
9
9u
2
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
14
· (u
5
− 4u
4
+ 9u
3
− 13u
2
+ 10u − 4)
2
· (3u
5
− 12u
4
+ 26u
3
− 36u
2
+ 28u − 8)(3u
6
+ 14u
4
+ 23u
2
+ 13)
c
5
, c
10
9u
3
(u + 1)
6
(u
2
− u + 1)(u
2
+ u + 1)
6
(u
4
+ u
3
− 2u + 1)
6
· (3u
5
− 15u
4
+ 35u
3
− 41u
2
+ 23u − 1)
· (3u
6
− 9u
5
+ ··· + u + 1)(u
10
− 10u
9
+ ··· − 95u + 19)
37
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
8
(y
2
+ y + 1)(y
3
− y
2
+ 2y −1)(y
5
+ y
4
+ 9y
3
− y
2
+ 15y −9)
· (y
6
+ 3y
5
+ 10y
4
+ 13y
3
+ 16y
2
+ 12y + 9)
· (y
6
+ 3y
5
+ 16y
4
+ 18y
3
+ 12y
2
+ 4y + 1)
· (y
10
+ 2y
9
+ 9y
8
+ 9y
7
+ 16y
6
+ 13y
5
+ 7y
4
+ 4y
3
+ 2y
2
+ 1)
· (y
12
+ 3y
11
+ ··· + 4y
2
+ 1)(y
24
+ 9y
23
+ ··· + 68200y + 4489)
c
2
, c
7
(y
2
+ y + 1)(y
3
− 2y
2
+ 5y −1)
2
(y
3
− y
2
+ 2y −1)
3
· (y
5
− 6y
4
+ 23y
3
− 42y
2
+ 49y −16)(y
5
− y
4
+ 2y
2
− 1)
2
· ((y
12
− 13y
11
+ ··· − 2096y + 361)
2
)(y
12
+ 7y
11
+ ··· − 228y + 49)
c
4
, c
9
81y
2
(y
3
+ 3y
2
+ 2y −1)
15
(3y
3
+ 14y
2
+ 23y + 13)
2
· (y
5
+ 2y
4
− 3y
3
− 21y
2
− 4y −16)
2
· (9y
5
+ 12y
4
− 20y
3
− 32y
2
+ 208y −64)
c
5
, c
10
81y
3
(y −1)
6
(y
2
+ y + 1)
7
(y
4
− y
3
+ 6y
2
− 4y + 1)
6
· (9y
5
− 15y
4
+ 133y
3
− 101y
2
+ 447y −1)
· (9y
6
− 15y
5
+ 49y
4
− 51y
3
+ 37y
2
− 7y + 1)
· (y
10
− 4y
9
+ ··· + 361y + 361)
38
