12a
1040
(K12a
1040
)
A knot diagram
1
Linearized knot diagam
4 7 8 12 11 9 3 2 1 6 5 10
Solving Sequence
2,7
3 8 4 9 1 10 6 11 5 12
c
2
c
7
c
3
c
8
c
1
c
9
c
6
c
10
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
57
− u
56
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 57 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
57
− u
56
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
3
+ 2u
−u
3
+ u
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
10
=
−u
17
+ 8u
15
− 25u
13
+ 36u
11
− 19u
9
− 4u
7
+ 2u
5
+ 2u
3
+ 3u
u
19
− 9u
17
+ 32u
15
− 55u
13
+ 43u
11
− 9u
9
− 4u
5
− u
3
+ u
a
6
=
u
7
− 4u
5
+ 4u
3
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
33
+ 16u
31
+ ··· + 2u
3
+ 3u
−u
33
+ 15u
31
+ ··· + 2u
3
+ u
a
5
=
−u
54
+ 25u
52
+ ··· + 2u
2
+ 1
u
56
− 26u
54
+ ··· + 4u
4
− 2u
2
a
12
=
u
28
− 13u
26
+ ··· + 5u
2
+ 1
−u
30
+ 14u
28
+ ··· − 4u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
55
+ 104u
53
+ ··· + 20u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
57
− 9u
56
+ ··· + 417u − 41
c
2
, c
3
, c
7
u
57
+ u
56
+ ··· + u − 1
c
4
, c
5
, c
10
c
11
u
57
+ u
56
+ ··· − u − 1
c
8
u
57
− 3u
56
+ ··· − 313u + 175
c
9
, c
12
u
57
+ 11u
56
+ ··· + 57u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
57
+ 43y
56
+ ··· − 48987y −1681
c
2
, c
3
, c
7
y
57
− 53y
56
+ ··· − 7y −1
c
4
, c
5
, c
10
c
11
y
57
+ 63y
56
+ ··· − 7y −1
c
8
y
57
− 17y
56
+ ··· + 297469y −30625
c
9
, c
12
y
57
+ 27y
56
+ ··· − 3483y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.167470 + 0.169882I
5.94879 − 1.26768I 0
u = 1.167470 − 0.169882I
5.94879 + 1.26768I 0
u = −0.380989 + 0.687075I
7.59135 − 9.78879I 4.20807 + 7.63690I
u = −0.380989 − 0.687075I
7.59135 + 9.78879I 4.20807 − 7.63690I
u = −1.210720 + 0.186692I
−0.388499 − 1.147720I 0
u = −1.210720 − 0.186692I
−0.388499 + 1.147720I 0
u = −0.450772 + 0.625585I
12.14170 − 2.06019I 8.03202 + 3.36390I
u = −0.450772 − 0.625585I
12.14170 + 2.06019I 8.03202 − 3.36390I
u = 0.370067 + 0.674356I
0.31418 + 7.17616I 0.93396 − 9.10668I
u = 0.370067 − 0.674356I
0.31418 − 7.17616I 0.93396 + 9.10668I
u = −0.535939 + 0.537357I
8.22131 + 5.67967I 5.83026 − 1.65476I
u = −0.535939 − 0.537357I
8.22131 − 5.67967I 5.83026 + 1.65476I
u = 1.236620 + 0.206975I
−0.13889 + 5.01254I 0
u = 1.236620 − 0.206975I
−0.13889 − 5.01254I 0
u = −0.355064 + 0.654949I
−0.47604 − 3.30732I −1.43106 + 3.04352I
u = −0.355064 − 0.654949I
−0.47604 + 3.30732I −1.43106 − 3.04352I
u = 0.418277 + 0.595875I
3.97873 + 1.92695I 7.08631 − 3.98477I
u = 0.418277 − 0.595875I
3.97873 − 1.92695I 7.08631 + 3.98477I
