12n
0276
(K12n
0276
)
A knot diagram
1
Linearized knot diagam
3 4 8 2 9 4 12 10 6 3 7 11
Solving Sequence
7,12 3,8
4 2 5 6 11 1 10 9
c
7
c
3
c
2
c
4
c
6
c
11
c
12
c
10
c
9
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
3
− u
2
+ b + u + 1, −u
2
+ a − u, u
4
+ 2u
3
+ u
2
− 2u − 1i
I
u
2
= hu
3
− u
2
+ b − u + 1, −2u
3
+ u
2
+ a + u, u
4
− u
2
+ 1i
I
u
3
= h2u
7
− 3u
6
+ 3u
5
+ 3u
3
+ 2u
2
+ 2b − 3u − 1, −3u
7
+ 4u
6
− 3u
5
− 3u
4
− 3u
3
− 3u
2
+ 2a + 4u + 3,
u
8
− 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1i
I
u
4
= h2u
7
− 3u
6
+ 3u
5
+ 3u
3
+ 2u
2
+ 2b − 3u − 1, −u
7
+ u
6
− 2u
5
+ u
4
− 4u
3
− u
2
+ 2a − u,
u
8
− 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1i
I
u
5
= hu
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 3u
2
+ 4b + 5u + 6, −u
7
+ 3u
6
+ 2u
5
+ 3u
4
− 10u
3
+ 5u
2
+ 8a + 11u + 10,
u
8
+ 3u
7
+ 4u
6
+ u
5
+ 7u
3
+ 15u
2
+ 12u + 4i
I
u
6
= hu
3
+ b − u − 1, −u
2
+ a + 1, u
4
− u
2
+ 1i
I
u
7
= hu
3
+ b − u − 1, −2u
3
− u
2
+ a + u + 1, u
4
− u
2
+ 1i
I
u
8
= hu
3
+ u
2
+ b − u, a − 1, u
4
− u
2
+ 1i
* 8 irreducible components of dim
C
= 0, with total 44 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
3
− u
2
+ b + u + 1, −u
2
+ a − u, u
4
+ 2u
3
+ u
2
− 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
u
2
+ u
u
3
+ u
2
− u − 1
a
8
=
1
−u
2
a
4
=
u
2
+ 2u
u
2
− u − 1
a
2
=
2u
2
− u − 1
4u
3
+ 3u
2
− 3u − 2
a
5
=
5u
3
+ 4u
2
− 2u − 2
−3u
3
− 10u
2
+ 5u + 4
a
6
=
−u
3
− 4u
2
+ 2
−4u
3
− 2u
2
+ 4u + 2
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
−2u
3
− 3u
2
+ 1
3u
2
− 1
a
9
=
−4u
2
+ 2
−6u
3
− 5u
2
+ 6u + 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6u + 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ 10u
3
+ 27u
2
− 22u + 1
c
2
, c
4
, c
8
c
12
u
4
− 2u
3
+ 7u
2
− 6u + 1
c
3
, c
5
, c
7
c
9
, c
11
u
4
− 2u
3
+ u
2
+ 2u − 1
c
6
, c
10
u
4
+ 10u
2
− 16u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 46y
3
+ 1171y
2
− 430y + 1
c
2
, c
4
, c
8
c
12
y
4
+ 10y
3
+ 27y
2
− 22y + 1
c
3
, c
5
, c
7
c
9
, c
11
y
4
− 2y
3
+ 7y
2
− 6y + 1
c
6
, c
10
y
4
+ 20y
3
+ 108y
2
− 176y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883204
a = 1.66325
b = −0.414214
4.18641 21.2990
u = −0.468990
a = −0.249038
b = −0.414214
0.748389 13.1860
u = −1.20711 + 0.97832I
a = −0.70711 − 1.38355I
b = 2.41421
−17.2718 − 12.3509I 8.75736 + 5.86991I
u = −1.20711 − 0.97832I
a = −0.70711 + 1.38355I
b = 2.41421
−17.2718 + 12.3509I 8.75736 − 5.86991I
5
II. I
u
2
= hu
3
− u
2
+ b − u + 1, −2u
