12a
1202
(K12a
1202
)
A knot diagram
1
Linearized knot diagam
4 11 6 1 8 3 10 5 12 7 2 9
Solving Sequence
7,10
8
3,11
2 12 6 4 1 5 9
c
7
c
10
c
2
c
11
c
6
c
3
c
1
c
5
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= ⟨b + u, a + u − 1, u
8
− 3u
7
+ 8u
6
− 11u
5
+ 12u
4
− 7u
3
+ 2u
2
+ 1⟩
I
u
2
= ⟨b + u,
5u
13
+ 8u
12
+ 37u
11
+ 36u
10
+ 87u
9
+ 50u
8
+ 68u
7
+ 14u
6
− 24u
5
− 10u
4
− 31u
3
+ 14u
2
+ 4a + 31u + 8,
u
14
+ 2u
13
+ 8u
12
+ 10u
11
+ 20u
10
+ 16u
9
+ 17u
8
+ 6u
7
− 4u
6
− 6u
5
− 7u
4
+ 6u
2
+ 4u + 1⟩
I
u
3
= ⟨2u
13
+ 3u
12
+ 14u
11
+ 13u
10
+ 30u
9
+ 17u
8
+ 16u
7
+ 4u
6
− 20u
5
− 4u
4
− 14u
3
+ 3u
2
+ 4b + 12u + 5,
2u
13
+ 3u
12
+ 14u
11
+ 13u
10
+ 30u
9
+ 17u
8
+ 16u
7
+ 4u
6
− 20u
5
− 4u
4
− 14u
3
+ 3u
2
+ 4a + 12u + 1,
u
14
+ 2u
13
+ 8u
12
+ 10u
11
+ 20u
10
+ 16u
9
+ 17u
8
+ 6u
7
− 4u
6
− 6u
5
− 7u
4
+ 6u
2
+ 4u + 1⟩
I
u
4
= ⟨150778247696u
13
− 1269915907352u
12
+ ··· + 29523131488b − 694243865440,
− 45565437328u
13
+ 456270050744u
12
+ ··· + 59046262976a + 429363368096,
16u
14
− 152u
13
+ ··· − 384u + 64⟩
I
u
5
= ⟨b + u, a + u + 1, u
8
+ u
7
+ 4u
6
+ u
5
+ 4u
4
− u
3
+ 2u
2
+ 1⟩
I
u
6
= ⟨−4u
17
a − 67u
17
+ ··· − 4a + 48, u
17
a + 35u
17
+ ··· + 14a − 83, u
18
+ 3u
17
+ ··· − 5u + 1⟩
I
u
7
= ⟨−u
5
a
3
+ u
5
a
2
+ ··· + a + 2, −u
5
a
3
+ u
5
a
2
+ ··· − b − a,
u
5
a
2
+ u
3
a
2
+ u
5
− u
3
a − u
4
− u
2
a + bu − au − u
2
− b + u + 1,
u
6
a
2
+ 2u
4
a
2
+ u
6
− u
4
a − u
5
+ a
2
u
2
− u
3
a + u
4
− u
2
a − 2u
3
− au + u
2
+ 1⟩
* 6 irreducible components of dim
C
= 0, with total 94 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).
1
* 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
= ⟨b + u, a + u − 1, u
8
− 3u
7
+ 8u
6
− 11u
5
+ 12u
4
− 7u
3
+ 2u
2
+ 1⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
−u + 1
−u
a
11
=
u
u
a
2
=
u
2
− u + 1
u
2
− u
a
12
=
u
3
− u
2
+ 2u
u
3
− u
2
+ u
a
6
=
u
2
− u + 1
u
2
a
4
=
−u
3
+ u
2
− 2u + 1
−u
3
− u
a
1
=
−u
7
+ 2u
6
− 5u
5
+ 5u
4
− 5u
3
+ 3u
2
− u + 1
−u
7
+ u
6
− 3u
5
+ u
4
− 2u
3
+ u
2
− u
a
5
=
u
4
− u
3
+ 3u
2
− u + 1
−u
6
+ u
5
− 2u
4
+ u
2
a
9
=
u
7
− 2u
6
+ 5u
5
− 4u
4
+ 4u
3
u
7
− 2u
6
+ 4u
5
− 3u
4
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
7
+ 3u
6
− 6u
5
− 6u
4
+ 12u
3
− 15u
2
+ 9u
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
u
8
− 3u
7
+ 8u
6
− 11u
5
+ 12u
4
− 7u
3
+ 2u
2
+ 1
c
2
, c
3
, c
6
c
7
, c
10
, c
11
u
8
+ 3u
7
+ 8u
6
+ 11u
5
+ 12u
4
+ 7u
3
+ 2u
2
+ 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
8
+ 7y
7
+ 22y
6
+ 33y
5
+ 24y
4
+ 15y
3
+ 28y
2
+ 4y + 1
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802481 + 0.507921I
a = 0.197519 − 0.507921I
b = −0.802481 − 0.507921I
9.81664 − 1.80153I 6.98214 − 1.70884I
u = 0.802481 − 0.507921I
a = 0.197519 + 0.507921I
b = −0.802481 + 0.507921I
9.81664 + 1.80153I 6.98214 + 1.70884I
u = 0.36074 + 1.40947I
a = 0.63926 − 1.40947I
b = −0.36074 − 1.40947I