u = 0.514622 + 0.512995I
0.95022 − 3.20263I 2.71277 + 3.09003I
u = 0.514622 − 0.512995I
0.95022 + 3.20263I 2.71277 − 3.09003I
u = −1.255720 + 0.225833I
6.68945 − 7.58268I 0
u = −1.255720 − 0.225833I
6.68945 + 7.58268I 0
u = −1.27874
2.94486 0
u = 0.301202 + 0.630196I
5.12502 + 1.19979I 1.84526 − 3.54784I
u = 0.301202 − 0.630196I
5.12502 − 1.19979I 1.84526 + 3.54784I
u = −0.464588 + 0.473428I
0.149387 − 0.437986I 0.20836 + 3.87750I
u = −0.464588 − 0.473428I
0.149387 + 0.437986I 0.20836 − 3.87750I
u = 1.336280 + 0.067950I
4.76158 + 2.12463I 0
u = 1.336280 − 0.067950I
4.76158 − 2.12463I 0
u = 0.053954 + 0.654719I
2.66786 + 4.37051I −1.69929 − 3.89268I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053954 − 0.654719I
2.66786 − 4.37051I −1.69929 + 3.89268I
u = −0.019054 + 0.641634I
−3.95983 − 1.90551I −5.97209 + 4.06985I
u = −0.019054 − 0.641634I
−3.95983 + 1.90551I −5.97209 − 4.06985I
u = −1.395500 + 0.073443I
12.03160 − 3.33838I 0
u = −1.395500 − 0.073443I
12.03160 + 3.33838I 0
u = 0.521676 + 0.299528I
6.18669 + 2.12511I 5.30374 − 3.18757I
u = 0.521676 − 0.299528I
6.18669 − 2.12511I 5.30374 + 3.18757I
u = −1.42263 + 0.23603I
10.65770 − 4.35539I 0
u = −1.42263 − 0.23603I
10.65770 + 4.35539I 0
u = 1.44389 + 0.19016I
6.16952 + 2.93600I 0
u = 1.44389 − 0.19016I
6.16952 − 2.93600I 0
u = 1.44231 + 0.24847I
5.29940 + 6.61308I 0
u = 1.44231 − 0.24847I
5.29940 − 6.61308I 0
u = −1.45405 + 0.22055I
9.99378 − 4.92353I 0
u = −1.45405 − 0.22055I
9.99378 + 4.92353I 0
u = −1.46020 + 0.18074I
7.24551 + 0.69473I 0
u = −1.46020 − 0.18074I
7.24551 − 0.69473I 0
u = −1.44938 + 0.25463I
6.16341 − 10.57050I 0
u = −1.44938 − 0.25463I
6.16341 + 10.57050I 0
u = 1.45510 + 0.25844I
13.4982 + 13.2410I 0
u = 1.45510 − 0.25844I
13.4982 − 13.2410I 0
u = 1.47223 + 0.17915I
14.6669 − 3.1156I 0
u = 1.47223 − 0.17915I
14.6669 + 3.1156I 0
u = 1.46992 + 0.22438I
18.3360 + 5.1622I 0
u = 1.46992 − 0.22438I
18.3360 − 5.1622I 0
u = −0.209648 + 0.330630I
0.018322 − 0.795288I 0.54519 + 8.56502I
u = −0.209648 − 0.330630I
0.018322 + 0.795288I 0.54519 − 8.56502I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
57
− 9u
56
+ ··· + 417u − 41
c
2
, c
3
, c
7
u
57
+ u
56
+ ··· + u − 1
c
4
, c
5
, c
10
c
11
u
57
+ u
56
+ ··· − u − 1
c
8
u
57
− 3u
56
+ ··· − 313u + 175
c
9
, c
12
u
57
+ 11u
56
+ ··· + 57u + 11
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
57
+ 43y
56
+ ··· − 48987y −1681
c
2
, c
3
, c
7
y
57
− 53y
56
+ ··· − 7y −1
c
4
, c
5
, c
10
c
11
y
57
+ 63y
56
+ ··· − 7y −1
c
8
y
57
− 17y
56
+ ··· + 297469y −30625
c
9
, c
12
y
57
+ 27y
56
+ ··· − 3483y −121
8
