12a
0300
(K12a
0300
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 1 5 12 11 4 9 7
Solving Sequence
4,11
10 5 9 12 8 3 7 1 2 6
c
10
c
4
c
9
c
11
c
8
c
3
c
7
c
12
c
1
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
77
+ u
76
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 77 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
77
+ u
76
+ · · · + u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
9
=
u
2
+ 1
u
2
a
12
=
u
4
+ u
2
+ 1
u
4
a
8
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
3
=
u
13
+ 2u
11
+ 5u
9
+ 6u
7
+ 6u
5
+ 4u
3
+ u
u
13
+ u
11
+ 3u
9
+ 2u
7
+ 2u
5
+ u
3
+ u
a
7
=
−u
10
− u
8
− 2u
6
− u
4
+ u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 4u
6
− 3u
4
a
1
=
−u
26
− 3u
24
+ ··· + u
2
+ 1
−u
28
− 4u
26
+ ··· − 12u
8
+ u
4
a
2
=
u
54
+ 7u
52
+ ··· + 2u
2
+ 1
u
54
+ 6u
52
+ ··· + 4u
4
+ u
2
a
6
=
−u
42
− 5u
40
+ ··· + u
2
+ 1
−u
44
− 6u
42
+ ··· − 4u
6
− 3u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
75
− 4u
74
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 41u
76
+ ··· − u + 1
c
2
, c
5
u
77
+ u
76
+ ··· + 3u + 1
c
3
u
77
+ u
76
+ ··· − 3u + 1
c
4
, c
10
u
77
+ u
76
+ ··· + u + 1
c
6
, c
12
u
77
+ 3u
76
+ ··· + 15u + 3
c
7
u
77
− 9u
76
+ ··· − 303u + 29
c
8
, c
9
, c
11
u
77
+ 19u
76
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
− 9y
76
+ ··· − y −1
c
2
, c
5
y
77
− 41y
76
+ ··· − y −1
c
3
y
77
− y
76
+ ··· − 193y −1
c
4
, c
10
y
77
+ 19y
76
+ ··· − y −1
c
6
, c
12
y
77
+ 59y
76
+ ··· − 1401y −9
c
7
y
77
+ 11y
76
+ ··· + 15191y −841
c
8
, c
9
, c
11
y
77
+ 79y
76
+ ··· + 7y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.384157 + 0.916651I
−0.08016 − 6.28454I 0. + 10.45893I
u = −0.384157 − 0.916651I
−0.08016 + 6.28454I 0. − 10.45893I
u = −0.359432 + 0.963246I
−3.28646 − 6.49921I 0
u = −0.359432 − 0.963246I
−3.28646 + 6.49921I 0
u = 0.181375 + 0.954789I
−8.18742 + 3.05866I −13.52379 − 3.93661I
u = 0.181375 − 0.954789I
−8.18742 − 3.05866I −13.52379 + 3.93661I
u = 0.344445 + 0.969057I
−7.25591 + 2.51870I 0
u = 0.344445 − 0.969057I
−7.25591 − 2.51870I 0
u = 0.151839 + 0.956150I
−7.61091 − 5.67836I −12.50459 + 3.10607I
u = 0.151839 − 0.956150I
−7.61091 + 5.67836I −12.50459 − 3.10607I
u = 0.364368 + 0.973455I
−6.39842 + 11.27770I 0
u = 0.364368 − 0.973455I
−6.39842 − 11.27770I 0
u = 0.387418 + 0.873983I
0.51259 + 2.09295I −1.92214 − 3.70673I
u = 0.387418 − 0.873983I
0.51259 − 2.09295I −1.92214 + 3.70673I
u = −0.162879 + 0.940953I
−4.40542 + 1.03814I −9.57563 + 0.I
u = −0.162879 − 0.940953I
−4.40542 − 1.03814I −9.57563 + 0.I
u = −0.279119 + 0.907947I
−3.80142 − 2.48917I −13.3851 + 5.1983I
u = −0.279119 − 0.907947I
−3.80142 + 2.48917I −13.3851 − 5.1983I
u = −0.735571 + 0.878240I
−2.84182 + 1.57464I 0
u = −0.735571 − 0.878240I
−2.84182 − 1.57464I 0
u = −0.529170 + 0.664612I
−3.03277 + 2.04853I −4.86577 + 0.18647I
u = −0.529170 − 0.664612I
−3.03277 − 2.04853I −4.86577 − 0.18647I
u = −0.099359 + 0.832534I
−1.57015 + 1.62706I −8.90717 − 3.48380I
u = −0.099359 − 0.832534I
−1.57015 − 1.62706I −8.90717 + 3.48380I
u = 0.328773 + 0.768032I
−0.30487 + 1.47590I −2.27756 − 4.79967I
u = 0.328773 − 0.768032I
−0.30487 − 1.47590I −2.27756 + 4.79967I
u = 0.752498 + 0.891905I
0.60818 + 2.85389I 0
u = 0.752498 − 0.891905I
