12a
1138
(K12a
1138
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 12 11 2 3 1 7 6 5
Solving Sequence
4,9
3 8 2 1 10 5 7 11 6 12
c
3
c
8
c
2
c
1
c
9
c
4
c
7
c
10
c
6
c
12
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
39
− u
38
+ ··· + 4u
3
− 1i
* 1 irreducible components of dim
C
= 0, with total 39 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
39
− u
38
+ · · · + 4u
3
− 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
1
=
u
4
− 3u
2
+ 1
u
4
− 2u
2
a
10
=
u
9
− 6u
7
+ 11u
5
− 6u
3
+ u
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
5
=
−u
18
+ 11u
16
− 48u
14
+ 105u
12
− 121u
10
+ 75u
8
− 30u
6
+ 8u
4
− u
2
+ 1
−u
18
+ 10u
16
− 39u
14
+ 74u
12
− 71u
10
+ 38u
8
− 18u
6
+ 4u
4
− u
2
a
7
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
11
=
u
17
− 10u
15
+ 39u
13
− 74u
11
+ 71u
9
− 38u
7
+ 18u
5
− 4u
3
+ u
−u
19
+ 11u
17
− 48u
15
+ 105u
13
− 121u
11
+ 75u
9
− 30u
7
+ 8u
5
− u
3
+ u
a
6
=
−u
31
+ 18u
29
+ ··· − 12u
7
+ 2u
u
33
− 19u
31
+ ··· − 2u
3
+ u
a
12
=
u
32
− 19u
30
+ ··· − 2u
2
+ 1
u
32
− 18u
30
+ ··· + 12u
8
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
36
− 84u
34
+ 788u
32
+ 4u
31
− 4352u
30
− 72u
29
+ 15712u
28
+
568u
27
−38992u
26
−2576u
25
+ 68272u
24
+ 7412u
23
−85520u
22
−14120u
21
+ 77072u
20
+
18120u
19
− 49428u
18
− 15728u
17
+ 21212u
16
+ 9112u
15
− 4912u
14
− 3220u
13
− 12u
12
+
432u
11
+ 284u
10
+ 36u
9
+ 88u
8
+ 52u
7
− 84u
6
− 64u
5
+ 44u
4
+ 20u
3
− 4u
2
− 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
− 11u
38
+ ··· + 360u − 41
c
2
, c
3
, c
7
c
8
u
39
+ u
38
+ ··· + 4u
3
+ 1
c
4
u
39
− u
38
+ ··· + 112u + 29
c
5
, c
6
, c
10
c
11
, c
12
u
39
− u
38
+ ··· − 2u + 1
c
9
u
39
− 5u
38
+ ··· + 112u − 95
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
− 9y
38
+ ··· + 3156y −1681
c
2
, c
3
, c
7
c
8
y
39
− 45y
38
+ ··· − 10y
2
− 1
c
4
y
39
+ 11y
38
+ ··· + 5352y −841
c
5
, c
6
, c
10
c
11
, c
12
y
39
+ 51y
38
+ ··· − 2y
2
− 1
c
9
y
39
+ 19y
38
+ ··· − 71816y −9025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841792 + 0.292424I
−15.1182 + 1.5057I −8.40858 + 0.97265I
u = 0.841792 − 0.292424I
−15.1182 − 1.5057I −8.40858 − 0.97265I
u = −0.729257 + 0.492469I
−13.7612 + 8.1189I −6.01582 − 6.71736I
u = −0.729257 − 0.492469I
−13.7612 − 8.1189I −6.01582 + 6.71736I
u = 0.707989 + 0.470053I
−4.12575 − 6.63014I −5.12153 + 8.45771I
u = 0.707989 − 0.470053I
−4.12575 + 6.63014I −5.12153 − 8.45771I
u = −0.774155 + 0.278442I
−5.35026 − 0.56012I −8.31402 − 0.25589I
u = −0.774155 − 0.278442I
−5.35026 + 0.56012I −8.31402 + 0.25589I
u = −0.668788 + 0.436144I
−0.40953 + 3.91689I 0.46864 − 8.35859I
u = −0.668788 − 0.436144I
−0.40953 − 3.91689I 0.46864 + 8.35859I
u = 0.635570 + 0.340805I
−1.13161 − 1.10437I −2.87714 + 0.84766I
u = 0.635570 − 0.340805I
−1.13161 + 1.10437I −2.87714 − 0.84766I
u = −0.451697 + 0.506497I
−9.02178 + 1.76146I −1.28786 − 3.92479I
u = −0.451697 − 0.506497I
−9.02178 − 1.76146I −1.28786 + 3.92479I
u = −0.136161 + 0.598793I
−12.02260 − 4.41211I −2.43306 + 1.96254I
u = −0.136161 − 0.598793I
−12.02260 + 4.41211I −2.43306 − 1.96254I
u = 0.143045 + 0.548355I
−2.49224 + 3.13322I −1.35770 − 3.51211I
u = 0.143045 − 0.548355I
−2.49224 − 3.13322I −1.35770 + 3.51211I
u = 0.394285 + 0.400255I
−0.58188 − 1.38142I −0.08240 + 6.03363I
u = 0.394285 − 0.400255I
−0.58188 + 1.38142I −0.08240 − 6.03363I
u = 1.49254
−4.41211 0
u = 1.49483 + 0.09365I
−15.3639 − 3.7798I 0
u = 1.49483 − 0.09365I
−15.3639 + 3.7798I 0
u = −1.50080 + 0.04783I
−6.77867 + 2.73633I 0
u = −1.50080 − 0.04783I
−6.77867 − 2.73633I 0
u = −0.196225 + 0.449165I
0.943197 − 0.763976I 6.20859 + 2.38716I
u = −0.196225 − 0.449165I
0.943197 + 0.763976I 6.20859 − 2.38716I
u = −1.59322 + 0.10217I
−8.77741 + 2.76966I 0
u = −1.59322 − 0.10217I
−8.77741 − 2.76966I 0
u = 1.59721 + 0.12385I
−8.12235 − 5.98293I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59721 − 0.12385I
−8.12235 + 5.98293I 0
u = −1.60787 + 0.13573I
−11.9998 + 8.8902I 0
u = −1.60787 − 0.13573I
−11.9998 − 8.8902I 0
u = 1.61669 + 0.08086I
−13.52220 − 0.80582I 0
u = 1.61669 − 0.08086I
−13.52220 + 0.80582I 0
u = 1.61512 + 0.14352I
17.7470 − 10.5062I 0
u = 1.61512 − 0.14352I
17.7470 + 10.5062I 0
u = −1.63463 + 0.07714I
15.8667 − 0.1255I 0
u = −1.63463 − 0.07714I
15.8667 + 0.1255I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
39
− 11u
38
+ ··· + 360u − 41
c
2
, c
3
, c
7
c
8
u
39
+ u
38
+ ··· + 4u
3
+ 1
c
4
u
39
− u
38
+ ··· + 112u + 29
c
5
, c
6
, c
10
c
11
, c
12
u
39
− u
38
+ ··· − 2u + 1
c
9
u
39
− 5u
38
+ ··· + 112u − 95
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
39
− 9y
38
+ ··· + 3156y −1681
c
2
, c
3
, c
7
c
8
y
39
− 45y
38
+ ··· − 10y
2
− 1
c
4
y
39
+ 11y
38
+ ··· + 5352y −841
c
5
, c
6
, c
10
c
11
, c
12
y
39
+ 51y
38
+ ··· − 2y
2
− 1
c
9
y
39
+ 19y
38
+ ··· − 71816y −9025
8