3
+ u
2
+ a + u, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
2u
3
− u
2
− u
−u
3
+ u
2
+ u − 1
a
8
=
1
−u
2
a
4
=
2u
3
− u
2
− 2u
u
2
+ u − 1
a
2
=
2u
3
+ u − 1
−2u
3
+ u
2
+ u
a
5
=
−u
3
u
3
− u
a
6
=
−3u
3
2u
3
− 2u
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
u
2
− 3
u
2
+ 1
a
9
=
−2u
2
u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
2
+ 16
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
2
− u + 1)
2
c
2
, c
8
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
u
4
+ 2u
3
+ 2u
2
+ 4u + 4
c
10
u
4
− 2u
3
+ 2u
2
− 4u + 4
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
, c
10
y
4
− 4y
2
+ 16
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −1.36603 + 0.63397I
b = 0.366025 + 0.366025I
6.08965I 10.0000 − 10.3923I
u = 0.866025 − 0.500000I
a = −1.36603 − 0.63397I
b = 0.366025 − 0.366025I
− 6.08965I 10.0000 + 10.3923I
u = −0.866025 + 0.500000I
a = 0.36603 + 2.36603I
b = −1.36603 − 1.36603I
− 6.08965I 10.0000 + 10.3923I
u = −0.866025 − 0.500000I
a = 0.36603 − 2.36603I
b = −1.36603 + 1.36603I
6.08965I 10.0000 − 10.3923I
9
III. I
u
3
= h2u
7
− 3u
6
+ 3u
5
+ 3u
3
+ 2u
2
+ 2b − 3u − 1, −3u
7
+ 4u
6
+ · · · +
2a + 3, u
8
− 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
3
2
u
7
− 2u
6
+ ··· − 2u −
3
2
−u
7
+
3
2
u
6
+ ··· +
3
2
u +
1
2
a
8
=
1
−u
2
a
4
=
u
7
− u
6
+ 2u
4
+ u
3
+ u
2
− 2u − 2
−
1
2
u
7
+ u
6
+ ··· + u +
1
2
a
2
=
2u
7
−
5
2
u
6
+ ··· −
1
2
u −
3
2
−u
7
+
1
2
u
6
+ ··· +
3
2
u +
1
2
a
5
=
−2u
7
+ 3u
6
− 2u
5
− 2u
4
− 3u
3
+ 2u + 1
2u
5
− u
4
+ u
3
+ u
2
− u − 1
a
6
=
3
2
u
7
− 2u
6
+ ··· − 2u −
1
2
−
1
2
u
7
+
1
2
u
6
+ ··· +
1
2
u + 1
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
3
2
u
7
− 2u
6
+ ··· − 2u −
3
2
−
1
2
u
7
+
1
2
u
6
+ ··· +
3
2
u + 1
a
9
=
1
2
u
7
−
1
2
u
6
+ ··· +
1
2
u
2
−
3
2
u
1
2
u
6
−
1
2
u
5
+ ··· +
1
2
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 4u
6
− 2u
5
− 4u
4
− 8u
3
− 4u
2
+ 6u + 16
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 19u
7
+ ··· + 1248u + 256
c
2
, c
4
u
8
− u
7
+ 10u
6
− 13u
5
+ 42u
4
− 41u
3
+ 57u
2
− 24u + 16
c
3
u
8
− 3u
7
+ 4u
6
− u
5
− 7u
3
+ 15u
2
− 12u + 4
c
5
, c
7
, c
9
c
11
u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1
c
6
, c
10
u
8
+ 7u
7
+ 25u
6
+ 52u
5
+ 54u
4
+ 16u
3
− 8u
2
+ 4
c
8
, c
12
u
8
+ 6u
6
− 5u
4
+ 6u
2
− 4u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 45y
7
+ ··· − 213504y + 65536
c
2
, c
4
y
8
+ 19y
7
+ ··· + 1248y + 256
c
3
y
8
− y
7
+ 10y
6
− 13y
5
+ 42y
4
− 41y