−9.81664 + 1.80153I −6.98214 + 1.70884I
u = 0.36074 − 1.40947I
a = 0.63926 + 1.40947I
b = −0.36074 + 1.40947I
−9.81664 − 1.80153I −6.98214 − 1.70884I
u = −0.252888 + 0.365077I
a = 1.252890 − 0.365077I
b = 0.252888 − 0.365077I
− 1.13765I 0. + 6.26766I
u = −0.252888 − 0.365077I
a = 1.252890 + 0.365077I
b = 0.252888 + 0.365077I
1.13765I 0. − 6.26766I
u = 0.58967 + 1.51917I
a = 0.41033 − 1.51917I
b = −0.58967 − 1.51917I
18.0487I 0. − 8.38908I
u = 0.58967 − 1.51917I
a = 0.41033 + 1.51917I
b = −0.58967 + 1.51917I
− 18.0487I 0. + 8.38908I
6
II. I
u
2
= ⟨b + u, 5u
13
+ 8u
12
+ · · · + 4a + 8, u
14
+ 2u
13
+ · · · + 4u + 1⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
−
5
4
u
13
− 2u
12
+ ··· −
31
4
u − 2
−u
a
11
=
u
u
a
2
=
−
3
2
u
13
−
5
2
u
12
+ ··· −
17
2
u −
5
2
−
1
4
u
13
−
1
2
u
12
+ ··· −
7
4
u −
1
2
a
12
=
u
13
+
3
2
u
12
+ ··· + 5u + 2
3
16
u
13
+
1
8
u
12
+ ··· +
31
16
u +
3
4
a
6
=
−
1
2
u
13
−
3
4
u
12
+ ··· − 3u −
1
4
u
2
a
4
=
−
3
2
u
13
−
5
2
u
12
+ ··· −
19
2
u −
5
2
−u
3
− u
a
1
=
−
1
2
u
12
−
1
2
u
11
+ ··· − 4u −
3
2
−
3
4
u
13
−
3
2
u
12
+ ··· −
17
4
u −
3
2
a
5
=
−
1
2
u
13
− u
12
+ ··· −
7
2
u −
1
2
−
1
2
u
13
−
3
4
u
12
+ ··· − u −
1
4
a
9
=
u
13
+
3
2
u
12
+ ··· + 3u +
3
2
−
1
4
u
13
−
1
16
u
12
+ ··· + u +
3
16
(ii) Obstruction class = −1
(iii) Cusp Shapes =
71
8
u
13
+
61
4
u
12
+
541
8
u
11
+
137
2
u
10
+
1283
8
u
9
+
175
2
u
8
+ 125u
7
+
5
4
u
6
−
79
2
u
5
−
87
2
u
4
−
381
8
u
3
+ 27u
2
+
411
8
u +
39
2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
c
12
u
14
+ 2u
13
+ ··· + 4u + 1
c
2
, c
11
16(16u
14
+ 152u
13
+ ··· + 384u + 64)
c
3
, c
6
, c
7
c
10
u
14
− 2u
13
+ ··· − 4u + 1
c
5
, c
8
16(16u
14
− 152u
13
+ ··· − 384u + 64)
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
7
, c
9
c
10
, c
12
y
14
+ 12y
13
+ ··· − 4y + 1
c
2
, c
5
, c
8
c
11
256(256y
14
+ 736y
13
+ ··· + 22528y + 4096)
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735177 + 0.243598I
a = −0.31889 − 1.70839I
b = −0.735177 − 0.243598I
8.49202 − 7.10507I 5.55614 + 2.56250I
u = 0.735177 − 0.243598I
a = −0.31889 + 1.70839I
b = −0.735177 + 0.243598I
8.49202 + 7.10507I 5.55614 − 2.56250I
u = 0.330527 + 1.221190I
a = 0.11627 − 2.33392I
b = −0.330527 − 1.221190I
5.35568 + 10.94750I 1.20768 − 7.19213I
u = 0.330527 − 1.221190I
a = 0.11627 + 2.33392I
b = −0.330527 + 1.221190I
5.35568 − 10.94750I 1.20768 + 7.19213I
u = −0.104132 + 1.285370I
a = 0.14969 − 1.95386I
b = 0.104132 − 1.285370I
−4.77245 − 2.59879I −6.95245 + 3.73921I
u = −0.104132 − 1.285370I
a = 0.14969 + 1.95386I
b = 0.104132 + 1.285370I
−4.77245 + 2.59879I −6.95245 − 3.73921I
u = −0.672210 + 0.160128I
a = −0.586673 + 0.704036I
b = 0.672210 − 0.160128I
4.77245 − 2.59879I 6.95245 + 3.73921I
u = −0.672210 − 0.160128I
a = −0.586673 − 0.704036I
b = 0.672210 + 0.160128I
4.77245 + 2.59879I 6.95245 − 3.73921I
u = −0.44398 + 1.43884I
a = −0.70423 − 1.58491I
