12a
0727
(K12a
0727
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 1 2 7 6 5 4
Solving Sequence
3,8
2 9 4 1 7 10 5 12 6 11
c
2
c
8
c
3
c
1
c
7
c
9
c
4
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
78
− u
77
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 78 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
78
− u
77
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
u
2
a
9
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
1
=
u
2
+ 1
u
2
a
7
=
u
5
+ 2u
3
+ u
u
5
+ u
3
+ u
a
10
=
−u
13
− 4u
11
− 7u
9
− 6u
7
− 2u
5
+ u
−u
13
− 3u
11
− 5u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
5
=
−u
32
− 9u
30
+ ··· + 2u
2
+ 1
−u
32
− 8u
30
+ ··· + 4u
4
+ 2u
2
a
12
=
−u
12
− 3u
10
− 5u
8
− 4u
6
− 2u
4
+ u
2
+ 1
−u
14
− 4u
12
− 7u
10
− 6u
8
− 2u
6
+ u
2
a
6
=
−u
31
− 8u
29
+ ··· + 4u
3
+ 2u
−u
33
− 9u
31
+ ··· + 2u
3
+ u
a
11
=
−u
77
− 20u
75
+ ··· − 2u
3
+ u
−u
77
+ u
76
+ ··· + u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
77
− 4u
76
+ ··· + 24u
3
− 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
78
+ 41u
77
+ ··· − u + 1
c
2
, c
8
u
78
− u
77
+ ··· + u − 1
c
3
, c
7
u
78
+ u
77
+ ··· − 377u − 53
c
4
, c
6
u
78
− u
77
+ ··· − 3u − 1
c
5
, c
10
, c
11
u
78
+ u
77
+ ··· − 3u − 1
c
9
, c
12
u
78
− 7u
77
+ ··· + 17u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
78
− 7y
77
+ ··· − 25y + 1
c
2
, c
8
y
78
+ 41y
77
+ ··· − y + 1
c
3
, c
7
y
78
− 55y
77
+ ··· − 132377y + 2809
c
4
, c
6
y
78
− 43y
77
+ ··· − y + 1
c
5
, c
10
, c
11
y
78
+ 65y
77
+ ··· − y + 1
c
9
, c
12
y
78
+ 45y
77
+ ··· + 351y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578901 + 0.820690I
5.58025 − 9.66694I −3.02999 + 8.66670I
u = −0.578901 − 0.820690I
5.58025 + 9.66694I −3.02999 − 8.66670I
u = 0.564180 + 0.819146I
0.77390 + 5.79656I −8.00000 − 7.45829I
u = 0.564180 − 0.819146I
0.77390 − 5.79656I −8.00000 + 7.45829I
u = 0.126915 + 0.981484I
−0.758555 − 1.060210I −12.70969 + 0.I
u = 0.126915 − 0.981484I
−0.758555 + 1.060210I −12.70969 + 0.I
u = −0.188582 + 0.998058I
−4.15960 − 2.63280I −15.9415 + 4.4696I
u = −0.188582 − 0.998058I
−4.15960 + 2.63280I −15.9415 − 4.4696I
u = 0.586068 + 0.770581I
9.87181 + 2.31305I 0.87298 − 3.50878I
u = 0.586068 − 0.770581I
9.87181 − 2.31305I 0.87298 + 3.50878I
u = −0.524243 + 0.802290I
3.35909 − 2.09213I −4.14215 + 3.78128I
u = −0.524243 − 0.802290I
3.35909 + 2.09213I −4.14215 − 3.78128I
u = 0.228006 + 1.032790I
0.23030 + 6.39957I 0
u = 0.228006 − 1.032790I
0.23030 − 6.39957I 0
u = −0.536678 + 0.763397I
3.42631 − 2.16410I −2.80015 + 4.33324I
u = −0.536678 − 0.763397I
3.42631 + 2.16410I −2.80015 − 4.33324I
u = −0.587628 + 0.712984I
5.88785 + 5.05739I −2.00225 − 2.01742I
u = −0.587628 − 0.712984I
5.88785 − 5.05739I −2.00225 + 2.01742I
u = 0.566932 + 0.711290I
1.08131 − 1.28672I −6.69250 + 0.65759I
u = 0.566932 − 0.711290I
1.08131 + 1.28672I −6.69250 − 0.65759I
u = 0.436106 + 1.077000I
0.62586 + 6.51824I 0
u = 0.436106 − 1.077000I
0.62586 − 6.51824I 0
u = 0.794491 + 0.182712I
2.53319 − 10.66910I −4.99373 + 6.90803I
u = 0.794491 − 0.182712I
2.53319 + 10.66910I −4.99373 − 6.90803I
u = −0.787999 + 0.174370I
−2.22038 + 6.64799I −9.69976 − 5.44355I
u = −0.787999 − 0.174370I
−2.22038 − 6.64799I −9.69976 + 5.44355I
u = −0.454756 + 0.666376I
3.63436 − 1.97058I −2.14073 + 3.77447I
u = −0.454756 − 0.666376I