3
+ 57y
2
− 24y + 16
c
5
, c
7
, c
9
c
11
y
8
+ 6y
6
− 5y
4
+ 6y
2
− 4y + 1
c
6
, c
10
y
8
+ y
7
+ 5y
6
− 244y
5
+ 860y
4
− 920y
3
+ 496y
2
− 64y + 16
c
8
, c
12
y
8
+ 12y
7
+ 26y
6
− 48y
5
+ 99y
4
− 48y
3
+ 26y
2
− 4y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273242 + 1.017440I
a = −0.038323 + 1.295230I
b = 0.307345 + 0.392902I
−3.00645 − 3.35673I 6.09240 + 3.01308I
u = −0.273242 − 1.017440I
a = −0.038323 − 1.295230I
b = 0.307345 − 0.392902I
−3.00645 + 3.35673I 6.09240 − 3.01308I
u = 0.796321 + 0.241667I
a = −1.41328 + 1.73710I
b = 0.545221 − 1.041750I
1.17763 + 4.62470I 15.0023 − 5.8935I
u = 0.796321 − 0.241667I
a = −1.41328 − 1.73710I
b = 0.545221 + 1.041750I
1.17763 − 4.62470I 15.0023 + 5.8935I
u = −0.666028 + 0.230992I
a = 0.439021 − 0.264857I
b = −0.768780 − 0.277812I
0.403528 − 0.080080I 11.24335 + 0.17507I
u = −0.666028 − 0.230992I
a = 0.439021 + 0.264857I
b = −0.768780 + 0.277812I
0.403528 + 0.080080I 11.24335 − 0.17507I
u = 1.14295 + 1.14532I
a = 0.512578 − 0.434756I
b = −2.08379 − 0.09016I
−18.3139 + 4.2344I 7.66195 − 1.86062I
u = 1.14295 − 1.14532I
a = 0.512578 + 0.434756I
b = −2.08379 + 0.09016I
−18.3139 − 4.2344I 7.66195 + 1.86062I
13
IV. I
u
4
= h2u
7
− 3u
6
+ 3u
5
+ 3u
3
+ 2u
2
+ 2b − 3u − 1, −u
7
+ u
6
− 2u
5
+ u
4
−
4u
3
− u
2
+ 2a − u, u
8
− 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
1
2
u
7
−
1
2
u
6
+ ··· +
1
2
u
2
+
1
2
u
−u
7
+
3
2
u
6
+ ··· +
3
2
u +
1
2
a
8
=
1
−u
2
a
4
=
1
2
u
7
−
1
2
u
6
+ ··· +
1
2
u
2
+
3
2
u
−u
7
+
3
2
u
6
+ ··· +
3
2
u +
1
2
a
2
=
−
1
2
u
7
+ u
6
+ ··· + u +
1
2
−
1
2
u
7
+
1
2
u
6
+ ··· −
1
2
u
2
+
1
2
u
a
5
=
u
5
+ 2u
3
+ u
−u
7
− u
5
− 2u
3
+ u
a
6
=
−2u
7
+
5
2
u
6
+ ··· +
5
2
u +
9
2
−
1
2
u
6
+
3
2
u
5
+ ··· −
3
2
u −
1
2
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
−
3
2
u
7
+ 2u
6
+ ··· −
3
2
u
2
+
1
2
u
7
− u
6
+ u
5
+ u
4
+ u
3
+ u
2
− u − 1
a
9
=
−
5
2
u
7
+ 3u
6
+ ··· + 3u +
9
2
−
1
2
u
6
+
1
2
u
5
+ ··· −
3
2
u −
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 4u
6
− 2u
5
− 4u
4
− 8u
3
− 4u
2
+ 6u + 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 12u
7
+ 26u
6
− 48u
5
+ 99u
4
− 48u
3
+ 26u
2
− 4u + 1
c
2
, c
4
, c
12
u
8
+ 6u
6
− 5u
4
+ 6u
2
− 4u + 1
c
3
, c
7
, c
11
u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1
c
5
, c
9
u
8
− 3u
7
+ 4u
6
− u
5
− 7u
3
+ 15u
2
− 12u + 4
c
6
u
8
+ 12u
6
− 16u
5
+ 49u
4
− 56u
3
+ 78u
2
− 54u + 27
c
8
u
8
− u
7
+ 10u
6
− 13u
5
+ 42u
4
− 41u
3
+ 57u
2
− 24u + 16
c
10
u
8
− 4u
7
+ 18u
6
− 58u