b = 0.44398 − 1.43884I
−5.35568 − 10.94750I −1.20768 + 7.19213I
u = −0.44398 − 1.43884I
a = −0.70423 + 1.58491I
b = 0.44398 + 1.43884I
−5.35568 + 10.94750I −1.20768 − 7.19213I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362798 + 0.314516I
a = 1.21504 − 0.98313I
b = 0.362798 − 0.314516I
− 1.12378I 0. + 6.09178I
u = −0.362798 − 0.314516I
a = 1.21504 + 0.98313I
b = 0.362798 + 0.314516I
1.12378I 0. − 6.09178I
u = −0.48258 + 1.50879I
a = −0.37121 − 1.49894I
b = 0.48258 − 1.50879I
−8.49202 − 7.10507I −5.55614 + 2.56250I
u = −0.48258 − 1.50879I
a = −0.37121 + 1.49894I
b = 0.48258 + 1.50879I
−8.49202 + 7.10507I −5.55614 − 2.56250I
11
III.
I
u
3
= ⟨2u
13
+3u
12
+· · ·+4b +5, 2u
13
+3u
12
+· · ·+4a +1, u
14
+2u
13
+· · ·+4u +1⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
−
1
2
u
13
−
3
4
u
12
+ ··· − 3u −
1
4
−
1
2
u
13
−
3
4
u
12
+ ··· − 3u −
5
4
a
11
=
u
u
a
2
=
−
1
2
u
13
−
3
4
u
12
+ ··· − 3u −
1
4
−
1
2
u
13
−
3
4
u
12
+ ··· − 3u −
5
4
a
12
=
1
4
u
13
+
1
2
u
12
+ ··· +
11
4
u +
1
2
1
4
u
13
+
1
2
u
12
+ ··· +
7
4
u +
1
2
a
6
=
−
3
4
u
13
−
21
16
u
12
+ ··· − 5u −
17
16
−
1
4
u
13
−
9
16
u
12
+ ··· − 2u −
13
16
a
4
=
−0.812500u
13
− 1.54688u
12
+ ··· − 4.25000u − 0.984375
−0.0625000u
13
− 0.234375u
12
+ ··· + 0.750000u + 0.0781250
a
1
=
0.421875u
13
+ 1.03125u
12
+ ··· + 2.23438u + 1.18750
0.609375u
13
+ 1.65625u
12
+ ··· + 3.17188u + 0.937500
a
5
=
−
5
4
u
13
−
29
16
u
12
+ ··· − 7u −
33
16
1
4
u
13
+
7
16
u
12
+ ··· −
1
2
u −
5
16
a
9
=
−0.687500u
13
− 1.12500u
12
+ ··· − 3.43750u − 0.750000
−
7
16
u
13
−
9
8
u
12
+ ··· −
35
16
u −
3
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
71
8
u
13
+
61
4
u
12
+
541
8
u
11
+
137
2
u
10
+
1283
8
u
9
+
175
2
u
8
+ 125u
7
+
5
4
u
6
−
79
2
u
5
−
87
2
u
4
−
381
8
u
3
+ 27u
2
+
411
8
u +
39
2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
u
14
+ 2u
13
+ ··· + 4u + 1
c
2
, c
7
, c
10
c
11
u
14
− 2u
13
+ ··· − 4u + 1
c
3
, c
6
16(16u
14
+ 152u
13
+ ··· + 384u + 64)
c
9
, c
12
16(16u
14
− 152u
13
+ ··· − 384u + 64)
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
10
, c
11
y
14
+ 12y
13
+ ··· − 4y + 1
c
3
, c
6
, c
9
c
12
256(256y
14
+ 736y
13
+ ··· + 22528y + 4096)
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735177 + 0.243598I
a = 0.337138 + 0.975478I
b = −0.662862 + 0.975478I
8.49202 − 7.10507I 5.55614 + 2.56250I
u = 0.735177 − 0.243598I
a = 0.337138 − 0.975478I
b = −0.662862 − 0.975478I
8.49202 + 7.10507I 5.55614 − 2.56250I
u = 0.330527 + 1.221190I
a = −0.506537 − 0.177835I
b = −1.50654 − 0.17783I
5.35568 + 10.94750I 1.20768 − 7.19213I
u = 0.330527 − 1.221190I
a = −0.506537 + 0.177835I
b = −1.50654 + 0.17783I
5.35568 − 10.94750I 1.20768 + 7.19213I
u = −0.104132 + 1.285370I
a = 0.145481 − 0.128174I
b = −0.854519 − 0.128174I
−4.77245 − 2.59879I −6.95245 + 3.73921I
u = −0.104132 − 1.285370I
a = 0.145481 + 0.128174I
b = −0.854519 + 0.128174I
