12a
0600
(K12a
0600
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 12 8 2 6 1 4 5 10
Solving Sequence
2,8
7 3 1 6 9 4 10 11 12 5
c
7
c
2
c
1
c
6
c
8
c
3
c
9
c
10
c
12
c
5
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
+ u
53
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 54 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
54
+ u
53
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
6
=
u
2
+ 1
u
2
a
9
=
u
4
+ u
2
+ 1
u
4
a
4
=
−u
11
− 2u
9
− 4u
7
− 4u
5
− 3u
3
−u
11
− u
9
− 2u
7
− u
5
+ u
3
+ u
a
10
=
u
12
+ u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 6u
8
+ 6u
6
+ 4u
4
+ u
2
a
11
=
−u
36
− 5u
34
+ ··· + u
2
+ 1
−u
36
− 4u
34
+ ··· + 7u
4
+ 2u
2
a
12
=
u
21
+ 2u
19
+ ··· + 4u
3
+ u
u
23
+ 3u
21
+ ··· + 2u
3
+ u
a
5
=
−u
46
− 5u
44
+ ··· − 6u
4
+ 1
−u
48
− 6u
46
+ ··· − 16u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
52
+ 4u
51
+ ··· − 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
54
+ 13u
53
+ ··· − u + 1
c
2
, c
7
u
54
+ u
53
+ ··· − u − 1
c
3
u
54
+ u
53
+ ··· − 947u − 457
c
4
, c
5
, c
10
c
11
u
54
− u
53
+ ··· − 3u − 1
c
9
, c
12
u
54
− 9u
53
+ ··· + 607u − 89
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
54
+ 57y
53
+ ··· − 45y + 1
c
2
, c
7
y
54
+ 13y
53
+ ··· − y + 1
c
3
y
54
+ 17y
53
+ ··· + 468707y + 208849
c
4
, c
5
, c
10
c
11
y
54
− 59y
53
+ ··· − y + 1
c
9
, c
12
y
54
+ 37y
53
+ ··· + 87587y + 7921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.421756 + 0.905386I
1.46770 + 2.75588I −6.58826 − 3.20175I
u = 0.421756 − 0.905386I
1.46770 − 2.75588I −6.58826 + 3.20175I
u = −0.472307 + 0.861794I
−4.61385 − 0.50041I −9.83076 + 3.29327I
u = −0.472307 − 0.861794I
−4.61385 + 0.50041I −9.83076 − 3.29327I
u = 0.266117 + 0.940879I
−10.82780 + 2.68050I −17.4218 − 4.4521I
u = 0.266117 − 0.940879I
−10.82780 − 2.68050I −17.4218 + 4.4521I
u = −0.407861 + 0.938268I
0.96567 − 6.61313I −8.59494 + 9.79780I
u = −0.407861 − 0.938268I
0.96567 + 6.61313I −8.59494 − 9.79780I
u = 0.399116 + 0.961261I
−6.09084 + 9.22771I −12.2957 − 8.4163I
u = 0.399116 − 0.961261I
−6.09084 − 9.22771I −12.2957 + 8.4163I
u = 0.090589 + 0.936330I
−7.81225 − 3.84764I −15.8715 + 2.0065I
u = 0.090589 − 0.936330I
−7.81225 + 3.84764I −15.8715 − 2.0065I
u = −0.276477 + 0.881238I
−3.10584 − 2.34442I −16.9541 + 6.0409I
u = −0.276477 − 0.881238I
−3.10584 + 2.34442I −16.9541 − 6.0409I
u = −0.062430 + 0.882605I
−0.88339 + 1.63649I −12.53411 − 3.84361I
u = −0.062430 − 0.882605I
−0.88339 − 1.63649I −12.53411 + 3.84361I
u = −0.802323 + 0.832262I
