12a
0682
(K12a
0682
)
A knot diagram
1
Linearized knot diagam
3 7 11 12 9 8 2 6 1 5 4 10
Solving Sequence
2,8
7 3 1 6 9 10 5 11 12 4
c
7
c
2
c
1
c
6
c
8
c
9
c
5
c
10
c
12
c
4
c
3
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
53
+ u
52
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 53 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
53
+ u
52
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
6
=
u
2
+ 1
u
2
a
9
=
u
4
+ u
2
+ 1
u
4
a
10
=
−u
12
− u
10
− 3u
8
− 2u
6
+ u
2
+ 1
−u
14
− 2u
12
− 5u
10
− 6u
8
− 6u
6
− 2u
4
− u
2
a
5
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
11
=
u
26
+ 3u
24
+ ··· + 3u
2
+ 1
u
26
+ 2u
24
+ ··· − u
6
− u
2
a
12
=
u
21
+ 2u
19
+ 7u
17
+ 10u
15
+ 14u
13
+ 12u
11
+ 5u
9
− 2u
7
− 5u
5
− 2u
3
− u
u
23
+ 3u
21
+ ··· + 2u
3
+ u
a
4
=
−u
50
− 5u
48
+ ··· + 3u
2
+ 1
−u
52
− 6u
50
+ ··· − 26u
6
− 7u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
51
− 4u
50
+ ··· − 16u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
8
u
53
+ 11u
52
+ ··· − 5u − 1
c
2
, c
7
u
53
+ u
52
+ ··· + u + 1
c
3
, c
4
, c
11
u
53
+ u
52
+ ··· + 3u + 1
c
9
, c
12
u
53
+ 9u
52
+ ··· + 857u + 89
c
10
u
53
− 3u
52
+ ··· − 179u − 105
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
8
y
53
+ 63y
52
+ ··· − 13y −1
c
2
, c
7
y
53
+ 11y
52
+ ··· − 5y −1
c
3
, c
4
, c
11
y
53
− 49y
52
+ ··· − 5y −1
c
9
, c
12
y
53
+ 35y
52
+ ··· − 196313y −7921
c
10
y
53
− 13y
52
+ ··· + 120871y −11025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457945 + 0.892866I
−1.71286 + 2.75389I −6.34294 − 3.07234I
u = 0.457945 − 0.892866I
−1.71286 − 2.75389I −6.34294 + 3.07234I
u = 0.572730 + 0.813144I
−1.00719 + 4.98869I −3.18777 − 7.70135I
u = 0.572730 − 0.813144I
−1.00719 − 4.98869I −3.18777 + 7.70135I
u = −0.429825 + 0.920962I
−7.86744 − 0.15769I −10.16108 + 3.00425I
u = −0.429825 − 0.920962I
−7.86744 + 0.15769I −10.16108 − 3.00425I
u = −0.490682 + 0.914221I
−1.20646 − 6.61760I −4.55514 + 9.49134I
u = −0.490682 − 0.914221I
−1.20646 + 6.61760I −4.55514 − 9.49134I
u = 0.493153 + 0.936516I
−7.05643 + 9.90285I −8.45292 − 8.93815I
u = 0.493153 − 0.936516I
−7.05643 − 9.90285I −8.45292 + 8.93815I
u = −0.036116 + 0.938626I
−10.01760 − 4.89958I −13.7857 + 3.6935I
u = −0.036116 − 0.938626I
−10.01760 + 4.89958I −13.7857 − 3.6935I
u = −0.575852 + 0.733397I
2.95450 − 2.17059I 3.89779 + 4.69702I
u = −0.575852 − 0.733397I
2.95450 + 2.17059I 3.89779 − 4.69702I
u = 0.023560 + 0.907629I
−4.02491 + 1.91090I −10.66650 − 3.96746I
u = 0.023560 − 0.907629I
−4.02491 − 1.91090I −10.66650 + 3.96746I