−4.77245 + 2.59879I −6.95245 − 3.73921I
u = −0.672210 + 0.160128I
a = 0.292144 + 0.782483I
b = −0.707856 + 0.782483I
4.77245 − 2.59879I 6.95245 + 3.73921I
u = −0.672210 − 0.160128I
a = 0.292144 − 0.782483I
b = −0.707856 − 0.782483I
4.77245 + 2.59879I 6.95245 − 3.73921I
u = −0.44398 + 1.43884I
a = 0.28005 + 1.58724I
b = −0.71995 + 1.58724I
−5.35568 − 10.94750I −1.20768 + 7.19213I
u = −0.44398 − 1.43884I
a = 0.28005 − 1.58724I
b = −0.71995 − 1.58724I
−5.35568 + 10.94750I −1.20768 − 7.19213I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362798 + 0.314516I
a = 1.098900 − 0.510617I
b = 0.098902 − 0.510617I
− 1.12378I 0. + 6.09178I
u = −0.362798 − 0.314516I
a = 1.098900 + 0.510617I
b = 0.098902 + 0.510617I
1.12378I 0. − 6.09178I
u = −0.48258 + 1.50879I
a = 0.60282 + 1.29294I
b = −0.397177 + 1.292940I
−8.49202 − 7.10507I −5.55614 + 2.56250I
u = −0.48258 − 1.50879I
a = 0.60282 − 1.29294I
b = −0.397177 − 1.292940I
−8.49202 + 7.10507I −5.55614 − 2.56250I
16
IV. I
u
4
= ⟨1.51 × 10
11
u
13
− 1.27 × 10
12
u
12
+ · · · + 2.95 × 10
10
b − 6.94 ×
10
11
, −4.56 × 10
10
u
13
+ 4.56 × 10
11
u
12
+ · · · + 5.90 × 10
10
a + 4.29 ×
10
11
, 16u
14
− 152u
13
+ · · · − 384u + 64⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
0.771690u
13
− 7.72733u
12
+ ··· + 36.3451u − 7.27164
−5.10712u
13
+ 43.0143u
12
+ ··· − 110.305u + 23.5153
a
11
=
u
u
a
2
=
6.27509u
13
− 53.7103u
12
+ ··· + 135.401u − 27.7001
0.396272u
13
− 2.96866u
12
+ ··· − 11.2489u + 3.08676
a
12
=
−0.433597u
13
+ 3.07351u
12
+ ··· + 9.75173u − 3.28454
−1.39433u
13
+ 13.2245u
12
+ ··· − 39.2531u + 7.93893
a
6
=
−1.98473u
13
+ 17.4606u
12
+ ··· − 37.1706u + 8.38054
−1.02400u
13
+ 7.30966u
12
+ ··· + 11.8341u − 3.84294
a
4
=
−6.45812u
13
+ 53.4349u
12
+ ··· − 113.519u + 23.9546
5.19125u
13
− 46.5395u
12
+ ··· + 130.406u − 26.1690
a
1
=
2.29549u
13
− 18.6841u
12
+ ··· + 22.4712u − 3.09596
1.93780u
13
− 17.1761u
12
+ ··· + 35.1477u − 7.07687
a
5
=
−3.03039u
13
+ 26.1775u
12
+ ··· − 50.8615u + 10.1149
0.216231u
13
− 3.35036u
12
+ ··· + 36.8578u − 8.71066
a
9
=
0.379426u
13
− 2.77238u
12
+ ··· − 1.09120u + 0.400513
−0.177226u
13
+ 1.36624u
12
+ ··· − 8.94746u + 1.81095
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
22971118306
922597859
u
13
−
205737218319
922597859
u
12
+ ··· +
620526036416
922597859
u −
129937751014
922597859
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
16(16u
14
− 152u
13
+ ··· − 384u + 64)
c
2
, c
3
, c
6
c
11
u
14
− 2u
13
+ ··· − 4u + 1
c
5
, c
8
, c
9
c
12
u
14
+ 2u
13
+ ··· + 4u + 1
c
7
, c
10
16(16u
14
+ 152u
13
+ ··· + 384u + 64)
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
c
10
256(256y
14
+ 736y
13
+ ··· + 22528y + 4096)
c
2
, c
3
, c
5
c
6
, c
8
, c
9
c
11
, c
12
y
14
+ 12y
13
+ ··· − 4y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.707856 + 0.782483I
a = 0.132280 + 0.530765I
b = 0.672210 + 0.160128I
4.77245 + 2.59879I 6.95245 − 3.73921I
