12n
0113
(K12n
0113
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 10 3 11 12 5 7 8 9
Solving Sequence
7,10
11 8
3,12
6 5 2 1 4 9
c
10
c
7
c
11
c
6
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−647354734u
28
+ 978901627u
27
+ ··· + 206032449b − 1184912620,
− 64940111u
28
+ 106362659u
27
+ ··· + 206032449a + 214765723, u
29
− 2u
28
+ ··· + u − 1i
I
u
2
= hu
2
+ b − u − 2, a, u
3
− u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 32 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−6.47 × 10
8
u
28
+ 9.79 × 10
8
u
27
+ · · · + 2.06 × 10
8
b − 1.18 × 10
9
, −6.49 ×
10
7
u
28
+ 1.06× 10
8
u
27
+ · · · + 2.06 × 10
8
a +2.15 × 10
8
, u
29
− 2u
28
+ · · · + u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
3
+ u
a
3
=
0.315194u
28
− 0.516242u
27
+ ··· + 1.82950u − 1.04239
3.14200u
28
− 4.75120u
27
+ ··· + 6.60148u + 5.75110
a
12
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−0.839121u
28
+ 0.843763u
27
+ ··· − 1.98749u − 0.119530
0.215298u
28
− 0.607510u
27
+ ··· + 1.52402u + 1.00763
a
5
=
−1.05442u
28
+ 1.45127u
27
+ ··· − 3.51151u − 1.12716
0.215298u
28
− 0.607510u
27
+ ··· + 1.52402u + 1.00763
a
2
=
2.20636u
28
− 2.61370u
27
+ ··· + 2.80648u − 0.296715
3.57260u
28
− 4.96622u
27
+ ··· + 5.64951u + 5.76636
a
1
=
−u
4
+ 3u
2
− 1
u
6
− 4u
4
+ 3u
2
a
4
=
3.16326u
28
− 3.35382u
27
+ ··· − 0.465478u + 0.381491
3.74875u
28
− 5.35442u
27
+ ··· + 5.78774u + 6.35427
a
9
=
−u
3
+ 2u
u
5
− 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3792380055
68677483
u
28
+
5628748625
68677483
u
27
+ ··· −
5070709179
68677483
u −
6687860995
68677483
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 30u
28
+ ··· + 530u + 1
c
2
, c
4
u
29
− 4u
28
+ ··· + 18u − 1
c
3
, c
6
u
29
+ 5u
28
+ ··· + 84u − 8
c
5
, c
9
u
29
+ 2u
28
+ ··· − u − 1
c
7
, c
8
, c
10
c
11
, c
12
u
29
− 2u
28
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 58y
28
+ ··· + 261102y −1
c
2
, c
4
y
29
− 30y
28
+ ··· + 530y −1
c
3
, c
6
y
29
+ 21y
28
+ ··· + 2256y −64
c
5
, c
9
y
29
+ 30y
27
+ ··· + 9y −1
c
7
, c
8
, c
10
c
11
, c
12
y
29
− 36y
28
+ ··· + 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871800 + 0.572952I
a = −1.34659 + 0.79448I
b = −1.48468 − 0.59106I
−6.35449 − 8.78908I 6.18505 + 6.40374I
u = −0.871800 − 0.572952I
a = −1.34659 − 0.79448I
b = −1.48468 + 0.59106I
−6.35449 + 8.78908I 6.18505 − 6.40374I
u = 0.915102 + 0.577424I
a = −0.630350 − 1.126710I
b = −1.262120 − 0.106799I
−6.10118 + 0.29510I 5.18889 − 1.16439I
u = 0.915102 − 0.577424I
a = −0.630350 + 1.126710I
b = −1.262120 + 0.106799I
−6.10118 − 0.29510I 5.18889 + 1.16439I
u = −1.14574
a = 0.540876
b = −0.0550040
5.50698 18.3420
u = −0.020234 + 0.793792I
a = 1.86337 − 0.55939I
b = 1.41720 − 0.34042I
−8.92001 + 4.25864I 2.72812 − 2.59912I
u = −0.020234 − 0.793792I
a = 1.86337 + 0.55939I
b = 1.41720 + 0.34042I
−8.92001 − 4.25864I 2.72812 + 2.59912I
u = −0.699728 + 0.338099I
a = 1.36237 − 1.32693I
b = 0.968494 + 0.555673I
0.16525 − 3.96735I 8.32283 + 8.62955I
u = −0.699728 − 0.338099I
a = 1.36237 + 1.32693I
b = 0.968494 − 0.555673I
0.16525 + 3.96735I 8.32283 − 8.62955I
u = 0.680274 + 0.194448I
a = 0.272779 + 0.785923I
b = 1.128350 − 0.317013I
0.478397 + 0.446224I 9.33081 − 0.68417I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.680274 − 0.194448I
