12a
1157
(K12a
1157
)
A knot diagram
1
Linearized knot diagam
4 9 8 10 11 12 1 3 2 5 6 7
Solving Sequence
6,11
12 7 1 8 5 10 4 2 3 9
c
11
c
6
c
12
c
7
c
5
c
10
c
4
c
1
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
19
+ u
18
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 19 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
19
+ u
18
+ · · · − 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
7
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
u
3
− 2u
u
5
− 3u
3
+ u
a
5
=
u
u
a
10
=
−u
2
+ 1
−u
2
a
4
=
−u
3
+ 2u
−u
3
+ u
a
2
=
u
10
− 7u
8
+ 16u
6
− 13u
4
+ u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 8u
4
+ 3u
2
a
3
=
−u
11
+ 8u
9
− 22u
7
+ 24u
5
− 9u
3
+ 2u
−u
13
+ 9u
11
− 29u
9
+ 40u
7
− 22u
5
+ 3u
3
+ u
a
9
=
−u
18
+ 13u
16
+ ··· + 3u
2
+ 1
−u
18
+ 12u
16
− 57u
14
+ 138u
12
− 185u
10
+ 142u
8
− 62u
6
+ 12u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
14
−44u
12
+ 184u
10
−364u
8
+ 4u
7
+ 344u
6
−24u
5
−136u
4
+ 40u
3
+ 16u
2
−16u −10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 7u
18
+ ··· + 72u − 41
c
2
, c
3
, c
8
c
9
u
19
+ u
18
+ ··· − 2u − 1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
u
19
+ u
18
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 17y
18
+ ··· + 26586y −1681
c
2
, c
3
, c
8
c
9
y
19
+ 23y
18
+ ··· − 2y −1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
y
19
− 29y
18
+ ··· − 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845643 + 0.288890I
−10.86190 + 3.90709I −14.5654 − 4.4789I
u = −0.845643 − 0.288890I
−10.86190 − 3.90709I −14.5654 + 4.4789I
u = 0.747058 + 0.191235I
−2.97563 − 2.48429I −13.4435 + 6.6309I
u = 0.747058 − 0.191235I
−2.97563 + 2.48429I −13.4435 − 6.6309I
u = 1.35365
−7.74124 −9.76410
u = −1.387880 + 0.077610I
−10.14090 + 3.44117I −14.0567 − 4.3682I
u = −1.387880 − 0.077610I
−10.14090 − 3.44117I −14.0567 + 4.3682I
u = −0.604746
−1.09372 −8.26920
u = 1.43278 + 0.12906I
−18.5196 − 5.4586I −15.6445 + 3.0996I
u = 1.43278 − 0.12906I
−18.5196 + 5.4586I −15.6445 − 3.0996I
u = 0.263289 + 0.450878I
−7.42738 − 1.46197I −9.51323 + 3.95730I
u = 0.263289 − 0.450878I
−7.42738 + 1.46197I −9.51323 − 3.95730I
u = −0.156591 + 0.294132I
−0.229049 + 0.841361I −5.82037 − 7.86296I
u = −0.156591 − 0.294132I
−0.229049 − 0.841361I −5.82037 + 7.86296I
u = −1.83296
−19.7038 −10.2700
u = 1.83960 + 0.01849I
17.2008 − 3.9150I −14.0216 + 3.6447I
u = 1.83960 − 0.01849I
17.2008 + 3.9150I −14.0216 − 3.6447I
u = −1.85060 + 0.03225I
8.56699 + 6.28958I −15.7829 − 2.5323I
u = −1.85060 − 0.03225I
8.56699 − 6.28958I −15.7829 + 2.5323I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
19
− 7u
18
+ ··· + 72u − 41
c
2
, c
3
, c
8
c
9
u
19
+ u
18
+ ··· − 2u − 1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
u
19
+ u
18
+ ··· − 2u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
19
− 17y
18
+ ··· + 26586y −1681
c
2
, c
3
, c
8
c
9
y
19
+ 23y
18
+ ··· − 2y −1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
y
19
− 29y
18
+ ··· − 2y −1
7
