12a
0447
(K12a
0447
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 1 12 5 11 4 8 7
Solving Sequence
3,6
2 1 7 5 12 8 9 4 11 10
c
2
c
1
c
6
c
5
c
12
c
7
c
8
c
4
c
11
c
9
c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
60
− u
59
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 60 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
60
− u
59
+ · · · − u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
8
=
u
11
− 4u
9
+ 6u
7
− 2u
5
− 3u
3
+ 2u
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
9
=
−u
15
+ 4u
13
− 6u
11
+ 8u
7
− 6u
5
− 2u
3
+ 2u
u
17
− 5u
15
+ 11u
13
− 10u
11
− u
9
+ 10u
7
− 6u
5
+ u
a
4
=
u
29
− 8u
27
+ ··· + 2u
3
+ u
−u
31
+ 9u
29
+ ··· − 4u
5
+ u
a
11
=
−u
14
+ 5u
12
− 10u
10
+ 7u
8
+ 4u
6
− 8u
4
+ 2u
2
+ 1
−u
14
+ 4u
12
− 7u
10
+ 4u
8
+ 2u
6
− 4u
4
+ u
2
a
10
=
u
45
− 14u
43
+ ··· − 18u
5
+ 3u
u
45
− 13u
43
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
59
− 72u
57
+ ··· − 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
+ 35u
59
+ ··· + 2u + 1
c
2
, c
5
u
60
+ u
59
+ ··· − u
2
+ 1
c
3
, c
10
u
60
+ u
59
+ ··· + 2u + 1
c
4
, c
8
u
60
+ 3u
59
+ ··· − 453u
2
+ 77
c
6
, c
7
, c
11
c
12
u
60
+ 3u
59
+ ··· + 34u + 5
c
9
u
60
− 31u
59
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
− 19y
59
+ ··· − 10y + 1
c
2
, c
5
y
60
− 35y
59
+ ··· − 2y + 1
c
3
, c
10
y
60
− 31y
59
+ ··· − 2y + 1
c
4
, c
8
y
60
+ 37y
59
+ ··· − 69762y + 5929
c
6
, c
7
, c
11
c
12
y
60
+ 73y
59
+ ··· + 74y + 25
c
9
y
60
− 3y
59
+ ··· − 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.919475 + 0.342245I
0.08563 + 3.24816I 2.86695 − 8.06640I
u = −0.919475 − 0.342245I
0.08563 − 3.24816I 2.86695 + 8.06640I
u = −1.044190 + 0.193501I
0.32484 + 3.60424I −1.15833 − 4.66740I
u = −1.044190 − 0.193501I
0.32484 − 3.60424I −1.15833 + 4.66740I
u = 0.905641 + 0.075866I
−1.51462 − 0.22405I −6.40245 + 0.27111I
u = 0.905641 − 0.075866I
−1.51462 + 0.22405I −6.40245 − 0.27111I
u = −0.006041 + 0.904852I
−10.02580 − 2.42359I −2.65635 + 3.19391I
u = −0.006041 − 0.904852I
−10.02580 + 2.42359I −2.65635 − 3.19391I
u = 0.038465 + 0.899651I
−4.64353 + 8.98999I 1.72039 − 5.67712I
u = 0.038465 − 0.899651I
−4.64353 − 8.98999I 1.72039 + 5.67712I
u = −0.030149 + 0.897007I
−7.37251 − 4.03814I −1.44998 + 2.20533I
u = −0.030149 − 0.897007I
−7.37251 + 4.03814I −1.44998 − 2.20533I
u = 0.763924 + 0.465497I
5.00437 − 6.11953I 7.26352 + 7.85803I
u = 0.763924 − 0.465497I
5.00437 + 6.11953I 7.26352 − 7.85803I
u = 0.030712 + 0.880798I
−3.02518 + 0.62968I 3.76609 + 0.36863I
u = 0.030712 − 0.880798I
−3.02518 − 0.62968I 3.76609 − 0.36863I
u = 1.092890 + 0.282962I
−3.07831 − 0.54807I 0
u = 1.092890 − 0.282962I
−3.07831 + 0.54807I 0
u = 1.032740 + 0.462956I
2.05457 − 2.50514I 0
u = 1.032740 − 0.462956I
2.05457 + 2.50514I 0
