12a
0738
(K12a
0738
)
A knot diagram
1
Linearized knot diagam
3 8 9 11 12 10 2 1 7 6 5 4
Solving Sequence
6,12
5 11 4 1 10 7 9 3 8 2
c
5
c
11
c
4
c
12
c
10
c
6
c
9
c
3
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
59
− u
58
+ ··· + u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 59 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
59
− u
58
+ · · · + u
2
− 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
10
=
u
3
− 2u
−u
3
+ u
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
3
=
u
22
− 9u
20
+ ··· − 4u
2
+ 1
−u
22
+ 8u
20
+ ··· + 4u
4
+ 3u
2
a
8
=
u
21
− 8u
19
+ ··· − 4u
3
− 3u
u
23
− 9u
21
+ ··· − 4u
3
+ u
a
2
=
−u
51
+ 20u
49
+ ··· + 20u
5
+ 7u
3
u
51
− 19u
49
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
56
+ 84u
54
+ ··· + 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 29u
58
+ ··· + 2u + 1
c
2
, c
7
u
59
+ u
58
+ ··· + u
2
− 1
c
3
u
59
− u
58
+ ··· − 214u − 61
c
4
, c
5
, c
11
u
59
− u
58
+ ··· + u
2
− 1
c
6
, c
9
, c
10
c
12
u
59
+ 3u
58
+ ··· + 26u + 5
c
8
u
59
+ 3u
58
+ ··· + 274u − 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
+ 3y
58
+ ··· − 18y −1
c
2
, c
7
y
59
− 29y
58
+ ··· + 2y −1
c
3
y
59
+ 11y
58
+ ··· + 17370y −3721
c
4
, c
5
, c
11
y
59
− 45y
58
+ ··· + 2y −1
c
6
, c
9
, c
10
c
12
y
59
+ 71y
58
+ ··· − 54y −25
c
8
y
59
+ 23y
58
+ ··· − 139226y −34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.049650 + 0.244074I
−1.46822 + 3.88519I 2.11458 − 3.15684I
u = −1.049650 − 0.244074I
−1.46822 − 3.88519I 2.11458 + 3.15684I
u = −0.015995 + 0.915634I
−14.7136 − 0.7721I −3.56410 − 0.31715I
u = −0.015995 − 0.915634I
−14.7136 + 0.7721I −3.56410 + 0.31715I
u = −0.029257 + 0.912896I
−12.9183 − 9.0890I −1.27230 + 5.79658I
u = −0.029257 − 0.912896I
−12.9183 + 9.0890I −1.27230 − 5.79658I
u = 0.024127 + 0.908325I
−10.26760 + 4.09935I 1.75919 − 2.25179I
u = 0.024127 − 0.908325I
−10.26760 − 4.09935I 1.75919 + 2.25179I
u = 0.008156 + 0.888471I
−7.74257 + 2.40406I 2.67885 − 3.26207I
u = 0.008156 − 0.888471I
−7.74257 − 2.40406I 2.67885 + 3.26207I
u = 1.096820 + 0.205121I
1.080150 + 0.480738I 6.00000 + 0.I
u = 1.096820 − 0.205121I
1.080150 − 0.480738I 6.00000 + 0.I
u = −1.128910 + 0.272160I
−2.42286 − 3.69043I 0
u = −1.128910 − 0.272160I
−2.42286 + 3.69043I 0
u = 1.16156
2.06866 6.00000
u = 1.269780 + 0.147882I
2.98114 − 0.20812I 0
u = 1.269780 − 0.147882I
2.98114 + 0.20812I 0
u = 1.256570 + 0.266869I
−1.39782 + 3.10898I 0
u = 1.256570 − 0.266869I
−1.39782 − 3.10898I 0
u = −1.272580 + 0.192297I
3.97948 − 4.12493I 0
u = −1.272580 − 0.192297I
3.97948 + 4.12493I 0
u = −1.292070 + 0.025357I
5.86156 − 0.82447I 0