−4.20575 + 0.66399I −10.65156 + 0.I
u = −0.802323 − 0.832262I
−4.20575 − 0.66399I −10.65156 + 0.I
u = 0.818373 + 0.865309I
3.46423 + 0.45809I −8.00000 + 0.I
u = 0.818373 − 0.865309I
3.46423 − 0.45809I −8.00000 + 0.I
u = −0.823200 + 0.900365I
5.63050 − 3.07356I 0
u = −0.823200 − 0.900365I
5.63050 + 3.07356I 0
u = −0.886232 + 0.838665I
2.20397 + 6.81927I 0
u = −0.886232 − 0.838665I
2.20397 − 6.81927I 0
u = −0.782939 + 0.941062I
−4.53436 − 6.62284I 0
u = −0.782939 − 0.941062I
−4.53436 + 6.62284I 0
u = 0.883660 + 0.847398I
9.22964 − 3.95082I 0
u = 0.883660 − 0.847398I
9.22964 + 3.95082I 0
u = 0.803804 + 0.926221I
3.27760 + 5.61427I 0
u = 0.803804 − 0.926221I
3.27760 − 5.61427I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.880738 + 0.857162I
9.69162 − 0.23278I 0
u = −0.880738 − 0.857162I
9.69162 + 0.23278I 0
u = 0.878437 + 0.871151I
3.67628 + 3.01982I 0
u = 0.878437 − 0.871151I
3.67628 − 3.01982I 0
u = −0.610477 + 0.439255I
−3.29528 − 3.49644I −6.18778 + 3.39542I
u = −0.610477 − 0.439255I
−3.29528 + 3.49644I −6.18778 − 3.39542I
u = 0.229939 + 0.699250I
−0.424354 + 1.032670I −6.76973 − 6.18966I
u = 0.229939 − 0.699250I
−0.424354 − 1.032670I −6.76973 + 6.18966I
u = 0.844032 + 0.951939I
3.41989 + 3.36125I 0
u = 0.844032 − 0.951939I
3.41989 − 3.36125I 0
u = −0.836819 + 0.962125I
9.35926 − 6.13178I 0
u = −0.836819 − 0.962125I
9.35926 + 6.13178I 0
u = 0.832840 + 0.969452I
8.84361 + 10.31070I 0
u = 0.832840 − 0.969452I
8.84361 − 10.31070I 0
u = −0.829260 + 0.975631I
1.77109 − 13.17440I 0
u = −0.829260 − 0.975631I
1.77109 + 13.17440I 0
u = 0.596016 + 0.373336I
3.12910 + 1.02645I −2.02831 − 3.48790I
u = 0.596016 − 0.373336I
3.12910 − 1.02645I −2.02831 + 3.48790I
u = 0.635066 + 0.277401I
−3.94406 − 5.44870I −6.82965 + 3.24384I
u = 0.635066 − 0.277401I
−3.94406 + 5.44870I −6.82965 − 3.24384I
u = −0.610761 + 0.317401I
2.90528 + 2.85235I −2.90911 − 4.01001I
u = −0.610761 − 0.317401I
2.90528 − 2.85235I −2.90911 + 4.01001I
u = 0.540222
−8.09120 −10.3100
u = −0.376064
−0.895266 −10.7040
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
54
+ 13u
53
+ ··· − u + 1
c
2
, c
7
u
54
+ u
53
+ ··· − u − 1
c
3
u
54
+ u
53
+ ··· − 947u − 457
c
4
, c
5
, c
10
c
11
u
54
− u
53
+ ··· − 3u − 1
c
9
, c
12
u
54
− 9u
53
+ ··· + 607u − 89
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
54
+ 57y
53
+ ··· − 45y + 1
c
2
, c
7
y
54
+ 13y
53
+ ··· − y + 1
c
3
y
54
+ 17y
53
+ ··· + 468707y + 208849
c
4
, c
5
, c
10
c
11
y
54
− 59y
53
+ ··· − y + 1
c
9
, c
12
y
54
+ 37y
53
+ ··· + 87587y + 7921
8
