12a
1279
(K12a
1279
)
A knot diagram
1
Linearized knot diagam
5 8 9 10 1 12 11 4 3 2 7 6
Solving Sequence
6,12
7 1 5 2 11 8 3 10 4 9
c
6
c
12
c
5
c
1
c
11
c
7
c
2
c
10
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
− u
32
+ ··· − 3u + 1i
* 1 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
= hu
33
− u
32
+ · · · − 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
5
=
u
2
+ 1
−u
2
a
2
=
−u
3
− 2u
u
3
+ u
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
u
9
+ 6u
7
+ 11u
5
+ 6u
3
− u
u
11
+ 7u
9
+ 16u
7
+ 13u
5
+ 3u
3
+ u
a
10
=
−u
9
− 6u
7
− 11u
5
− 6u
3
+ u
u
9
+ 5u
7
+ 7u
5
+ 4u
3
+ u
a
4
=
−u
16
− 11u
14
− 47u
12
− 98u
10
− 101u
8
− 42u
6
+ 2u
2
+ 1
u
16
+ 10u
14
+ 38u
12
+ 70u
10
+ 68u
8
+ 36u
6
+ 10u
4
a
9
=
−u
29
− 20u
27
+ ··· − 8u
3
+ u
−u
31
− 21u
29
+ ··· + 6u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
32
− 4u
31
+ 96u
30
− 92u
29
+ 1028u
28
− 940u
27
+ 6476u
26
−
5620u
25
+ 26640u
24
− 21796u
23
+ 75088u
22
− 57436u
21
+ 147988u
20
− 104688u
19
+
204332u
18
− 131772u
17
+ 194992u
16
− 112484u
15
+ 124944u
14
− 63068u
13
+ 51396u
12
−
22528u
11
+ 12652u
10
−5244u
9
+ 1388u
8
−800u
7
−208u
6
−28u
5
−52u
4
−16u
2
+ 32u −6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
33
+ u
32
+ ··· − 3u − 1
c
2
, c
4
u
33
− u
32
+ ··· + 33u − 13
c
3
, c
8
, c
9
u
33
+ u
32
+ ··· + u − 1
c
10
u
33
− 7u
32
+ ··· − 815u + 215
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
33
+ 47y
32
+ ··· − 7y −1
c
2
, c
4
y
33
− 25y
32
+ ··· − 1667y −169
c
3
, c
8
, c
9
y
33
+ 27y
32
+ ··· − 7y −1
c
10
y
33
− 17y
32
+ ··· + 161125y −46225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135727 + 1.095360I
−0.48317 + 3.12381I 1.00988 − 3.98406I
u = −0.135727 − 1.095360I
−0.48317 − 3.12381I 1.00988 + 3.98406I
u = 0.052755 + 1.165150I
4.90112 − 1.50724I 6.17291 + 4.51787I
u = 0.052755 − 1.165150I
4.90112 + 1.50724I 6.17291 − 4.51787I
u = 0.196867 + 1.245830I
5.44294 − 8.78065I 5.04263 + 6.34982I
u = 0.196867 − 1.245830I
5.44294 + 8.78065I 5.04263 − 6.34982I
u = −0.171980 + 1.258180I
9.88543 + 4.54966I 9.59844 − 3.96601I
u = −0.171980 − 1.258180I
9.88543 − 4.54966I 9.59844 + 3.96601I
u = 0.135455 + 1.270780I
6.58142 − 0.29302I 6.45164 + 0.I
u = 0.135455 − 1.270780I
6.58142 + 0.29302I 6.45164 + 0.I
u = 0.302742 + 0.624808I
0.419041 + 1.219680I 4.08889 + 1.47779I
u = 0.302742 − 0.624808I
0.419041 − 1.219680I 4.08889 − 1.47779I
u = 0.407807 + 0.544208I
−0.34703 − 6.67794I 2.10309 + 8.18225I
u = 0.407807 − 0.544208I
−0.34703 + 6.67794I 2.10309 − 8.18225I
u = −0.363092 + 0.571858I
3.94486 + 2.68460I 7.39182 − 5.68857I
u = −0.363092 − 0.571858I
3.94486 − 2.68460I 7.39182 + 5.68857I
u = −0.398537 + 0.320533I
−4.91358 + 1.35189I −4.51051 − 4.98155I
u = −0.398537 − 0.320533I
−4.91358 − 1.35189I −4.51051 + 4.98155I
u = 0.476175 + 0.072408I
−1.74287 + 3.75371I −2.33384 − 2.56391I
u = 0.476175 − 0.072408I
−1.74287 − 3.75371I −2.33384 + 2.56391I
u = −0.456028
2.25176 2.33330
u = 0.199415 + 0.334719I
0.030917 − 0.754138I 1.01682 + 9.21232I
u = 0.199415 − 0.334719I
0.030917 + 0.754138I 1.01682 − 9.21232I
u = −0.02509 + 1.76282I
9.92457 + 3.73698I 0
u = −0.02509 − 1.76282I
9.92457 − 3.73698I 0
u = 0.01058 + 1.78001I
15.7033 − 1.7647I 0
u = 0.01058 − 1.78001I
15.7033 + 1.7647I 0
u = 0.04994 + 1.79686I
16.5996 − 9.9002I 0
u = 0.04994 − 1.79686I
16.5996 + 9.9002I 0
u = −0.04337 + 1.80000I
−18.3520 + 5.5330I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04337 − 1.80000I
−18.3520 − 5.5330I 0
u = 0.03408 + 1.80212I
17.8994 − 1.0723I 0
u = 0.03408 − 1.80212I
17.8994 + 1.0723I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
33
+ u
32
+ ··· − 3u − 1
c
2
, c
4
u
33
− u
32
+ ··· + 33u − 13
c
3
, c
8
, c
9
u
33
+ u
32
+ ··· + u − 1
c
10
u
33
− 7u
32
+ ··· − 815u + 215
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
33
+ 47y
32
+ ··· − 7y −1
c
2
, c
4
y
33
− 25y
32
+ ··· − 1667y −169
c
3
, c
8
, c
9
y
33
+ 27y
32
+ ··· − 7y −1
c
10
y
33
− 17y
32
+ ··· + 161125y −46225
8