u = 0.707856 − 0.782483I
a = 0.132280 − 0.530765I
b = 0.672210 − 0.160128I
4.77245 − 2.59879I 6.95245 + 3.73921I
u = 0.854519 + 0.128174I
a = 0.205611 + 0.203611I
b = 0.104132 − 1.285370I
−4.77245 − 2.59879I −6.95245 + 3.73921I
u = 0.854519 − 0.128174I
a = 0.205611 − 0.203611I
b = 0.104132 + 1.285370I
−4.77245 + 2.59879I −6.95245 − 3.73921I
u = 0.662862 + 0.975478I
a = −0.555661 − 0.388074I
b = −0.735177 + 0.243598I
8.49202 + 7.10507I 5.55614 − 2.56250I
u = 0.662862 − 0.975478I
a = −0.555661 + 0.388074I
b = −0.735177 − 0.243598I
8.49202 − 7.10507I 5.55614 + 2.56250I
u = 0.397177 + 1.292940I
a = −0.68850 + 1.52229I
b = 0.48258 + 1.50879I
−8.49202 + 7.10507I −5.55614 − 2.56250I
u = 0.397177 − 1.292940I
a = −0.68850 − 1.52229I
b = 0.48258 − 1.50879I
−8.49202 − 7.10507I −5.55614 + 2.56250I
u = −0.098902 + 0.510617I
a = 1.089120 + 0.255309I
b = 0.362798 − 0.314516I
− 1.12378I 0. + 6.09178I
u = −0.098902 − 0.510617I
a = 1.089120 − 0.255309I
b = 0.362798 + 0.314516I
1.12378I 0. − 6.09178I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50654 + 0.17783I
a = −0.019777 − 0.447277I
b = −0.330527 − 1.221190I
5.35568 + 10.94750I 1.20768 − 7.19213I
u = 1.50654 − 0.17783I
a = −0.019777 + 0.447277I
b = −0.330527 + 1.221190I
5.35568 − 10.94750I 1.20768 + 7.19213I
u = 0.71995 + 1.58724I
a = −0.413070 + 1.329820I
b = 0.44398 + 1.43884I
−5.35568 + 10.94750I −1.20768 − 7.19213I
u = 0.71995 − 1.58724I
a = −0.413070 − 1.329820I
b = 0.44398 − 1.43884I
−5.35568 − 10.94750I −1.20768 + 7.19213I
21
V. I
u
5
= ⟨b + u, a + u + 1, u
8
+ u
7
+ 4u
6
+ u
5
+ 4u
4
− u
3
+ 2u
2
+ 1⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
−u − 1
−u
a
11
=
u
u
a
2
=
−u
2
− u − 1
−u
2
− u
a
12
=
u
3
+ u
2
+ 2u
u
3
+ u
2
+ u
a
6
=
u
2
+ u + 1
u
2
a
4
=
−u
3
− u
2
− 2u − 1
−u
3
− u
a
1
=
−u
7
− 2u
6
− 5u
5
− 5u
4
− 5u
3
− 3u
2
− u − 1
−u
7
− u
6
− 3u
5
− u
4
− 2u
3
− u
2
− u
a
5
=
u
4
+ u
3
+ 3u
2
+ u + 1
−u
6
− u
5
− 2u
4
+ u
2
a
9
=
u
7
+ 2u
6
+ 5u
5
+ 4u
4
+ 4u
3
u
7
+ 2u
6
+ 4u
5
+ 3u
4
+ 2u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
7
− 3u
6
+ 6u
5
− 18u
4
+ 6u
3
− 21u
2
+ 9u − 6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
9
, c
10
u
8
− u
7
+ 4u
6
− u
5
+ 4u
4
+ u
3
+ 2u
2
+ 1
c
3
, c
4
, c
7
c
8
, c
11
, c
12
u
8
+ u
7
+ 4u
6
+ u
5
+ 4u
4
− u
3
+ 2u
2
+ 1
23
(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
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 36y
4
+ 23y
3
+ 12y
2
+ 4y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.200786 + 1.204120I
a = −0.79921 − 1.20412I
b = 0.200786 − 1.204120I
− 1.61656I − 60.10 + 1.306426I
u = −0.200786 − 1.204120I
a = −0.79921 + 1.20412I
b = 0.200786 + 1.204120I
1.61656I − 60.10 − 1.306426I
u = 0.537476 + 0.510510I
a = −1.53748 − 0.51051I
b = −0.537476 − 0.510510I
7.30226 + 8.49334I 1.28328 − 6.26325I
u = 0.537476 − 0.510510I
a = −1.53748 + 0.51051I
b = −0.537476 + 0.510510I