u = 0.610238 + 0.641474I
−0.472073 − 0.554107I −1.056775 + 0.178286I
u = 0.610238 − 0.641474I
−0.472073 + 0.554107I −1.056775 − 0.178286I
u = −0.217456 + 0.806943I
−4.96706 − 2.01723I −11.79175 + 5.17722I
u = −0.217456 − 0.806943I
−4.96706 + 2.01723I −11.79175 − 5.17722I
u = 0.661436 + 0.434620I
−5.46999 − 5.61580I −4.48224 + 3.23992I
u = 0.661436 − 0.434620I
−5.46999 + 5.61580I −4.48224 − 3.23992I
u = −0.618304 + 0.456294I
0.22206 + 2.44713I −0.32336 − 3.63578I
u = −0.618304 − 0.456294I
0.22206 − 2.44713I −0.32336 + 3.63578I
u = 0.876686 + 0.875322I
0.37975 + 3.02773I 0
u = 0.876686 − 0.875322I
0.37975 − 3.02773I 0
u = −0.890877 + 0.888837I
6.84069 − 0.89167I 0
u = −0.890877 − 0.888837I
6.84069 + 0.89167I 0
u = −0.907804 + 0.877338I
2.05866 + 6.62991I 0
u = −0.907804 − 0.877338I
2.05866 − 6.62991I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.903027 + 0.883843I
7.77793 − 3.11403I 0
u = 0.903027 − 0.883843I
7.77793 + 3.11403I 0
u = 0.847469 + 0.952356I
0.13857 + 3.36391I 0
u = 0.847469 − 0.952356I
0.13857 − 3.36391I 0
u = −0.898144 + 0.916667I
8.05683 + 0.13889I 0
u = −0.898144 − 0.916667I
8.05683 − 0.13889I 0
u = −0.862668 + 0.953089I
6.63594 − 5.59402I 0
u = −0.862668 − 0.953089I
6.63594 + 5.59402I 0
u = 0.891690 + 0.928721I
11.67710 + 3.29120I 0
u = 0.891690 − 0.928721I
11.67710 − 3.29120I 0
u = −0.886770 + 0.940938I
7.97899 − 6.72566I 0
u = −0.886770 − 0.940938I
7.97899 + 6.72566I 0
u = 0.866244 + 0.963279I
7.52338 + 9.64804I 0
u = 0.866244 − 0.963279I
7.52338 − 9.64804I 0
u = −0.864545 + 0.969690I
1.76241 − 13.17230I 0
u = −0.864545 − 0.969690I
1.76241 + 13.17230I 0
u = −0.598640 + 0.307693I
−6.03882 − 3.60466I −5.04712 + 3.30603I
u = −0.598640 − 0.307693I
−6.03882 + 3.60466I −5.04712 − 3.30603I
u = 0.498225 + 0.373224I
−0.283096 + 0.992412I −1.65563 − 4.45703I
u = 0.498225 − 0.373224I
−0.283096 − 0.992412I −1.65563 + 4.45703I
u = 0.297051 + 0.536713I
−0.193421 + 0.916328I −4.23122 − 6.90314I
u = 0.297051 − 0.536713I
−0.193421 − 0.916328I −4.23122 + 6.90314I
u = −0.443543
−2.70485 −1.55100
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
8
u
53
+ 11u
52
+ ··· − 5u − 1
c
2
, c
7
u
53
+ u
52
+ ··· + u + 1
c
3
, c
4
, c
11
u
53
+ u
52
+ ··· + 3u + 1
c
9
, c
12
u
53
+ 9u
52
+ ··· + 857u + 89
c
10
u
53
− 3u
52
+ ··· − 179u − 105
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
8
y
53
+ 63y
52
+ ··· − 13y −1
c
2
, c
7
y
53
+ 11y
52
+ ··· − 5y −1
c
3
, c
4
, c
11
y
53
− 49y
52
+ ··· − 5y −1
c
9
, c
12
y
53
+ 35y
52
+ ··· − 196313y −7921
c
10
y
53
− 13y
52
+ ··· + 120871y −11025
8