5
+ 111u
4
− 126u
3
+ 92u
2
− 40u + 11
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 92y
7
+ ··· + 36y + 1
c
2
, c
4
, c
12
y
8
+ 12y
7
+ 26y
6
− 48y
5
+ 99y
4
− 48y
3
+ 26y
2
− 4y + 1
c
3
, c
7
, c
11
y
8
+ 6y
6
− 5y
4
+ 6y
2
− 4y + 1
c
5
, c
9
y
8
− y
7
+ 10y
6
− 13y
5
+ 42y
4
− 41y
3
+ 57y
2
− 24y + 16
c
6
y
8
+ 24y
7
+ ··· + 1296y + 729
c
8
y
8
+ 19y
7
+ ··· + 1248y + 256
c
10
y
8
+ 20y
7
+ 82y
6
− 192y
5
+ 719y
4
+ 304y
3
+ 826y
2
+ 424y + 121
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273242 + 1.017440I
a = 0.170826 − 0.749091I
b = 0.307345 + 0.392902I
−3.00645 − 3.35673I 6.09240 + 3.01308I
u = −0.273242 − 1.017440I
a = 0.170826 + 0.749091I
b = 0.307345 − 0.392902I
−3.00645 + 3.35673I 6.09240 − 3.01308I
u = 0.796321 + 0.241667I
a = 1.33140 + 1.33913I
b = 0.545221 − 1.041750I
1.17763 + 4.62470I 15.0023 − 5.8935I
u = 0.796321 − 0.241667I
a = 1.33140 − 1.33913I
b = 0.545221 + 1.041750I
1.17763 − 4.62470I 15.0023 + 5.8935I
u = −0.666028 + 0.230992I
a = −0.471568 + 0.932013I
b = −0.768780 − 0.277812I
0.403528 − 0.080080I 11.24335 + 0.17507I
u = −0.666028 − 0.230992I
a = −0.471568 − 0.932013I
b = −0.768780 + 0.277812I
0.403528 + 0.080080I 11.24335 − 0.17507I
u = 1.14295 + 1.14532I
a = 0.469343 − 1.233450I
b = −2.08379 − 0.09016I
−18.3139 + 4.2344I 7.66195 − 1.86062I
u = 1.14295 − 1.14532I
a = 0.469343 + 1.233450I
b = −2.08379 + 0.09016I
−18.3139 − 4.2344I 7.66195 + 1.86062I
17
V. I
u
5
= hu
7
+ u
6
+ 2u
5
+ u
4
+ 2u
3
+ 3u
2
+ 4b + 5u + 6, −u
7
+ 3u
6
+ · · · +
8a + 10, u
8
+ 3u
7
+ 4u
6
+ u
5
+ 7u
3
+ 15u
2
+ 12u + 4i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
1
8
u
7
−
3
8
u
6
+ ··· −
11
8
u −
5
4
−
1
4
u
7
−
1
4
u
6
+ ··· −
5
4
u −
3
2
a
8
=
1
−u
2
a
4
=
11
8
u
7
+
15
8
u
6
+ ··· +
47
8
u +
1
4
−
5
4
u
7
−
13
4
u
6
+ ··· −
57
4
u −
15
2
a
2
=
−
9
8
u
7
−
17
8
u
6
+ ··· −
57
8
u −
9
4
5
4
u
7
+
17
4
u
6
+ ··· +
65
4
u +
13
2
a
5
=
u
7
+ u
6
+ u
5
− u
4
+ 2u
3
+ 5u
2
+ 4u
−3u
7
− 6u
6
− 3u
5
+ 2u
4
− 4u
3
− 18u
2
− 19u − 8
a
6
=
−
17
8
u
7
−
25
8
u
6
+ ··· −
81
8
u −
1
4
11
4
u
7
+
23
4
u
6
+ ··· +
99
4
u +
23
2
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
−2.37500u
7
− 5.37500u
6
+ ··· − 21.3750u − 8.75000
−
1
4
u
7
+
3
4
u
6
+ ··· +
19
4
u +
7
2
a
9
=
−
11
8
u
7
−
23
8
u
6
+ ··· −
87
8
u −
13
4
1
4
u
7
+
9
4
u
6
+ ··· +
29
4
u +
7
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
6
− 4u
5
− 2u
4
+ 6u
3
− 10u
2
− 20u − 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 12u
7
+ 26u
6