7.30226 − 8.49334I 1.28328 + 6.26325I
u = −0.327893 + 0.646046I
a = −0.672107 − 0.646046I
b = 0.327893 − 0.646046I
− 2.71955I 0. + 9.22661I
u = −0.327893 − 0.646046I
a = −0.672107 + 0.646046I
b = 0.327893 + 0.646046I
2.71955I 0. − 9.22661I
u = −0.50880 + 1.43795I
a = −0.49120 − 1.43795I
b = 0.50880 − 1.43795I
−7.30226 − 8.49334I −1.28328 + 6.26325I
u = −0.50880 − 1.43795I
a = −0.49120 + 1.43795I
b = 0.50880 + 1.43795I
−7.30226 + 8.49334I −1.28328 − 6.26325I
25
VI. I
u
6
= ⟨−4u
17
a − 67u
17
+ · · · − 4a + 48, u
17
a + 35u
17
+ · · · + 14a −
83, u
18
+ 3u
17
+ · · · − 5u + 1⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
a
0.0434783au
17
+ 0.728261u
17
+ ··· + 0.0434783a − 0.521739
a
11
=
u
u
a
2
=
−0.0434783au
17
+ 0.521739u
17
+ ··· + 0.956522a + 0.271739
5
4
u
17
+
15
4
u
16
+ ··· +
19
4
u −
1
4
a
12
=
−0.206522au
17
− 1.52174u
17
+ ··· + 0.793478a + 5.47826
0.521739au
17
+ 0.489130u
17
+ ··· + 0.271739a + 0.739130
a
6
=
0.271739au
17
− 3.01087u
17
+ ··· − 0.728261a + 6.73913
0.271739au
17
− 2.01087u
17
+ ··· − 0.728261a − 1.01087
a
4
=
0.304348au
17
+ 0.347826u
17
+ ··· + 3.05435a − 0.652174
0.902174au
17
− 3.07609u
17
+ ··· + 1.65217a + 3.42391
a
1
=
2.19565au
17
+ 2.90217u
17
+ ··· − 0.304348a − 14.3478
2.11957au
17
+ 2.56522u
17
+ ··· + 0.119565a + 1.06522
a
5
=
0.815217au
17
− 2.53261u
17
+ ··· − 0.934783a + 5.21739
0.978261au
17
− 1.48913u
17
+ ··· − 0.771739a − 0.739130
a
9
=
0.554348au
17
+ 0.597826u
17
+ ··· − 0.695652a − 17.1522
−
3
4
u
17
a −
5
4
u
17
+ ··· + 2a +
15
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
− 11u
16
− 33u
15
− 66u
14
− 122u
13
− 187u
12
− 278u
11
−
350u
10
− 429u
9
− 473u
8
− 456u
7
− 421u
6
− 311u
5
− 184u
4
− 100u
3
− 6u
2
− u + 3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
9
, c
12
(u
18
+ 3u
17
+ ··· − 5u + 1)
2
c
2
, c
3
, c
6
c
7
, c
10
, c
11
(u
18
− 3u
17
+ ··· + 5u + 1)
2
27
(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
18
+ 11y
17
+ ··· + 5y + 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033350 + 0.273029I
a = −0.433707 − 0.370047I
b = 0.201212 − 1.332210I
− 5.69302I 0. + 5.51057I
u = −1.033350 + 0.273029I
a = 0.1070220 + 0.0106006I
b = −0.393396 + 1.167600I
− 5.69302I 0. + 5.51057I
u = −1.033350 − 0.273029I
a = −0.433707 + 0.370047I
b = 0.201212 + 1.332210I
5.69302I 0. − 5.51057I
u = −1.033350 − 0.273029I
a = 0.1070220 − 0.0106006I
b = −0.393396 − 1.167600I
5.69302I 0. − 5.51057I
u = −0.142014 + 1.106070I
a = 0.071587 − 0.703715I
b = 1.15680 − 0.88478I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.142014 + 1.106070I
a = 0.96521 + 2.15390I
b = 0.046149 + 1.226040I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.142014 − 1.106070I
a = 0.071587 + 0.703715I
b = 1.15680 + 0.88478I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.142014 − 1.106070I
a = 0.96521 − 2.15390I
