12a
0552
(K12a
0552
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 10 1 2 6 12 5 4 9
Solving Sequence
4,11
5 12 10 6 9 1 7 8 3 2
c
4
c
11
c
10
c
5
c
9
c
12
c
6
c
8
c
3
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
65
+ u
64
+ ··· + 3u + 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
+ · · · + 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
12
=
−u
u
a
10
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
1
=
−u
9
− 4u
7
− 3u
5
+ 2u
3
− u
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
7
=
−u
22
− 11u
20
+ ··· − 3u
4
+ 1
u
22
+ 12u
20
+ ··· + 8u
4
+ 3u
2
a
8
=
u
11
+ 6u
9
+ 12u
7
+ 8u
5
+ u
3
+ 2u
u
13
+ 7u
11
+ 17u
9
+ 16u
7
+ 6u
5
+ 5u
3
+ u
a
3
=
−u
24
− 13u
22
+ ··· − 2u
2
+ 1
−u
26
− 14u
24
+ ··· − 10u
4
− u
2
a
2
=
−u
59
− 32u
57
+ ··· + 5u
3
− 2u
−u
61
− 33u
59
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
64
− 4u
63
+ ··· − 24u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
+ 35u
64
+ ··· − 3u − 1
c
2
, c
7
u
65
+ u
64
+ ··· + u + 1
c
3
, c
6
u
65
− u
64
+ ··· + u + 1
c
4
, c
5
, c
10
c
11
u
65
+ u
64
+ ··· + 3u + 1
c
8
u
65
− 9u
64
+ ··· − 871u + 109
c
9
, c
12
u
65
+ 11u
64
+ ··· + 1417u + 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
− 9y
64
+ ··· + y −1
c
2
, c
7
y
65
+ 35y
64
+ ··· − 3y −1
c
3
, c
6
y
65
− 53y
64
+ ··· − 99y −1
c
4
, c
5
, c
10
c
11
y
65
+ 71y
64
+ ··· − 3y −1
c
8
y
65
− 13y
64
+ ··· + 40113y −11881
c
9
, c
12
y
65
+ 43y
64
+ ··· − 640031y −34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.595719 + 0.578948I
−7.70647 + 11.34340I −8.26251 − 9.40428I
u = −0.595719 − 0.578948I
−7.70647 − 11.34340I −8.26251 + 9.40428I
u = −0.599254 + 0.561085I
−8.54295 + 2.41798I −9.80276 − 3.05774I
u = −0.599254 − 0.561085I
−8.54295 − 2.41798I −9.80276 + 3.05774I
u = 0.589572 + 0.570914I
−4.51819 − 6.51331I −5.31750 + 6.37538I
u = 0.589572 − 0.570914I
−4.51819 + 6.51331I −5.31750 − 6.37538I
u = 0.538749 + 0.569567I
−0.93086 − 6.41545I −3.67996 + 9.86351I
u = 0.538749 − 0.569567I
−0.93086 + 6.41545I −3.67996 − 9.86351I
u = 0.220912 + 0.733421I
−2.38478 − 6.60693I −2.78190 + 7.82097I
u = 0.220912 − 0.733421I
−2.38478 + 6.60693I −2.78190 − 7.82097I
u = 0.569041 + 0.489543I
−4.59319 − 1.95369I −11.39399 + 3.79158I
u = 0.569041 − 0.489543I
−4.59319 + 1.95369I −11.39399 − 3.79158I
u = −0.621187 + 0.418285I
−8.96370 + 1.72981I −11.03048 − 3.35966I
u = −0.621187 − 0.418285I
−8.96370 − 1.72981I −11.03048 + 3.35966I
u = −0.505578 + 0.547288I
−0.07972 + 2.16929I −1.40597 − 3.65142I
u = −0.505578 − 0.547288I
−0.07972 − 2.16929I −1.40597 + 3.65142I
u = −0.624357 + 0.395701I
−8.24591 − 7.19806I −9.88810 + 3.21124I
u = −0.624357 − 0.395701I
−8.24591 + 7.19806I −9.88810 − 3.21124I
u = 0.613226 + 0.403101I
−5.01179 + 2.41777I −6.90071 − 0.01179I
u = 0.613226 − 0.403101I
−5.01179 − 2.41777I −6.90071 + 0.01179I
u = 0.274381 + 0.668482I
−2.83652 + 1.62881I −4.05285 + 1.38314I