− 48u
5
+ 99u
4
− 48u
3
+ 26u
2
− 4u + 1
c
2
, c
4
, c
8
u
8
+ 6u
6
− 5u
4
+ 6u
2
− 4u + 1
c
3
, c
5
, c
9
u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1
c
6
u
8
− 4u
7
+ 18u
6
− 58u
5
+ 111u
4
− 126u
3
+ 92u
2
− 40u + 11
c
7
, c
11
u
8
− 3u
7
+ 4u
6
− u
5
− 7u
3
+ 15u
2
− 12u + 4
c
10
u
8
+ 12u
6
− 16u
5
+ 49u
4
− 56u
3
+ 78u
2
− 54u + 27
c
12
u
8
− u
7
+ 10u
6
− 13u
5
+ 42u
4
− 41u
3
+ 57u
2
− 24u + 16
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 92y
7
+ ··· + 36y + 1
c
2
, c
4
, c
8
y
8
+ 12y
7
+ 26y
6
− 48y
5
+ 99y
4
− 48y
3
+ 26y
2
− 4y + 1
c
3
, c
5
, c
9
y
8
+ 6y
6
− 5y
4
+ 6y
2
− 4y + 1
c
6
y
8
+ 20y
7
+ 82y
6
− 192y
5
+ 719y
4
+ 304y
3
+ 826y
2
+ 424y + 121
c
7
, c
11
y
8
− y
7
+ 10y
6
− 13y
5
+ 42y
4
− 41y
3
+ 57y
2
− 24y + 16
c
10
y
8
+ 24y
7
+ ··· + 1296y + 729
c
12
y
8
+ 19y
7
+ ··· + 1248y + 256
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937027 + 0.585611I
a = 0.68623 + 1.54063I
b = −1.261650 − 0.312913I
1.17763 − 4.62470I 15.0023 + 5.8935I
u = −0.937027 − 0.585611I
a = 0.68623 − 1.54063I
b = −1.261650 + 0.312913I
1.17763 + 4.62470I 15.0023 − 5.8935I
u = −0.678952 + 0.516253I
a = 0.018648 + 0.423357I
b = −0.966437 − 0.300245I
0.403528 + 0.080080I 11.24335 − 0.17507I
u = −0.678952 − 0.516253I
a = 0.018648 − 0.423357I
b = −0.966437 + 0.300245I
0.403528 − 0.080080I 11.24335 + 0.17507I
u = 1.064320 + 0.829887I
a = −0.584890 + 0.825215I
b = 1.44426 − 0.35067I
−3.00645 + 3.35673I 6.09240 − 3.01308I
u = 1.064320 − 0.829887I
a = −0.584890 − 0.825215I
b = 1.44426 + 0.35067I
−3.00645 − 3.35673I 6.09240 + 3.01308I
u = −0.94834 + 1.25418I
a = −0.369985 − 0.584379I
b = 2.28383 − 0.12843I
−18.3139 + 4.2344I 7.66195 − 1.86062I
u = −0.94834 − 1.25418I
a = −0.369985 + 0.584379I
b = 2.28383 + 0.12843I
−18.3139 − 4.2344I 7.66195 + 1.86062I
21
VI. I
u
6
= hu
3
+ b − u − 1, −u
2
+ a + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
u
2
− 1
−u
3
+ u + 1
a
8
=
1
−u
2
a
4
=
−u
3
+ u
2
+ u − 1
−u
3
+ 1
a
2
=
u
3
− 1
−u
3
+ u
2
+ 2u
a
5
=
−u
3
u
3
− u
a
6
=
−u
3
+ 2u
−2u
3
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
−u
2
+ 1
−u
2
− 1
a
9
=
2
−3u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
2
− u + 1)
2
c
2
, c
8
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
(u
2
− 2u + 2)
2
c
10
(u
2
+ 2u + 2)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
, c
10
(y
2
+ 4)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.500000 + 0.866025I
b = 1.86603 − 0.50000I