b = 0.046149 − 1.226040I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.273973 + 1.135890I
a = 0.470175 − 0.732350I
b = −0.137537 + 0.138392I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.273973 + 1.135890I
a = −0.965306 − 1.015510I
b = −0.822569 − 0.928852I
1.89061 − 0.92430I 3.71672 + 0.79423I
29
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273973 − 1.135890I
a = 0.470175 + 0.732350I
b = −0.137537 − 0.138392I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = −0.273973 − 1.135890I
a = −0.965306 + 1.015510I
b = −0.822569 + 0.928852I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = −0.046149 + 1.226040I
a = 0.260286 + 1.034350I
b = 1.15680 + 0.88478I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.046149 + 1.226040I
a = −0.54315 + 2.07539I
b = 0.142014 + 1.106070I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.046149 − 1.226040I
a = 0.260286 − 1.034350I
b = 1.15680 − 0.88478I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.046149 − 1.226040I
a = −0.54315 − 2.07539I
b = 0.142014 − 1.106070I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.393396 + 1.167600I
a = −0.0434586 + 0.0825532I
b = 1.033350 + 0.273029I
5.69302I 0. − 5.51057I
u = 0.393396 + 1.167600I
a = −0.27658 + 2.05625I
b = 0.201212 + 1.332210I
5.69302I 0. − 5.51057I
u = 0.393396 − 1.167600I
a = −0.0434586 − 0.0825532I
b = 1.033350 − 0.273029I
− 5.69302I 0. + 5.51057I
u = 0.393396 − 1.167600I
a = −0.27658 − 2.05625I
b = 0.201212 − 1.332210I
− 5.69302I 0. + 5.51057I
30
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.822569 + 0.928852I
a = 0.401451 + 0.910666I
b = −0.137537 + 0.138392I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.822569 + 0.928852I
a = 0.263961 − 1.292830I
b = 0.273973 − 1.135890I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.822569 − 0.928852I
a = 0.401451 − 0.910666I
b = −0.137537 − 0.138392I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.822569 − 0.928852I
a = 0.263961 + 1.292830I
b = 0.273973 + 1.135890I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = −0.201212 + 1.332210I
a = 0.132851 − 0.432317I
b = 1.033350 − 0.273029I
− 5.69302I 0. + 5.51057I
u = −0.201212 + 1.332210I
a = −0.07848 + 1.89570I
b = −0.393396 + 1.167600I
− 5.69302I 0. + 5.51057I
u = −0.201212 − 1.332210I
a = 0.132851 + 0.432317I
b = 1.033350 + 0.273029I
5.69302I 0. − 5.51057I
u = −0.201212 − 1.332210I
a = −0.07848 − 1.89570I
b = −0.393396 − 1.167600I
5.69302I 0. − 5.51057I
u = −1.15680 + 0.88478I
a = 0.584996 + 0.682030I
b = 0.046149 + 1.226040I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −1.15680 + 0.88478I
a = −0.344252 − 0.418138I
b = 0.142014 − 1.106070I
−1.89061 − 0.92430I −3.71672 + 0.79423I
31
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15680 − 0.88478I
a = 0.584996 − 0.682030I
b = 0.046149 − 1.226040I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −1.15680 − 0.88478I
a = −0.344252 + 0.418138I
