12a
1140
(K12a
1140
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 12 11 1 3 2 7 6 5
Solving Sequence
4,9
3 8 2 10 5 1 7 11 6 12
c
3
c
8
c
2
c
9
c
4
c
1
c
7
c
10
c
6
c
12
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
+ u
47
+ ··· + 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
+ u
47
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
8
=
−u
−u
3
+ u
a
2
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
5
=
u
12
− 5u
10
+ 9u
8
− 6u
6
+ u
2
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
7
=
−u
11
+ 4u
9
− 4u
7
− 2u
5
+ 3u
3
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
11
=
−u
29
+ 12u
27
+ ··· − 2u
3
+ u
−u
29
+ 13u
27
+ ··· + 3u
3
+ u
a
6
=
−u
47
+ 20u
45
+ ··· − 8u
5
+ 4u
3
−u
47
+ 21u
45
+ ··· + 2u
3
+ u
a
12
=
u
30
− 13u
28
+ ··· + 2u
2
+ 1
u
32
− 14u
30
+ ··· − 20u
8
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
45
+ 80u
43
+ ··· + 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
− 11u
47
+ ··· − 336u + 41
c
2
, c
3
, c
8
u
48
− u
47
+ ··· + 2u
2
+ 1
c
4
, c
7
u
48
+ u
47
+ ··· + 150u + 61
c
5
, c
6
, c
10
c
11
, c
12
u
48
+ u
47
+ ··· + 2u + 1
c
9
u
48
+ 3u
47
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 9y
47
+ ··· + 21912y + 1681
c
2
, c
3
, c
8
y
48
− 43y
47
+ ··· + 4y + 1
c
4
, c
7
y
48
− 27y
47
+ ··· + 17760y + 3721
c
5
, c
6
, c
10
c
11
, c
12
y
48
+ 61y
47
+ ··· + 4y + 1
c
9
y
48
+ y
47
+ ··· − 36y
2
+ 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.984705 + 0.170190I
0.63620 − 3.07400I −1.42622 + 5.04336I
u = −0.984705 − 0.170190I
0.63620 + 3.07400I −1.42622 − 5.04336I
u = 1.034970 + 0.229830I
9.29821 + 4.64078I 0.19063 − 3.74391I
u = 1.034970 − 0.229830I
9.29821 − 4.64078I 0.19063 + 3.74391I
u = 0.821678 + 0.119203I
−1.80692 − 0.00993I −6.31095 − 0.29160I
u = 0.821678 − 0.119203I
−1.80692 + 0.00993I −6.31095 + 0.29160I
u = 0.697074 + 0.345244I
9.79430 − 4.58712I 1.41766 + 1.42537I
u = 0.697074 − 0.345244I
9.79430 + 4.58712I 1.41766 − 1.42537I
u = 0.276656 + 0.724689I
8.24979 + 8.49657I −1.26312 − 6.40308I
u = 0.276656 − 0.724689I
8.24979 − 8.49657I −1.26312 + 6.40308I
u = −0.258333 + 0.712893I
−0.80898 − 6.73195I −3.03818 + 8.02768I
u = −0.258333 − 0.712893I
−0.80898 + 6.73195I −3.03818 − 8.02768I
u = −0.696113 + 0.263546I
0.85094 + 3.00932I −0.10546 − 3.28969I
u = −0.696113 − 0.263546I
0.85094 − 3.00932I −0.10546 + 3.28969I
u = 0.229854 + 0.703043I
−3.75638 + 3.54065I −8.92526 − 5.06196I
u = 0.229854 − 0.703043I
−3.75638 − 3.54065I −8.92526 + 5.06196I
u = 0.146777 + 0.708759I
6.63287 − 1.05371I −3.70281 − 0.77988I
u = 0.146777 − 0.708759I
6.63287 + 1.05371I −3.70281 + 0.77988I
u = −0.190207 + 0.689875I
−1.71125 − 0.36118I −5.08602 − 0.20285I
u = −0.190207 − 0.689875I
−1.71125 + 0.36118I −5.08602 + 0.20285I
u = −0.401505 + 0.556155I
13.18090 − 1.81273I 3.22900 + 3.77442I
u = −0.401505 − 0.556155I
13.18090 + 1.81273I 3.22900 − 3.77442I
u = −1.358150 + 0.117821I
3.75606 − 0.57966I 0
u = −1.358150 − 0.117821I
3.75606 + 0.57966I 0
u = −1.341400 + 0.274423I
11.31320 − 2.49652I 0
u = −1.341400 − 0.274423I
11.31320 + 2.49652I 0
u = 1.359690 + 0.179256I
4.62275 + 3.19043I 0
u = 1.359690 − 0.179256I
4.62275 − 3.19043I 0
u = 0.346107 + 0.516877I
3.67185 + 1.60748I 3.24996 − 4.72497I
u = 0.346107 − 0.516877I
3.67185 − 1.60748I 3.24996 + 4.72497I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.372900 + 0.269136I
3.24781 + 3.83280I 0
u = 1.372900 − 0.269136I
3.24781 − 3.83280I 0
u = 1.405940 + 0.096755I
7.05839 − 1.92770I 0
u = 1.405940 − 0.096755I
7.05839 + 1.92770I 0
u = −1.39090 + 0.27872I
1.39970 − 7.10603I 0
u = −1.39090 − 0.27872I
1.39970 + 7.10603I 0
u = −1.41073 + 0.20337I
9.24476 − 4.28144I 0
u = −1.41073 − 0.20337I
9.24476 + 4.28144I 0
u = 1.40430 + 0.28269I
4.48956 + 10.35090I 0
u = 1.40430 − 0.28269I
4.48956 − 10.35090I 0
u = −1.43192 + 0.09360I
16.3256 + 3.3059I 0
u = −1.43192 − 0.09360I
16.3256 − 3.3059I 0
u = −1.41356 + 0.28666I
13.6424 − 12.1723I 0
u = −1.41356 − 0.28666I
13.6424 + 12.1723I 0
u = 1.43291 + 0.20603I
19.0325 + 4.5978I 0
u = 1.43291 − 0.20603I
19.0325 − 4.5978I 0
u = −0.151330 + 0.440993I
−0.189683 − 0.842364I −4.63984 + 8.09333I
u = −0.151330 − 0.440993I
−0.189683 + 0.842364I −4.63984 − 8.09333I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
48
− 11u
47
+ ··· − 336u + 41
c
2
, c
3
, c
8
u
48
− u
47
+ ··· + 2u
2
+ 1
c
4
, c
7
u
48
+ u
47
+ ··· + 150u + 61
c
5
, c
6
, c
10
c
11
, c
12
u
48
+ u
47
+ ··· + 2u + 1
c
9
u
48
+ 3u
47
+ ··· + 4u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 9y
47
+ ··· + 21912y + 1681
c
2
, c
3
, c
8
y
48
− 43y
47
+ ··· + 4y + 1
c
4
, c
7
y
48
− 27y
47
+ ··· + 17760y + 3721
c
5
, c
6
, c
10
c
11
, c
12
y
48
+ 61y
47
+ ··· + 4y + 1
c
9
y
48
+ y
47
+ ··· − 36y
2
+ 1
8
