12a
0243
(K12a
0243
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 1 5 12 11 4 9 8
Solving Sequence
4,11
10 5 9 12 8 1 7 3 2 6
c
10
c
4
c
9
c
11
c
8
c
12
c
7
c
3
c
1
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
66
+ u
65
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 66 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
66
+ u
65
+ · · · + u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
2
a
12
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
1
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 2u
4
a
7
=
u
10
+ u
8
+ 4u
6
+ 3u
4
+ 3u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 6u
6
+ 3u
4
+ 2u
2
a
3
=
−u
21
− 2u
19
+ ··· − 6u
3
− u
−u
23
− 3u
21
+ ··· − 2u
3
+ u
a
2
=
u
52
+ 5u
50
+ ··· + u
2
+ 1
u
54
+ 6u
52
+ ··· − 17u
6
+ u
2
a
6
=
−u
28
− 3u
26
+ ··· + u
2
+ 1
−u
28
− 2u
26
+ ··· + 3u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
64
− 4u
63
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
+ 31u
65
+ ··· − u + 1
c
2
, c
5
u
66
+ u
65
+ ··· + 3u + 1
c
3
u
66
− u
65
+ ··· + 1669u + 673
c
4
, c
10
u
66
+ u
65
+ ··· + u + 1
c
6
u
66
+ 3u
65
+ ··· + 539u + 105
c
7
u
66
+ 9u
65
+ ··· + 113u + 29
c
8
, c
9
, c
11
c
12
u
66
+ 13u
65
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 9y
65
+ ··· + 9y + 1
c
2
, c
5
y
66
− 31y
65
+ ··· + y + 1
c
3
y
66
− 23y
65
+ ··· − 12012391y + 452929
c
4
, c
10
y
66
+ 13y
65
+ ··· + y + 1
c
6
y
66
+ 13y
65
+ ··· + 356909y + 11025
c
7
y
66
− 11y
65
+ ··· + 23481y + 841
c
8
, c
9
, c
11
c
12
y
66
+ 81y
65
+ ··· − 7y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599044 + 0.826443I
2.20023 + 0.03981I 1.90801 + 0.I
u = 0.599044 − 0.826443I
2.20023 − 0.03981I 1.90801 + 0.I
u = 0.516168 + 0.894544I
−2.24111 + 4.14051I −5.37917 − 5.76586I
u = 0.516168 − 0.894544I
−2.24111 − 4.14051I −5.37917 + 5.76586I
u = −0.575209 + 0.860059I
3.33392 − 4.67344I 3.60111 + 7.51773I
u = −0.575209 − 0.860059I
3.33392 + 4.67344I 3.60111 − 7.51773I
u = −0.417668 + 0.858179I
−3.47104 − 4.65742I −7.34835 + 7.77657I
u = −0.417668 − 0.858179I
−3.47104 + 4.65742I −7.34835 − 7.77657I
u = −0.548997 + 0.901918I
2.20323 − 6.68220I 0. + 7.34850I
u = −0.548997 − 0.901918I
2.20323 + 6.68220I 0. − 7.34850I
u = 0.662569 + 0.668001I
2.71906 + 4.65572I 3.37494 − 5.91636I
u = 0.662569 − 0.668001I
2.71906 − 4.65572I 3.37494 + 5.91636I
u = 0.545262 + 0.916750I
−0.02627 + 11.64450I 0. − 11.11786I
u = 0.545262 − 0.916750I
−0.02627 − 11.64450I 0. + 11.11786I
u = −0.658358 + 0.624266I
4.09825 + 0.06503I 6.21402 − 0.17680I
u = −0.658358 − 0.624266I
4.09825 − 0.06503I 6.21402 + 0.17680I
u = −0.331173 + 0.844557I
−2.52809 + 2.55717I −6.16177 + 0.11362I
u = −0.331173 − 0.844557I
−2.52809 − 2.55717I −6.16177 − 0.11362I
u = −0.111108 + 0.897806I
−3.65266 − 7.15580I −8.25035 + 7.79317I
u = −0.111108 − 0.897806I
−3.65266 + 7.15580I −8.25035 − 7.79317I
u = −0.056026 + 0.881651I
−5.32447 + 0.22926I −11.87724 + 0.46623I
u = −0.056026 − 0.881651I
−5.32447 − 0.22926I −11.87724 − 0.46623I
u = 0.112571 + 0.866237I
−1.39262 + 2.45864I −5.10441 − 4.27623I