u = −0.739994 + 0.426951I
1.82247 + 1.86091I 4.36406 − 4.47008I
u = −0.739994 − 0.426951I
1.82247 − 1.86091I 4.36406 + 4.47008I
u = −1.117990 + 0.254452I
−0.50349 − 3.93794I 0
u = −1.117990 − 0.254452I
−0.50349 + 3.93794I 0
u = −1.062020 + 0.457339I
−1.79262 + 6.16892I 0
u = −1.062020 − 0.457339I
−1.79262 − 6.16892I 0
u = 0.701269 + 0.462491I
5.17636 + 2.18925I 8.10847 + 0.13060I
u = 0.701269 − 0.462491I
5.17636 − 2.18925I 8.10847 − 0.13060I
u = 1.109480 + 0.360438I
−4.69760 − 1.44356I 0
u = 1.109480 − 0.360438I
−4.69760 + 1.44356I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.065550 + 0.475941I
1.11940 − 10.83400I 0
u = 1.065550 − 0.475941I
1.11940 + 10.83400I 0
u = −1.104060 + 0.403777I
−4.38057 + 5.70362I 0
u = −1.104060 − 0.403777I
−4.38057 − 5.70362I 0
u = 0.255046 + 0.618563I
3.38358 + 6.59803I 5.15553 − 6.30688I
u = 0.255046 − 0.618563I
3.38358 − 6.59803I 5.15553 + 6.30688I
u = −1.257920 + 0.450457I
−6.94466 + 4.07293I 0
u = −1.257920 − 0.450457I
−6.94466 − 4.07293I 0
u = 1.249740 + 0.482651I
−6.70940 − 5.51033I 0
u = 1.249740 − 0.482651I
−6.70940 + 5.51033I 0
u = 1.267950 + 0.452530I
−11.34370 − 0.73251I 0
u = 1.267950 − 0.452530I
−11.34370 + 0.73251I 0
u = −1.270740 + 0.447700I
−8.65827 − 4.23519I 0
u = −1.270740 − 0.447700I
−8.65827 + 4.23519I 0
u = −1.257410 + 0.485584I
−11.0988 + 8.9801I 0
u = −1.257410 − 0.485584I
−11.0988 − 8.9801I 0
u = 1.256940 + 0.490183I
−8.3433 − 13.9630I 0
u = 1.256940 − 0.490183I
−8.3433 + 13.9630I 0
u = 1.268500 + 0.467782I
−13.92050 − 2.45161I 0
u = 1.268500 − 0.467782I
−13.92050 + 2.45161I 0
u = −1.266320 + 0.474454I
−13.8709 + 7.3329I 0
u = −1.266320 − 0.474454I
−13.8709 − 7.3329I 0
u = 0.306849 + 0.559155I
4.05629 − 1.56504I 7.07085 + 0.73954I
u = 0.306849 − 0.559155I
4.05629 + 1.56504I 7.07085 − 0.73954I
u = −0.234349 + 0.574464I
0.48435 − 2.11140I 1.91014 + 3.36891I
u = −0.234349 − 0.574464I
0.48435 + 2.11140I 1.91014 − 3.36891I
u = −0.061807 + 0.591217I
−1.52087 − 1.95278I −1.21392 + 4.59969I
u = −0.061807 − 0.591217I
−1.52087 + 1.95278I −1.21392 − 4.59969I
u = −0.473230 + 0.288232I
1.236790 − 0.098801I 8.77548 + 0.26744I
u = −0.473230 − 0.288232I
1.236790 + 0.098801I 8.77548 − 0.26744I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
60
+ 35u
59
+ ··· + 2u + 1
c
2
, c
5
u
60
+ u
59
+ ··· − u
2
+ 1
c
3
, c
10
u
60
+ u
59
+ ··· + 2u + 1
c
4
, c
8
u
60
+ 3u
59
+ ··· − 453u
2
+ 77
c
6
, c
7
, c
11
c
12
u
60
+ 3u
59
+ ··· + 34u + 5
c
9
u
60
− 31u
59
+ ··· − 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
60
− 19y
59
+ ··· − 10y + 1
c
2
, c
5
y
60
− 35y
59
+ ··· − 2y + 1
c
3
, c
10
y
60
− 31y
59
+ ··· − 2y + 1
c
4
, c
8
y
60
+ 37y
59
+ ··· − 69762y + 5929
c
6
, c
7
, c
11
c
12
y
60
+ 73y
59
+ ··· + 74y + 25
c
9
y
60
− 3y
59
+ ··· − 2y + 1
8
