12a
0582
(K12a
0582
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 2 1 12 6 5 4 8
Solving Sequence
6,11
5 10 4 12 9 3 8 1 2 7
c
5
c
10
c
4
c
11
c
9
c
3
c
8
c
12
c
1
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
65
− u
64
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 65 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
65
− u
64
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
10
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
u
3
− 2u
−u
3
+ u
a
3
=
u
10
− 5u
8
+ 8u
6
− 3u
4
− 3u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 3u
2
a
8
=
u
15
− 6u
13
+ 14u
11
− 14u
9
+ 2u
7
+ 6u
5
− 2u
3
− 2u
u
17
− 7u
15
+ 19u
13
− 22u
11
+ 3u
9
+ 14u
7
− 6u
5
− 4u
3
+ u
a
1
=
u
25
− 10u
23
+ ··· + 4u
3
+ u
u
27
− 11u
25
+ ··· − u
3
+ u
a
2
=
−u
47
+ 20u
45
+ ··· − 8u
5
+ 14u
3
u
47
− 19u
45
+ ··· − 4u
3
+ u
a
7
=
u
35
− 14u
33
+ ··· − 5u
3
− 2u
u
37
− 15u
35
+ ··· − 7u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
63
+ 104u
61
+ ··· − 8u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 37u
64
+ ··· + 5u + 1
c
2
, c
6
u
65
− u
64
+ ··· + 3u − 1
c
3
u
65
− u
64
+ ··· − 975u − 1789
c
4
, c
5
, c
10
u
65
+ u
64
+ ··· + u − 1
c
7
, c
8
, c
12
u
65
− 3u
64
+ ··· + 97u − 7
c
9
, c
11
u
65
− 3u
64
+ ··· − 159u + 77
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 17y
64
+ ··· − 23y −1
c
2
, c
6
y
65
− 37y
64
+ ··· + 5y −1
c
3
y
65
+ 23y
64
+ ··· − 57349307y −3200521
c
4
, c
5
, c
10
y
65
− 53y
64
+ ··· + 5y −1
c
7
, c
8
, c
12
y
65
+ 71y
64
+ ··· + 3781y −49
c
9
, c
11
y
65
+ 47y
64
+ ··· + 71481y −5929
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.094573 + 0.834098I
−13.51750 − 0.44803I −2.98623 + 0.17507I
u = −0.094573 − 0.834098I
−13.51750 + 0.44803I −2.98623 − 0.17507I
u = −0.106309 + 0.831780I
−13.1248 − 9.9780I −2.29837 + 6.37976I
u = −0.106309 − 0.831780I
−13.1248 + 9.9780I −2.29837 − 6.37976I
u = 0.100233 + 0.828509I
−9.52777 + 5.06782I 0.64782 − 3.34296I
u = 0.100233 − 0.828509I
−9.52777 − 5.06782I 0.64782 + 3.34296I
u = 1.160000 + 0.299339I
−1.25708 − 2.56686I 0
u = 1.160000 − 0.299339I
−1.25708 + 2.56686I 0
u = 0.044240 + 0.791420I
−6.38103 + 0.21871I −4.02948 + 0.02486I
u = 0.044240 − 0.791420I
−6.38103 − 0.21871I −4.02948 − 0.02486I
u = −1.151480 + 0.383952I
−9.92789 + 5.59071I 0
u = −1.151480 − 0.383952I
−9.92789 − 5.59071I 0
u = 0.101141 + 0.776834I
−4.45615 + 6.50629I 0.43803 − 8.00885I
u = 0.101141 − 0.776834I
−4.45615 − 6.50629I 0.43803 + 8.00885I
u = 1.159270 + 0.378976I
−6.28819 − 0.70922I 0
u = 1.159270 − 0.378976I
−6.28819 + 0.70922I 0
u = −1.166850 + 0.385537I
−10.23340 − 3.94733I 0
u = −1.166850 − 0.385537I
−10.23340 + 3.94733I 0
u = −0.078114 + 0.754804I
−2.51311 − 2.38180I 3.80371 + 3.48935I
u = −0.078114 − 0.754804I
−2.51311 + 2.38180I 3.80371 − 3.48935I
u = −1.210410 + 0.285230I
0.91435 − 1.38824I 0
u = −1.210410 − 0.285230I
0.91435 + 1.38824I 0
u = −1.25678
2.32752 0