u = −1.292070 − 0.025357I
5.86156 + 0.82447I 0
u = 1.303410 + 0.050369I
4.08832 + 5.40748I 0
u = 1.303410 − 0.050369I
4.08832 − 5.40748I 0
u = −1.284990 + 0.240189I
2.75808 − 5.72388I 0
u = −1.284990 − 0.240189I
2.75808 + 5.72388I 0
u = 1.296950 + 0.252884I
0.47013 + 10.52840I 0
u = 1.296950 − 0.252884I
0.47013 − 10.52840I 0
u = −0.154537 + 0.652088I
−4.02672 − 7.30062I −0.57198 + 8.02266I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154537 − 0.652088I
−4.02672 + 7.30062I −0.57198 − 8.02266I
u = −0.082927 + 0.664867I
−5.50022 + 0.23449I −3.62552 + 0.57133I
u = −0.082927 − 0.664867I
−5.50022 − 0.23449I −3.62552 − 0.57133I
u = −1.261370 + 0.449534I
−9.10474 + 4.22835I 0
u = −1.261370 − 0.449534I
−9.10474 − 4.22835I 0
u = 1.264440 + 0.443767I
−6.42613 + 0.72715I 0
u = 1.264440 − 0.443767I
−6.42613 − 0.72715I 0
u = 1.273510 + 0.421789I
−3.81526 + 2.28316I 0
u = 1.273510 − 0.421789I
−3.81526 − 2.28316I 0
u = −1.273610 + 0.447529I
−10.81480 − 4.09220I 0
u = −1.273610 − 0.447529I
−10.81480 + 4.09220I 0
u = −1.286810 + 0.419585I
−3.71576 − 7.08524I 0
u = −1.286810 − 0.419585I
−3.71576 + 7.08524I 0
u = 0.135360 + 0.620016I
−1.62134 + 2.64544I 2.55643 − 4.49292I
u = 0.135360 − 0.620016I
−1.62134 − 2.64544I 2.55643 + 4.49292I
u = 1.298440 + 0.437752I
−10.62320 + 5.60619I 0
u = 1.298440 − 0.437752I
−10.62320 − 5.60619I 0
u = −1.302440 + 0.430305I
−6.13573 − 8.88432I 0
u = −1.302440 − 0.430305I
−6.13573 + 8.88432I 0
u = 1.307160 + 0.432172I
−8.7535 + 13.8960I 0
u = 1.307160 − 0.432172I
−8.7535 − 13.8960I 0
u = 0.143619 + 0.486456I
−0.31966 + 1.64759I 3.71266 − 6.34085I
u = 0.143619 − 0.486456I
−0.31966 − 1.64759I 3.71266 + 6.34085I
u = −0.436286 + 0.252853I
−1.03116 − 4.55655I 4.61891 + 7.76047I
u = −0.436286 − 0.252853I
−1.03116 + 4.55655I 4.61891 − 7.76047I
u = −0.280522 + 0.375413I
−1.54969 + 2.03091I 2.13878 + 1.09449I
u = −0.280522 − 0.375413I
−1.54969 − 2.03091I 2.13878 − 1.09449I
u = 0.392822 + 0.121836I
0.952284 + 0.399884I 10.51926 − 2.51736I
u = 0.392822 − 0.121836I
0.952284 − 0.399884I 10.51926 + 2.51736I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
59
+ 29u
58
+ ··· + 2u + 1
c
2
, c
7
u
59
+ u
58
+ ··· + u
2
− 1
c
3
u
59
− u
58
+ ··· − 214u − 61
c
4
, c
5
, c
11
u
59
− u
58
+ ··· + u
2
− 1
c
6
, c
9
, c
10
c
12
u
59
+ 3u
58
+ ··· + 26u + 5
c
8
u
59
+ 3u
58
+ ··· + 274u − 187
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
59
+ 3y
58
+ ··· − 18y −1
c
2
, c
7
y
59
− 29y
58
+ ··· + 2y −1
c
3
y
59
+ 11y
58
+ ··· + 17370y −3721
c
4
, c
5
, c
11
y
59
− 45y
58
+ ··· + 2y −1
c
6
, c
9
, c
10
c
12
y
59
+ 71y
58
+ ··· − 54y −25
c
8
y
59
+ 23y
58
+ ··· − 139226y −34969
8