b = 0.142014 + 1.106070I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = 0.137537 + 0.138392I
a = −0.13089 − 5.21023I
b = 0.273973 + 1.135890I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.137537 + 0.138392I
a = −5.94172 − 2.17896I
b = −0.822569 + 0.928852I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.137537 − 0.138392I
a = −0.13089 + 5.21023I
b = 0.273973 − 1.135890I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.137537 − 0.138392I
a = −5.94172 + 2.17896I
b = −0.822569 − 0.928852I
1.89061 − 0.92430I 3.71672 + 0.79423I
32
VII. I
u
7
= ⟨−u
5
a
3
+ u
5
a
2
+ · · · + a + 2, −u
5
a
3
+ u
5
a
2
+ · · · − b − a, u
5
a
2
+
u
5
+ · · · − b + 1, u
6
a
2
+ u
6
+ · · · − au + 1⟩
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
a
b
a
11
=
u
u
a
2
=
u
5
a
2
− u
4
a
2
+ u
3
a
2
+ u
5
− a
2
u
2
− u
3
a − 2u
4
+ u
3
− u
2
− b + a + 2u
u
5
a
2
− u
4
a
2
+ u
3
a
2
+ u
5
− a
2
u
2
− u
3
a − 2u
4
+ u
3
− u
2
+ 2u
a
12
=
u
5
a
2
+ u
5
+ ··· − b − 1
−
1
2
u
5
a
3
+
1
2
u
5
a
2
+ ··· −
1
2
a − 1
a
6
=
1
2
u
5
a
3
−
1
2
u
5
a
2
+ ··· +
1
2
a + 1
1
2
u
5
a
3
−
1
2
u
5
a
2
+ ··· −
1
2
a − 1
a
4
=
1
2
u
5
a
4
−
1
4
u
5
a
3
+ ··· −
1
2
a
2
+
1
4
a
1
2
u
5
a
4
−
3
4
u
5
a
3
+ ··· −
1
2
a
2
−
1
4
a
a
1
=
−
1
2
u
5
a
4
−
1
4
u
5
a
3
+ ··· +
5
4
a − 1
−
1
2
u
5
a
4
+
1
4
u
5
a
3
+ ··· +
3
4
a − 1
a
5
=
1
2
u
5
a
3
−
3
2
u
5
a
2
+ ··· +
3
2
b +
1
2
a
1
2
u
5
a
3
−
1
2
u
5
a
2
+ ··· −
1
2
a − 1
a
9
=
1
2
u
5
a
3
+
1
2
u
5
a
2
+ ··· +
1
2
b −
1
2
a
u
5
a
3
+ 2u
5
a
2
+ ··· − b + 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(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.
33
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
34
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
9
16(u
8
− 3u
7
+ 8u
6
− 11u
5
+ 12u
4
− 7u
3
+ 2u
2
+ 1)
· (u
8
− u
7
+ ··· + 2u
2
+ 1)(u
14
+ 2u
13
+ ··· + 4u + 1)
2
· (16u
14
− 152u
13
+ ··· − 384u + 64)(u
18
+ 3u
17
+ ··· − 5u + 1)
2
c
2
, c
6
, c
10
16(u
8
− u
7
+ 4u
6
− u
5
+ 4u
4
+ u
3
+ 2u
2
+ 1)
· (u
8
+ 3u
7
+ 8u
6
+ 11u
5
+ 12u
4
+ 7u
3
+ 2u
2
+ 1)
· ((u
14
− 2u
13
+ ··· − 4u + 1)
2
)(16u
14
+ 152u
13
+ ··· + 384u + 64)
· (u
18
− 3u
17
+ ··· + 5u + 1)
2
c
3
, c
7
, c
11
16(u
8
+ u
7
+ 4u
6
+ u
5
+ 4u
4
− u
3
+ 2u
2
+ 1)
· (u
8
+ 3u
7
+ 8u
6
+ 11u
5
+ 12u
4
+ 7u
3
+ 2u
2
+ 1)
· ((u
14
− 2u
13
+ ··· − 4u + 1)
2
)(16u
14
+ 152u
13
+ ··· + 384u + 64)
· (u
18
− 3u
17
+ ··· + 5u + 1)
2
c
4
, c
8
, c
12
16(u
8
− 3u
7
+ 8u
6
− 11u
5
+ 12u
4
− 7u
3
+ 2u
2
+ 1)
· (u
8
+ u
7
+ ··· + 2u
2
+ 1)(u
14
+ 2u
13
+ ··· + 4u + 1)
2
· (16u
14
− 152u
13
+ ··· − 384u + 64)(u
18
+ 3u
17
+ ··· − 5u + 1)
2
35
IX. 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
256(y
8
+ 7y
7
+ 22y
6
+ 33y
5
+ 24y
4
+ 15y
3
+ 28y
2
+ 4y + 1)
· (y
8
+ 7y
7
+ 22y
6
+ 37y
5
+ 36y
4
+ 23y
3
+ 12y
2
+ 4y + 1)
· (y
14
+ 12y
13
+ ··· − 4y + 1)
2
· (256y
14
+ 736y
13
+ ··· + 22528y + 4096)
· (y
18
+ 11y
17
+ ··· + 5y + 1)
2
36