a = 0.272779 − 0.785923I
b = 1.128350 + 0.317013I
0.478397 − 0.446224I 9.33081 + 0.68417I
u = −0.439691 + 0.314107I
a = −1.42146 − 2.04429I
b = −0.346882 − 0.207064I
−2.81354 − 1.22096I 1.65575 + 5.11958I
u = −0.439691 − 0.314107I
a = −1.42146 + 2.04429I
b = −0.346882 + 0.207064I
−2.81354 + 1.22096I 1.65575 − 5.11958I
u = 0.536642
a = −0.443928
b = −3.69157
−0.846423 87.1400
u = 1.55407 + 0.03946I
a = 0.992776 − 0.855482I
b = 0.766756 + 0.115816I
3.99647 + 2.19066I 0
u = 1.55407 − 0.03946I
a = 0.992776 + 0.855482I
b = 0.766756 − 0.115816I
3.99647 − 2.19066I 0
u = −1.59090
a = 0.405019
b = 3.31575
6.62367 25.1550
u = 0.394545
a = −0.532583
b = 0.353791
0.662854 15.1320
u = −0.079696 + 0.381721I
a = −2.52365 + 0.46294I
b = −0.986678 + 0.376786I
−1.55597 + 1.38501I 1.25824 − 2.95729I
u = −0.079696 − 0.381721I
a = −2.52365 − 0.46294I
b = −0.986678 − 0.376786I
−1.55597 − 1.38501I 1.25824 + 2.95729I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61444 + 0.08862I
a = −0.653048 − 0.970484I
b = −1.011500 + 0.774939I
8.13246 + 5.52553I 0
u = 1.61444 − 0.08862I
a = −0.653048 + 0.970484I
b = −1.011500 − 0.774939I
8.13246 − 5.52553I 0
u = −1.62438 + 0.04713I
a = −0.178840 + 0.450917I
b = −1.17354 − 1.05585I
8.53322 − 1.28090I 0
u = −1.62438 − 0.04713I
a = −0.178840 − 0.450917I
b = −1.17354 + 1.05585I
8.53322 + 1.28090I 0
u = 1.66621 + 0.17240I
a = 0.679212 + 0.775786I
b = 1.53044 − 0.82697I
2.31087 + 11.70390I 0
u = 1.66621 − 0.17240I
a = 0.679212 − 0.775786I
b = 1.53044 + 0.82697I
2.31087 − 11.70390I 0
u = −1.68491 + 0.18549I
a = 0.244062 − 0.717045I
b = 1.081240 + 0.132670I
2.80677 − 3.35130I 0
u = −1.68491 − 0.18549I
a = 0.244062 + 0.717045I
b = 1.081240 − 0.132670I
2.80677 + 3.35130I 0
u = 1.78613
a = −0.290652
b = −0.177069
16.3052 0
7
II. I
u
2
= hu
2
+ b − u − 2, a, u
3
− u
2
− 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
2
− u + 1
a
3
=
0
−u
2
+ u + 2
a
12
=
−u
2
+ 1
u
2
+ u − 1
a
6
=
0
u
a
5
=
−u
u
a
2
=
u
−u
2
+ 2
a
1
=
u
−u
a
4
=
0
−u
2
+ u + 2
a
9
=
−u
2
+ 1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
2
− 7u − 14
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
, c
7
, c
8
u
3
+ u
2
− 2u − 1
c
9
, c
10
, c
11
c
12
u
3
− u
2
− 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
y
3
c
5
, c
7
, c
8
c
9
, c
10
, c
11
c
12
y
3
− 5y
2
+ 6y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24698
a = 0
b = −0.801938
4.69981 7.16850
u = 0.445042
a = 0
b = 2.24698
−0.939962 −15.5310
u = 1.80194
a = 0
b = 0.554958
15.9794 −0.637730
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
29
+ 30u
28
+ ··· + 530u + 1)
c
2
((u − 1)
3
)(u
29
− 4u
28
+ ··· + 18u − 1)
c
3
, c
6
u
3
(u
29
+ 5u
28
+ ··· + 84u − 8)
c
4
((u + 1)
3
)(u
29
− 4u
28
+ ··· + 18u − 1)
c
5
(u
3
+ u
2
− 2u − 1)(u
29
+ 2u
28
+ ··· − u − 1)
c
7
, c
8
(u
3
+ u
2
− 2u − 1)(u
29
− 2u
28
+ ··· + u − 1)
c
9
(u
3
− u
2
− 2u + 1)(u
29
+ 2u
28
+ ··· − u − 1)
c
10
, c
11
, c
12
(u
3
− u
2
− 2u + 1)(u
29
− 2u
28
+ ··· + u − 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
29
− 58y
28
+ ··· + 261102y −1)
c
2
, c
4
((y −1)
3
)(y
29
− 30y
28
+ ··· + 530y −1)
c
3
, c
6
y
3
(y
29
+ 21y
28
+ ··· + 2256y −64)
c
5
, c
9
(y
3
− 5y
2
+ 6y −1)(y
29
+ 30y
27
+ ··· + 9y −1)
c
7
, c
8
, c
10
c
11
, c
12
(y
3
− 5y
2
+ 6y −1)(y
29
− 36y
28
+ ··· + 9y −1)
13