u = 0.112571 − 0.866237I
−1.39262 − 2.45864I −5.10441 + 4.27623I
u = −0.669205 + 0.554761I
3.32166 + 2.13457I 5.05558 − 0.87891I
u = −0.669205 − 0.554761I
3.32166 − 2.13457I 5.05558 + 0.87891I
u = 0.683206 + 0.533126I
1.20996 − 7.07293I 1.66097 + 5.05839I
u = 0.683206 − 0.533126I
1.20996 + 7.07293I 1.66097 − 5.05839I
u = 0.397569 + 0.766288I
−0.23774 + 1.55359I −1.92023 − 4.37944I
u = 0.397569 − 0.766288I
−0.23774 − 1.55359I −1.92023 + 4.37944I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610588 + 0.515135I
−1.056340 + 0.121936I −1.71551 − 0.70249I
u = 0.610588 − 0.515135I
−1.056340 − 0.121936I −1.71551 + 0.70249I
u = 0.188820 + 0.739972I
−0.49246 + 1.40224I −3.25312 − 5.95695I
u = 0.188820 − 0.739972I
−0.49246 − 1.40224I −3.25312 + 5.95695I
u = 0.868041 + 0.906909I
4.33013 − 0.66559I 0
u = 0.868041 − 0.906909I
4.33013 + 0.66559I 0
u = 0.860634 + 0.928908I
4.26183 + 7.07643I 0
u = 0.860634 − 0.928908I
4.26183 − 7.07643I 0
u = −0.873798 + 0.921550I
7.45184 − 3.23504I 0
u = −0.873798 − 0.921550I
7.45184 + 3.23504I 0
u = −0.906361 + 0.896191I
6.91112 + 0.26195I 0
u = −0.906361 − 0.896191I
6.91112 − 0.26195I 0
u = −0.918035 + 0.894590I
9.54527 + 7.87292I 0
u = −0.918035 − 0.894590I
9.54527 − 7.87292I 0
u = 0.916098 + 0.898640I
11.73460 − 2.74151I 0
u = 0.916098 − 0.898640I
11.73460 + 2.74151I 0
u = 0.913249 + 0.910862I
12.86730 − 0.20173I 0
u = 0.913249 − 0.910862I
12.86730 + 0.20173I 0
u = −0.911288 + 0.917800I
11.72190 − 4.80348I 0
u = −0.911288 − 0.917800I
11.72190 + 4.80348I 0
u = −0.876349 + 0.959209I
6.70835 − 6.84097I 0
u = −0.876349 − 0.959209I
6.70835 + 6.84097I 0
u = −0.894477 + 0.950445I
11.61560 − 1.85123I 0
u = −0.894477 − 0.950445I
11.61560 + 1.85123I 0
u = 0.890410 + 0.955883I
12.7211 + 6.8493I 0
u = 0.890410 − 0.955883I
12.7211 − 6.8493I 0
u = 0.883095 + 0.964486I
11.5212 + 9.3733I 0
u = 0.883095 − 0.964486I
11.5212 − 9.3733I 0
u = −0.881274 + 0.967913I
9.3076 − 14.5044I 0
u = −0.881274 − 0.967913I
9.3076 + 14.5044I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.536662 + 0.126308I
−0.45344 − 5.38731I 1.77316 + 5.79640I
u = −0.536662 − 0.126308I
−0.45344 + 5.38731I 1.77316 − 5.79640I
u = −0.469047 + 0.278278I
−1.96507 + 1.34680I −1.73694 − 0.71589I
u = −0.469047 − 0.278278I
−1.96507 − 1.34680I −1.73694 + 0.71589I
u = 0.487711 + 0.078072I
1.49223 + 0.76367I 5.93436 − 1.14172I
u = 0.487711 − 0.078072I
1.49223 − 0.76367I 5.93436 + 1.14172I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
66
+ 31u
65
+ ··· − u + 1
c
2
, c
5
u
66
+ u
65
+ ··· + 3u + 1
c
3
u
66
− u
65
+ ··· + 1669u + 673
c
4
, c
10
u
66
+ u
65
+ ··· + u + 1
c
6
u
66
+ 3u
65
+ ··· + 539u + 105
c
7
u
66
+ 9u
65
+ ··· + 113u + 29
c
8
, c
9
, c
11
c
12
u
66
+ 13u
65
+ ··· + u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 9y
65
+ ··· + 9y + 1
c
2
, c
5
y
66
− 31y
65
+ ··· + y + 1
c
3
y
66
− 23y
65
+ ··· − 12012391y + 452929
c
4
, c
10
y
66
+ 13y
65
+ ··· + y + 1
c
6
y
66
+ 13y
65
+ ··· + 356909y + 11025
c
7
y
66
− 11y
65
+ ··· + 23481y + 841
c
8
, c
9
, c
11
c
12
y
66
+ 81y
65
+ ··· − 7y + 1
9