2.02988I 10.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −0.500000 − 0.866025I
b = 1.86603 + 0.50000I
− 2.02988I 10.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = −0.500000 − 0.866025I
b = 0.133975 − 0.500000I
− 2.02988I 10.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = −0.500000 + 0.866025I
b = 0.133975 + 0.500000I
2.02988I 10.00000 − 3.46410I
25
VII. I
u
7
= hu
3
+ b − u − 1, −2u
3
− u
2
+ a + u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
2u
3
+ u
2
− u − 1
−u
3
+ u + 1
a
8
=
1
−u
2
a
4
=
2u
3
+ u
2
− 2u − 1
u + 1
a
2
=
2u
3
+ u
2
+ u
−2u
3
− u
2
+ u + 1
a
5
=
−u
3
u
3
− u
a
6
=
3u
3
+ u
2
− 3u − 2
u
2
+ 2u + 1
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
u
3
+ 2u
2
+ u + 1
−2u
3
− 2u
2
+ u + 1
a
9
=
−u
3
− u
2
+ 2u + 4
−u
3
− 2u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 12
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
2
− u + 1)
2
c
2
, c
8
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
u
4
− 4u
3
+ 5u
2
− 2u + 1
c
10
u
4
− 2u
3
+ 5u
2
− 4u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
y
4
− 6y
3
+ 11y
2
+ 6y + 1
c
10
y
4
+ 6y
3
+ 11y
2
− 6y + 1
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −1.36603 + 2.36603I
b = 1.86603 − 0.50000I
2.02988I 10.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −1.36603 − 2.36603I
b = 1.86603 + 0.50000I
− 2.02988I 10.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = 0.366025 + 0.633975I
b = 0.133975 − 0.500000I
− 2.02988I 10.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 0.366025 − 0.633975I
b = 0.133975 + 0.500000I
2.02988I 10.00000 − 3.46410I
29
VIII. I
u
8
= hu
3
+ u
2
+ b − u, a − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
3
=
1
−u
3
− u
2
+ u
a
8
=
1
−u
2
a
4
=
−u
3
+ u + 1
−u
3
− u
2
a
2
=
u
3
+ u
2
−u
3
− u
2
+ 2u + 1
a
5
=
−u
3
u
3
− u
a
6
=
−u
3
− 2u
2
− u + 1
2u
3
+ u
2
− 2u − 2
a
11
=
−u
u
a
1
=
u
3
−u
3
+ u
a
10
=
u
3
− 2u − 1
u
3
+ 2u
2
+ u − 1
a
9
=
2u
3
+ u
2
− u
−u
3
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
2
+ 8
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
(u
2
− u + 1)
2
c
2
, c
8
(u
2
+ u + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
u
4
− u
2
+ 1
c
6
u
4
+ 2u
3
+ 5u
2
+ 4u + 1
c
10
u
4
+ 4u
3
+ 5u
2
+ 2u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
12
(y
2
+ y + 1)
2
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
2
c
6
y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
10
y
4
− 6y
3
+ 11y
2
+ 6y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.00000