u = 1.225780 + 0.337681I
−2.74836 + 3.85748I 0
u = 1.225780 − 0.337681I
−2.74836 − 3.85748I 0
u = −0.048386 + 0.684959I
−1.42383 − 1.84364I 4.80084 + 4.67821I
u = −0.048386 − 0.684959I
−1.42383 + 1.84364I 4.80084 − 4.67821I
u = −1.287820 + 0.269388I
2.46404 − 1.51677I 0
u = −1.287820 − 0.269388I
2.46404 + 1.51677I 0
u = 1.307270 + 0.296498I
2.83926 + 5.43289I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307270 − 0.296498I
2.83926 − 5.43289I 0
u = −1.296820 + 0.344926I
−2.19604 − 4.31467I 0
u = −1.296820 − 0.344926I
−2.19604 + 4.31467I 0
u = 1.348140 + 0.018843I
6.21518 + 0.45322I 0
u = 1.348140 − 0.018843I
6.21518 − 0.45322I 0
u = −0.460545 + 0.448848I
−7.99941 − 6.33251I 0.97978 + 6.99711I
u = −0.460545 − 0.448848I
−7.99941 + 6.33251I 0.97978 − 6.99711I
u = 1.318160 + 0.325546I
1.86620 + 6.29334I 0
u = 1.318160 − 0.325546I
1.86620 − 6.29334I 0
u = −1.357310 + 0.046814I
4.98134 − 4.45057I 0
u = −1.357310 − 0.046814I
4.98134 + 4.45057I 0
u = −1.360890 + 0.109523I
1.21860 − 3.40283I 0
u = −1.360890 − 0.109523I
1.21860 + 3.40283I 0
u = 1.359500 + 0.126402I
−2.55503 − 1.02133I 0
u = 1.359500 − 0.126402I
−2.55503 + 1.02133I 0
u = −0.424540 + 0.468915I
−8.11205 + 2.96450I 0.512038 + 0.590116I
u = −0.424540 − 0.468915I
−8.11205 − 2.96450I 0.512038 − 0.590116I
u = −1.329800 + 0.335920I
0.03580 − 10.52840I 0
u = −1.329800 − 0.335920I
0.03580 + 10.52840I 0
u = 1.373990 + 0.109382I
−2.26088 + 8.10639I 0
u = 1.373990 − 0.109382I
−2.26088 − 8.10639I 0
u = 0.434819 + 0.442821I
−4.36631 + 1.63515I 4.04889 − 3.95460I
u = 0.434819 − 0.442821I
−4.36631 − 1.63515I 4.04889 + 3.95460I
u = 1.331870 + 0.368474I
−9.04383 + 4.77398I 0
u = 1.331870 − 0.368474I
−9.04383 − 4.77398I 0
u = −1.334750 + 0.364272I
−5.02433 − 9.36081I 0
u = −1.334750 − 0.364272I
−5.02433 + 9.36081I 0
u = 1.338820 + 0.365504I
−8.5870 + 14.2869I 0
u = 1.338820 − 0.365504I
−8.5870 − 14.2869I 0
u = 0.466465 + 0.249612I
−0.58098 + 3.59821I 5.77066 − 8.87995I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.466465 − 0.249612I
−0.58098 − 3.59821I 5.77066 + 8.87995I
u = 0.188336 + 0.389034I
−1.44853 − 1.18673I 0.463992 + 0.219440I
u = 0.188336 − 0.389034I
−1.44853 + 1.18673I 0.463992 − 0.219440I
u = −0.421061 + 0.080852I
0.842001 − 0.137199I 12.42572 + 1.52219I
u = −0.421061 − 0.080852I
0.842001 + 0.137199I 12.42572 − 1.52219I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
65
+ 37u
64
+ ··· + 5u + 1
c
2
, c
6
u
65
− u
64
+ ··· + 3u − 1
c
3
u
65
− u
64
+ ··· − 975u − 1789
c
4
, c
5
, c
10
u
65
+ u
64
+ ··· + u − 1
c
7
, c
8
, c
12
u
65
− 3u
64
+ ··· + 97u − 7
c
9
, c
11
u
65
− 3u
64
+ ··· − 159u + 77
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
65
− 17y
64
+ ··· − 23y −1
c
2
, c
6
y
65
− 37y
64
+ ··· + 5y −1
c
3
y
65
+ 23y
64
+ ··· − 57349307y −3200521
c
4
, c
5
, c
10
y
65
− 53y
64
+ ··· + 5y −1
c
7
, c
8
, c
12
y
65
+ 71y
64
+ ··· + 3781y −49
c
9
, c
11
y
65
+ 47y
64
+ ··· + 71481y −5929
9