0.60818 − 2.85389I 0
u = −0.743580 + 0.908600I
−2.94895 − 7.20020I 0
u = −0.743580 − 0.908600I
−2.94895 + 7.20020I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.829686 + 0.851767I
3.00542 + 0.05293I 0
u = 0.829686 − 0.851767I
3.00542 − 0.05293I 0
u = −0.866902 + 0.822657I
0.526126 + 0.450966I 0
u = −0.866902 − 0.822657I
0.526126 − 0.450966I 0
u = −0.571449 + 0.558788I
−2.66165 − 6.09408I −3.39785 + 6.85504I
u = −0.571449 − 0.558788I
−2.66165 + 6.09408I −3.39785 − 6.85504I
u = 0.872860 + 0.828358I
4.63295 − 4.30393I 0
u = 0.872860 − 0.828358I
4.63295 + 4.30393I 0
u = −0.877082 + 0.825271I
1.61683 + 9.16430I 0
u = −0.877082 − 0.825271I
1.61683 − 9.16430I 0
u = 0.871205 + 0.847546I
7.84743 − 3.55756I 0
u = 0.871205 − 0.847546I
7.84743 + 3.55756I 0
u = −0.866793 + 0.857025I
8.30654 − 0.96474I 0
u = −0.866793 − 0.857025I
8.30654 + 0.96474I 0
u = −0.853289 + 0.875111I
6.87444 − 2.22139I 0
u = −0.853289 − 0.875111I
6.87444 + 2.22139I 0
u = 0.856094 + 0.889460I
4.50479 + 6.65127I 0
u = 0.856094 − 0.889460I
4.50479 − 6.65127I 0
u = 0.803005 + 0.940435I
2.73012 + 6.05042I 0
u = 0.803005 − 0.940435I
2.73012 − 6.05042I 0
u = −0.829553 + 0.934385I
6.68687 − 4.03643I 0
u = −0.829553 − 0.934385I
6.68687 + 4.03643I 0
u = 0.840447 + 0.924665I
4.39202 − 0.35136I 0
u = 0.840447 − 0.924665I
4.39202 + 0.35136I 0
u = 0.501322 + 0.543345I
0.26130 + 1.71903I 0.35401 − 4.09536I
u = 0.501322 − 0.543345I
0.26130 − 1.71903I 0.35401 + 4.09536I
u = −0.828463 + 0.953823I
8.00145 − 5.32992I 0
u = −0.828463 − 0.953823I
8.00145 + 5.32992I 0
u = −0.810631 + 0.973613I
0.05425 − 6.68536I 0
u = −0.810631 − 0.973613I
0.05425 + 6.68536I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825978 + 0.962044I
7.48701 + 9.85702I 0
u = 0.825978 − 0.962044I
7.48701 − 9.85702I 0
u = 0.816534 + 0.973747I
4.17669 + 10.57610I 0
u = 0.816534 − 0.973747I
4.17669 − 10.57610I 0
u = −0.817106 + 0.977544I
1.1384 − 15.4505I 0
u = −0.817106 − 0.977544I
1.1384 + 15.4505I 0
u = 0.623531 + 0.204993I
−4.00857 − 7.70709I −3.80654 + 5.68511I
u = 0.623531 − 0.204993I
−4.00857 + 7.70709I −3.80654 − 5.68511I
u = 0.530715 + 0.375956I
2.03844 + 1.38009I 3.17761 − 3.81848I
u = 0.530715 − 0.375956I
2.03844 − 1.38009I 3.17761 + 3.81848I
u = −0.555511 + 0.305962I
1.78912 + 2.77247I 2.09005 − 4.48939I
u = −0.555511 − 0.305962I
1.78912 − 2.77247I 2.09005 + 4.48939I
u = −0.597425 + 0.204656I
−0.95439 + 3.01743I −0.62538 − 2.65931I
u = −0.597425 − 0.204656I
−0.95439 − 3.01743I −0.62538 + 2.65931I
u = 0.599590 + 0.165461I
−4.79659 + 0.87508I −5.38352 − 0.79253I
u = 0.599590 − 0.165461I
−4.79659 − 0.87508I −5.38352 + 0.79253I
u = −0.428418
−1.41624 −6.46210
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
77
+ 41u
76
+ ··· − u + 1
c
2
, c
5
u
77
+ u
76
+ ··· + 3u + 1
c
3
u
77
+ u
76
+ ··· − 3u + 1
c
4
, c
10
u
77
+ u
76
+ ··· + u + 1
c
6
, c
12
u
77
+ 3u
76
+ ··· + 15u + 3
c
7
u
77
− 9u
76
+ ··· − 303u + 29
c
8
, c
9
, c
11
u
77
+ 19u
76
+ ··· − u − 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
77
− 9y
76
+ ··· − y −1
c
2
, c
5
y
77
− 41y
76
+ ··· − y −1
c
3
y
77
− y
76
+ ··· − 193y −1
c
4
, c
10
y
77
+ 19y
76
+ ··· − y −1
c
6
, c
12
y
77
+ 59y
76
+ ··· − 1401y −9
c
7
y
77
+ 11y
76
+ ··· + 15191y −841
c
8
, c
9
, c
11
y
77
+ 79y
76
+ ··· + 7y −1
9