b = 0.36603 − 1.36603I
− 2.02988I 10.00000 + 3.46410I
u = 0.866025 − 0.500000I
a = 1.00000
b = 0.36603 + 1.36603I
2.02988I 10.00000 − 3.46410I
u = −0.866025 + 0.500000I
a = 1.00000
b = −1.36603 + 0.36603I
2.02988I 10.00000 − 3.46410I
u = −0.866025 − 0.500000I
a = 1.00000
b = −1.36603 − 0.36603I
− 2.02988I 10.00000 + 3.46410I
33
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
8
(u
4
+ 10u
3
+ 27u
2
− 22u + 1)
· (u
8
+ 12u
7
+ 26u
6
− 48u
5
+ 99u
4
− 48u
3
+ 26u
2
− 4u + 1)
2
· (u
8
+ 19u
7
+ ··· + 1248u + 256)
c
2
, c
8
(u
2
+ u + 1)
8
(u
4
− 2u
3
+ 7u
2
− 6u + 1)
· (u
8
+ 6u
6
− 5u
4
+ 6u
2
− 4u + 1)
2
· (u
8
− u
7
+ 10u
6
− 13u
5
+ 42u
4
− 41u
3
+ 57u
2
− 24u + 16)
c
3
, c
5
, c
7
c
9
, c
11
(u
4
− u
2
+ 1)
4
(u
4
− 2u
3
+ u
2
+ 2u − 1)
· (u
8
− 3u
7
+ 4u
6
− u
5
− 7u
3
+ 15u
2
− 12u + 4)
· (u
8
+ 2u
7
+ 2u
6
+ u
4
− 2u
2
+ 1)
2
c
4
, c
12
(u
2
− u + 1)
8
(u
4
− 2u
3
+ 7u
2
− 6u + 1)
· (u
8
+ 6u
6
− 5u
4
+ 6u
2
− 4u + 1)
2
· (u
8
− u
7
+ 10u
6
− 13u
5
+ 42u
4
− 41u
3
+ 57u
2
− 24u + 16)
c
6
(u
2
− 2u + 2)
2
(u
4
+ 10u
2
− 16u + 4)(u
4
− 4u
3
+ 5u
2
− 2u + 1)
· (u
4
+ 2u
3
+ 2u
2
+ 4u + 4)(u
4
+ 2u
3
+ 5u
2
+ 4u + 1)
· (u
8
+ 12u
6
− 16u
5
+ 49u
4
− 56u
3
+ 78u
2
− 54u + 27)
· (u
8
− 4u
7
+ 18u
6
− 58u
5
+ 111u
4
− 126u
3
+ 92u
2
− 40u + 11)
· (u
8
+ 7u
7
+ 25u
6
+ 52u
5
+ 54u
4
+ 16u
3
− 8u
2
+ 4)
c
10
(u
2
+ 2u + 2)
2
(u
4
+ 10u
2
− 16u + 4)(u
4
− 2u
3
+ 2u
2
− 4u + 4)
· (u
4
− 2u
3
+ 5u
2
− 4u + 1)(u
4
+ 4u
3
+ 5u
2
+ 2u + 1)
· (u
8
+ 12u
6
− 16u
5
+ 49u
4
− 56u
3
+ 78u
2
− 54u + 27)
· (u
8
− 4u
7
+ 18u
6
− 58u
5
+ 111u
4
− 126u
3
+ 92u
2
− 40u + 11)
· (u
8
+ 7u
7
+ 25u
6
+ 52u
5
+ 54u
4
+ 16u
3
− 8u
2
+ 4)
34
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
8
(y
4
− 46y
3
+ 1171y
2
− 430y + 1)
· ((y
8
− 92y
7
+ ··· + 36y + 1)
2
)(y
8
− 45y
7
+ ··· − 213504y + 65536)
c
2
, c
4
, c
8
c
12
(y
2
+ y + 1)
8
(y
4
+ 10y
3
+ 27y
2
− 22y + 1)
· (y
8
+ 12y
7
+ 26y
6
− 48y
5
+ 99y
4
− 48y
3
+ 26y
2
− 4y + 1)
2
· (y
8
+ 19y
7
+ ··· + 1248y + 256)
c
3
, c
5
, c
7
c
9
, c
11
(y
2
− y + 1)
8
(y
4
− 2y
3
+ 7y
2
− 6y + 1)
· (y
8
+ 6y
6
− 5y
4
+ 6y
2
− 4y + 1)
2
· (y
8
− y
7
+ 10y
6
− 13y
5
+ 42y
4
− 41y
3
+ 57y
2
− 24y + 16)
c
6
, c
10
(y
2
+ 4)
2
(y
4
− 4y
2
+ 16)(y
4
− 6y
3
+ 11y
2
+ 6y + 1)
· (y
4
+ 6y
3
+ 11y
2
− 6y + 1)(y
4
+ 20y
3
+ 108y
2
− 176y + 16)
· (y
8
+ y
7
+ 5y
6
− 244y
5
+ 860y
4
− 920y
3
+ 496y
2
− 64y + 16)
· (y
8
+ 20y
7
+ 82y
6
− 192y
5
+ 719y
4
+ 304y
3
+ 826y
2
+ 424y + 121)
· (y
8
+ 24y
7
+ ··· + 1296y + 729)
35
