12a
0330
(K12a
0330
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 7 2 5 1 12 4 10 9
Solving Sequence
2,7
6 3 1 5 8 4 9 12 10 11
c
6
c
2
c
1
c
5
c
7
c
3
c
8
c
12
c
9
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
47
+ u
46
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 47 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
47
+ u
46
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
5
=
u
2
+ 1
u
2
a
8
=
u
4
+ u
2
+ 1
u
4
a
4
=
−u
11
− 2u
9
− 4u
7
− 4u
5
− 3u
3
−u
11
− u
9
− 2u
7
− u
5
+ u
3
+ u
a
9
=
u
12
+ u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 6u
8
+ 6u
6
+ 4u
4
+ u
2
a
12
=
u
21
+ 2u
19
+ ··· + 4u
3
+ u
u
23
+ 3u
21
+ ··· + 2u
3
+ u
a
10
=
u
30
+ 3u
28
+ ··· + 2u
2
+ 1
u
32
+ 4u
30
+ ··· + 8u
4
+ 2u
2
a
11
=
u
39
+ 4u
37
+ ··· + 8u
3
+ 2u
u
41
+ 5u
39
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
46
− 20u
44
+ ··· + 20u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
47
+ 11u
46
+ ··· + 16u
2
− 1
c
2
, c
6
u
47
− u
46
+ ··· + 2u + 1
c
3
u
47
− u
46
+ ··· − 6060u + 3361
c
4
, c
10
u
47
− u
46
+ ··· + 2u + 1
c
8
, c
9
, c
11
c
12
u
47
+ 9u
46
+ ··· + 4u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
47
+ 51y
46
+ ··· + 32y −1
c
2
, c
6
y
47
+ 11y
46
+ ··· + 16y
2
− 1
c
3
y
47
+ 31y
46
+ ··· + 5775512y −11296321
c
4
, c
10
y
47
− 9y
46
+ ··· − 4y
2
− 1
c
8
, c
9
, c
11
c
12
y
47
+ 59y
46
+ ··· − 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382879 + 0.913206I
−0.08570 + 6.28148I −8.16298 − 10.47100I
u = 0.382879 − 0.913206I
−0.08570 − 6.28148I −8.16298 + 10.47100I
u = 0.008475 + 0.965301I
6.38651 − 3.25280I −8.46380 + 2.37401I
u = 0.008475 − 0.965301I
6.38651 + 3.25280I −8.46380 − 2.37401I
u = −0.413985 + 0.853429I
0.89586 − 2.03383I −4.23793 + 3.81818I
u = −0.413985 − 0.853429I
0.89586 + 2.03383I −4.23793 − 3.81818I
u = −0.456667 + 0.956333I
9.00501 − 2.08590I −4.31423 + 3.31096I
u = −0.456667 − 0.956333I
9.00501 + 2.08590I −4.31423 − 3.31096I
u = 0.446885 + 0.962913I
8.85349 + 8.66849I −4.72563 − 8.03831I
u = 0.446885 − 0.962913I
8.85349 − 8.66849I −4.72563 + 8.03831I
u = 0.276872 + 0.873166I
−3.20238 + 2.30452I −16.3116 − 5.9470I
u = 0.276872 − 0.873166I
−3.20238 − 2.30452I −16.3116 + 5.9470I
u = 0.112869 + 0.850703I
−1.52782 − 1.56803I −12.46880 + 3.57703I
u = 0.112869 − 0.850703I
−1.52782 + 1.56803I −12.46880 − 3.57703I
u = −0.820103 + 0.872946I
3.33252 − 0.63798I −8.00000 − 1.61055I
u = −0.820103 − 0.872946I
3.33252 + 0.63798I −8.00000 + 1.61055I
u = −0.866477 + 0.852451I
7.76984 + 3.47355I −2.51866 − 3.95961I
u = −0.866477 − 0.852451I
7.76984 − 3.47355I −2.51866 + 3.95961I
u = −0.808162 + 0.922528I
3.18030 − 5.45437I −8.00000 + 6.66748I
u = −0.808162 − 0.922528I
3.18030 + 5.45437I −8.00000 − 6.66748I
u = −0.680659 + 0.361501I
10.90210 − 2.07362I 0.04088 + 2.30391I
u = −0.680659 − 0.361501I
10.90210 + 2.07362I 0.04088 − 2.30391I
u = 0.867742 + 0.871991I
8.77828 + 1.40174I 0. − 2.33106I
u = 0.867742 − 0.871991I
8.77828 − 1.40174I 0. + 2.33106I
u = 0.835618 + 0.904887I
6.11156 + 3.11267I 0. − 2.66928I
u = 0.835618 − 0.904887I
6.11156 − 3.11267I 0. + 2.66928I
u = 0.681301 + 0.344571I
10.82780 − 4.54766I −0.10220 + 2.48977I
u = 0.681301 − 0.344571I
10.82780 + 4.54766I −0.10220 − 2.48977I
u = −0.284938 + 0.707717I
−0.343803 − 1.199580I −4.23003 + 5.53729I
u = −0.284938 − 0.707717I
−0.343803 + 1.199580I −4.23003 − 5.53729I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.900013 + 0.851367I
17.6045 + 6.0118I 0. − 2.53476I
u = −0.900013 − 0.851367I
17.6045 − 6.0118I 0. + 2.53476I
u = 0.900037 + 0.855771I
17.8006 + 0.6918I 0. − 2.07521I
u = 0.900037 − 0.855771I
17.8006 − 0.6918I 0. + 2.07521I
u = 0.838574 + 0.946010I
8.54527 + 4.93007I 0
u = 0.838574 − 0.946010I
8.54527 − 4.93007I 0
u = −0.826944 + 0.956994I
7.44238 − 9.76256I 0. + 8.96106I
u = −0.826944 − 0.956994I
7.44238 + 9.76256I 0. − 8.96106I
u = −0.844018 + 0.977145I
17.2039 − 12.4586I −8.00000 + 7.31264I
u = −0.844018 − 0.977145I
17.2039 + 12.4586I −8.00000 − 7.31264I
u = 0.846803 + 0.974825I
17.4212 + 5.7646I 0
u = 0.846803 − 0.974825I
17.4212 − 5.7646I 0
u = −0.522799 + 0.418058I
2.21181 − 1.52903I −0.12044 + 3.94143I
u = −0.522799 − 0.418058I
2.21181 + 1.52903I −0.12044 − 3.94143I
u = 0.542166 + 0.291549I
1.78563 − 2.82233I −1.69698 + 4.51706I
u = 0.542166 − 0.291549I
1.78563 + 2.82233I −1.69698 − 4.51706I
u = 0.369088
−1.03563 −9.31600
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
47
+ 11u
46
+ ··· + 16u
2
− 1
c
2
, c
6
u
47
− u
46
+ ··· + 2u + 1
c
3
u
47
− u
46
+ ··· − 6060u + 3361
c
4
, c
10
u
47
− u
46
+ ··· + 2u + 1
c
8
, c
9
, c
11
c
12
u
47
+ 9u
46
+ ··· + 4u
2
+ 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
47
+ 51y
46
+ ··· + 32y −1
c
2
, c
6
y
47
+ 11y
46
+ ··· + 16y
2
− 1
c
3
y
47
+ 31y
46
+ ··· + 5775512y −11296321
c
4
, c
10
y
47
− 9y
46
+ ··· − 4y
2
− 1
c
8
, c
9
, c
11
c
12
y
47
+ 59y
46
+ ··· − 8y −1
8