u = 0.274381 − 0.668482I
−2.83652 − 1.62881I −4.05285 − 1.38314I
u = −0.043462 + 0.719036I
2.69348 + 2.02135I 4.11374 − 4.67175I
u = −0.043462 − 0.719036I
2.69348 − 2.02135I 4.11374 + 4.67175I
u = −0.195350 + 0.687690I
0.60698 + 2.16613I 0.97582 − 4.91748I
u = −0.195350 − 0.687690I
0.60698 − 2.16613I 0.97582 + 4.91748I
u = 0.537336 + 0.377380I
−1.48399 + 2.68474I −5.93567 − 3.09855I
u = 0.537336 − 0.377380I
−1.48399 − 2.68474I −5.93567 + 3.09855I
u = −0.463936 + 0.448567I
−0.422225 + 1.251880I −2.42688 − 4.39107I
u = −0.463936 − 0.448567I
−0.422225 − 1.251880I −2.42688 + 4.39107I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15190 + 1.44967I
−2.33616 − 4.48271I 0
u = −0.15190 − 1.44967I
−2.33616 + 4.48271I 0
u = 0.14927 + 1.46063I
0.981805 − 0.236082I 0
u = 0.14927 − 1.46063I
0.981805 + 0.236082I 0
u = −0.16115 + 1.46529I
−2.88598 + 4.47628I 0
u = −0.16115 − 1.46529I
−2.88598 − 4.47628I 0
u = 0.09486 + 1.50450I
4.62328 + 0.70657I 0
u = 0.09486 − 1.50450I
4.62328 − 0.70657I 0
u = 0.486503 + 0.034595I
−4.82132 − 4.20427I −10.67761 + 3.89462I
u = 0.486503 − 0.034595I
−4.82132 + 4.20427I −10.67761 − 3.89462I
u = 0.15753 + 1.51877I
2.03909 − 4.52101I 0
u = 0.15753 − 1.51877I
2.03909 + 4.52101I 0
u = −0.12554 + 1.53196I
6.27220 + 3.29095I 0
u = −0.12554 − 1.53196I
6.27220 − 3.29095I 0
u = −0.14729 + 1.54850I
6.93976 + 4.52566I 0
u = −0.14729 − 1.54850I
6.93976 − 4.52566I 0
u = −0.18149 + 1.54544I
−1.55418 + 5.25395I 0
u = −0.18149 − 1.54544I
−1.55418 − 5.25395I 0
u = 0.05974 + 1.55575I
4.61583 + 0.48659I 0
u = 0.05974 − 1.55575I
4.61583 − 0.48659I 0
u = −0.440342
−1.55260 −7.73470
u = 0.17813 + 1.55071I
2.53593 − 9.30655I 0
u = 0.17813 − 1.55071I
2.53593 + 9.30655I 0
u = 0.15865 + 1.55295I
6.15977 − 8.94433I 0
u = 0.15865 − 1.55295I
6.15977 + 8.94433I 0
u = −0.18134 + 1.55369I
−0.6147 + 14.1782I 0
u = −0.18134 − 1.55369I
−0.6147 − 14.1782I 0
u = −0.03741 + 1.57557I
8.26236 + 2.91932I 0
u = −0.03741 − 1.57557I
8.26236 − 2.91932I 0
u = −0.00764 + 1.58238I
10.48530 + 2.18126I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00764 − 1.58238I
10.48530 − 2.18126I 0
u = 0.04591 + 1.58470I
5.45364 − 7.49920I 0
u = 0.04591 − 1.58470I
5.45364 + 7.49920I 0
u = −0.311030 + 0.259147I
−0.362697 + 1.022000I −5.86257 − 6.20252I
u = −0.311030 − 0.259147I
−0.362697 − 1.022000I −5.86257 + 6.20252I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
65
+ 35u
64
+ ··· − 3u − 1
c
2
, c
7
u
65
+ u
64
+ ··· + u + 1
c
3
, c
6
u
65
− u
64
+ ··· + u + 1
c
4
, c
5
, c
10
c
11
u
65
+ u
64
+ ··· + 3u + 1
c
8
u
65
− 9u
64
+ ··· − 871u + 109
c
9
, c
12
u
65
+ 11u
64
+ ··· + 1417u + 187
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
65
− 9y
64
+ ··· + y −1
c
2
, c
7
y
65
+ 35y
64
+ ··· − 3y −1
c
3
, c
6
y
65
− 53y
64
+ ··· − 99y −1
c
4
, c
5
, c
10
c
11
y
65
+ 71y
64
+ ··· − 3y −1
c
8
y
65
− 13y
64
+ ··· + 40113y −11881
c
9
, c
12
y
65
+ 43y
64
+ ··· − 640031y −34969
9