3.63436 + 1.97058I −2.14073 − 3.77447I
u = −0.336071 + 1.154890I
3.31959 + 0.07641I 0
u = −0.336071 − 1.154890I
3.31959 − 0.07641I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.417832 + 1.133420I
−3.94716 − 3.62664I 0
u = −0.417832 − 1.133420I
−3.94716 + 3.62664I 0
u = 0.773320 + 0.160143I
0.56432 − 2.64520I −6.76601 + 1.68251I
u = 0.773320 − 0.160143I
0.56432 + 2.64520I −6.76601 − 1.68251I
u = −0.758374 + 0.212450I
7.37800 + 3.50504I −0.66245 − 2.81741I
u = −0.758374 − 0.212450I
7.37800 − 3.50504I −0.66245 + 2.81741I
u = 0.374455 + 1.156650I
−2.70435 + 0.70430I 0
u = 0.374455 − 1.156650I
−2.70435 − 0.70430I 0
u = −0.771864 + 0.021540I
−2.45068 + 4.03806I −9.57286 − 3.60585I
u = −0.771864 − 0.021540I
−2.45068 − 4.03806I −9.57286 + 3.60585I
u = 0.770221
−6.34762 −13.9660
u = 0.512327 + 1.132430I
1.51982 + 0.85953I 0
u = 0.512327 − 1.132430I
1.51982 − 0.85953I 0
u = 0.369523 + 1.188730I
−3.41759 + 1.14172I 0
u = 0.369523 − 1.188730I
−3.41759 − 1.14172I 0
u = 0.733419 + 0.176644I
1.09971 − 2.87927I −4.76575 + 4.38124I
u = 0.733419 − 0.176644I
1.09971 + 2.87927I −4.76575 − 4.38124I
u = −0.356853 + 1.193820I
−6.31821 + 2.88878I 0
u = −0.356853 − 1.193820I
−6.31821 − 2.88878I 0
u = 0.349156 + 1.196430I
−1.62767 − 6.93096I 0
u = 0.349156 − 1.196430I
−1.62767 + 6.93096I 0
u = −0.498310 + 1.142680I
−3.33385 − 4.23839I 0
u = −0.498310 − 1.142680I
−3.33385 + 4.23839I 0
u = 0.153987 + 0.736438I
−0.528165 + 0.894862I −9.40631 − 7.34603I
u = 0.153987 − 0.736438I
−0.528165 − 0.894862I −9.40631 + 7.34603I
u = 0.694959 + 0.256300I
4.06421 + 3.75062I −2.75383 − 2.73497I
u = 0.694959 − 0.256300I
4.06421 − 3.75062I −2.75383 + 2.73497I
u = 0.508450 + 1.163050I
−1.75841 + 7.54329I 0
u = 0.508450 − 1.163050I
−1.75841 − 7.54329I 0
u = −0.524201 + 1.160870I
4.60438 − 8.30483I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524201 − 1.160870I
4.60438 + 8.30483I 0
u = −0.440440 + 1.197610I
−6.00210 − 0.27240I 0
u = −0.440440 − 1.197610I
−6.00210 + 0.27240I 0
u = 0.449901 + 1.196690I
−9.82963 + 4.37268I 0
u = 0.449901 − 1.196690I
−9.82963 − 4.37268I 0
u = −0.458822 + 1.196290I
−5.87231 − 8.47661I 0
u = −0.458822 − 1.196290I
−5.87231 + 8.47661I 0
u = 0.513114 + 1.178070I
−2.41053 + 7.41642I 0
u = 0.513114 − 1.178070I
−2.41053 − 7.41642I 0
u = −0.520654 + 1.179930I
−5.17476 − 11.49350I 0
u = −0.520654 − 1.179930I
−5.17476 + 11.49350I 0
u = 0.524977 + 1.180090I
−0.4034 + 15.5519I 0
u = 0.524977 − 1.180090I
−0.4034 − 15.5519I 0
u = −0.663438 + 0.222302I
−0.669046 − 0.243771I −7.95579 + 1.30313I
u = −0.663438 − 0.222302I
−0.669046 + 0.243771I −7.95579 − 1.30313I
u = 0.523024 + 0.313762I
2.74897 − 2.61573I −2.67127 + 3.03594I
u = 0.523024 − 0.313762I
2.74897 + 2.61573I −2.67127 − 3.03594I
u = −0.525544
−0.955751 −10.6020
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
78
+ 41u
77
+ ··· − u + 1
c
2
, c
8
u
78
− u
77
+ ··· + u − 1
c
3
, c
7
u
78
+ u
77
+ ··· − 377u − 53
c
4
, c
6
u
78
− u
77
+ ··· − 3u − 1
c
5
, c
10
, c
11
u
78
+ u
77
+ ··· − 3u − 1
c
9
, c
12
u
78
− 7u
77
+ ··· + 17u + 5
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
78
− 7y
77
+ ··· − 25y + 1
c
2
, c
8
y
78
+ 41y
77
+ ··· − y + 1
c
3
, c
7
y
78
− 55y
77
+ ··· − 132377y + 2809
c
4
, c
6
y
78
− 43y
77
+ ··· − y + 1
c
5
, c
10
, c
11
y
78
+ 65y
77
+ ··· − y + 1
c
9
, c
12
y
78
+ 45y
77
+ ··· + 351y + 25
9
