12a
0797
(K12a
0797
)
A knot diagram
1
Linearized knot diagam
3 8 11 12 1 10 9 2 7 6 5 4
Solving Sequence
2,9
8 3 1 7 10 6 11 4 5 12
c
8
c
2
c
1
c
7
c
9
c
6
c
10
c
3
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
41
+ u
40
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 41 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
41
+ u
40
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
u
2
+ 1
u
2
a
10
=
u
4
+ u
2
+ 1
u
4
a
6
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
11
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 2u
4
a
4
=
−u
19
− 2u
17
− 8u
15
− 12u
13
− 21u
11
− 22u
9
− 20u
7
− 12u
5
− 5u
3
−u
19
− u
17
− 6u
15
− 5u
13
− 11u
11
− 7u
9
− 6u
7
− 2u
5
+ u
3
+ u
a
5
=
−u
14
− u
12
− 4u
10
− 3u
8
− 2u
6
+ 2u
2
+ 1
−u
16
− 2u
14
− 6u
12
− 8u
10
− 10u
8
− 6u
6
− 4u
4
a
12
=
u
38
+ 3u
36
+ ··· + 2u
2
+ 1
u
40
+ 4u
38
+ ··· + 25u
8
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
40
−12u
38
+ 4u
37
−72u
36
+ 12u
35
−172u
34
+ 68u
33
−532u
32
+ 156u
31
−1020u
30
+
456u
29
−2104u
28
+808u
27
−3232u
26
+1556u
25
−4840u
24
+2116u
23
−5884u
22
+2876u
21
−
6544u
20
+ 2924u
19
− 6116u
18
+ 2796u
17
− 4940u
16
+ 1988u
15
− 3316u
14
+ 1224u
13
−
1768u
12
+472u
11
−688u
10
+92u
9
−148u
8
−68u
7
+24u
6
−44u
5
+24u
4
−24u
3
−4u
2
+8u−6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
u
41
+ 7u
40
+ ··· − 3u − 1
c
2
, c
8
u
41
− u
40
+ ··· − u + 1
c
3
, c
5
u
41
+ u
40
+ ··· + 7u + 1
c
4
, c
11
, c
12
u
41
− u
40
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
y
41
+ 55y
40
+ ··· + 21y −1
c
2
, c
8
y
41
+ 7y
40
+ ··· − 3y −1
c
3
, c
5
y
41
− 17y
40
+ ··· − 3y −1
c
4
, c
11
, c
12
y
41
+ 35y
40
+ ··· − 3y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.746721 + 0.668302I
6.12347 − 4.43186I −0.64976 + 2.52749I
u = 0.746721 − 0.668302I
6.12347 + 4.43186I −0.64976 − 2.52749I
u = 0.640826 + 0.762779I
3.41343 + 2.37839I −1.91604 − 4.49876I
u = 0.640826 − 0.762779I
3.41343 − 2.37839I −1.91604 + 4.49876I
u = 0.577712 + 0.822944I
3.32469 + 2.15500I −4.15170 − 3.81656I
u = 0.577712 − 0.822944I
3.32469 − 2.15500I −4.15170 + 3.81656I
u = −0.699230 + 0.665301I
1.31088 + 0.84318I −5.61398 − 1.15748I
u = −0.699230 − 0.665301I
1.31088 − 0.84318I −5.61398 + 1.15748I
u = −0.624667 + 0.879172I
0.61729 − 5.77850I −7.67117 + 7.41312I
u = −0.624667 − 0.879172I
0.61729 + 5.77850I −7.67117 − 7.41312I
u = −0.729895 + 0.807771I
9.55876 − 2.69232I 1.62765 + 3.28476I
u = −0.729895 − 0.807771I
9.55876 + 2.69232I 1.62765 − 3.28476I
u = −0.261594 + 0.866448I
0.30761 − 5.87325I −8.98780 + 8.12941I
u = −0.261594 − 0.866448I
0.30761 + 5.87325I −8.98780 − 8.12941I
u = 0.646192 + 0.901469I
5.35322 + 9.58701I −2.83138 − 8.65051I
u = 0.646192 − 0.901469I
5.35322 − 9.58701I −2.83138 + 8.65051I
u = 0.211383 + 0.848155I
−3.89636 + 2.17908I −14.9383 − 5.2468I
u = 0.211383 − 0.848155I
−3.89636 − 2.17908I −14.9383 + 5.2468I
u = −0.143224 + 0.847989I
−0.30668 + 1.42021I −11.22317 + 0.51661I
u = −0.143224 − 0.847989I
−0.30668 − 1.42021I −11.22317 − 0.51661I
u = 0.536289 + 0.522200I
3.94243 + 1.95655I −0.40351 − 3.68221I
u = 0.536289 − 0.522200I
3.94243 − 1.95655I −0.40351 + 3.68221I
u = −0.918409 + 0.933266I
12.96880 − 3.08508I −2.25641 + 3.40948I
u = −0.918409 − 0.933266I
12.96880 + 3.08508I −2.25641 − 3.40948I
u = 0.928532 + 0.923939I
10.84470 − 1.03628I −5.06255 + 1.18461I
u = 0.928532 − 0.923939I
10.84470 + 1.03628I −5.06255 − 1.18461I
u = −0.909755 + 0.948945I
12.91700 − 3.64558I −2.38906 + 1.25453I
u = −0.909755 − 0.948945I
12.91700 + 3.64558I −2.38906 − 1.25453I
u = −0.936924 + 0.922936I
15.9484 + 4.9714I −0.68196 − 2.33270I
u = −0.936924 − 0.922936I
15.9484 − 4.9714I −0.68196 + 2.33270I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.908129 + 0.961589I
10.72100 + 7.79340I −5.31261 − 5.70338I
u = 0.908129 − 0.961589I
10.72100 − 7.79340I −5.31261 + 5.70338I
u = 0.930424 + 0.949937I
−19.2344 + 3.4189I 1.88979 − 2.27252I
u = 0.930424 − 0.949937I
−19.2344 − 3.4189I 1.88979 + 2.27252I
u = −0.911356 + 0.968477I
15.7979 − 11.7662I −0.97634 + 6.84571I
u = −0.911356 − 0.968477I
15.7979 + 11.7662I −0.97634 − 6.84571I
u = −0.193562 + 0.561475I
−0.310431 − 0.802598I −7.57849 + 8.41194I
u = −0.193562 − 0.561475I
−0.310431 + 0.802598I −7.57849 − 8.41194I
u = −0.534709 + 0.122960I
2.61523 + 3.18305I −0.67808 − 2.90815I
u = −0.534709 − 0.122960I
2.61523 − 3.18305I −0.67808 + 2.90815I
u = 0.474234
−1.44617 −6.39030
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
u
41
+ 7u
40
+ ··· − 3u − 1
c
2
, c
8
u
41
− u
40
+ ··· − u + 1
c
3
, c
5
u
41
+ u
40
+ ··· + 7u + 1
c
4
, c
11
, c
12
u
41
− u
40
+ ··· + 3u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
9
, c
10
y
41
+ 55y
40
+ ··· + 21y −1
c
2
, c
8
y
41
+ 7y
40
+ ··· − 3y −1
c
3
, c
5
y
41
− 17y
40
+ ··· − 3y −1
c
4
, c
11
, c
12
y
41
+ 35y
40
+ ··· − 3y −1
8
