12a
0482
(K12a
0482
)
A knot diagram
1
Linearized knot diagam
3 6 11 10 7 2 1 12 5 4 9 8
Solving Sequence
5,9
10 4 11 12 3 8 1 7 6 2
c
9
c
4
c
10
c
11
c
3
c
8
c
12
c
7
c
5
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
46
− u
45
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 46 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
46
− u
45
+ · · · − 3u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
u
4
+ 3u
2
+ 1
u
4
+ 2u
2
a
3
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
8
=
u
8
+ 5u
6
+ 7u
4
+ 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
1
=
u
12
+ 7u
10
+ 17u
8
+ 16u
6
+ 6u
4
+ 5u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
7
=
u
16
+ 9u
14
+ 31u
12
+ 50u
10
+ 39u
8
+ 22u
6
+ 18u
4
+ 4u
2
+ 1
u
16
+ 8u
14
+ 24u
12
+ 32u
10
+ 18u
8
+ 8u
6
+ 8u
4
a
6
=
−u
33
− 18u
31
+ ··· − 8u
3
− u
−u
33
− 17u
31
+ ··· − 8u
5
+ u
a
2
=
u
20
+ 11u
18
+ ··· + 7u
2
+ 1
u
22
+ 12u
20
+ ··· + 8u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
45
− 4u
44
+ ··· + 28u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
46
+ 17u
45
+ ··· + 7u + 1
c
2
, c
6
u
46
− u
45
+ ··· − u + 1
c
3
, c
4
, c
9
c
10
u
46
+ u
45
+ ··· + 3u + 1
c
7
, c
8
, c
11
c
12
u
46
+ 5u
45
+ ··· + 17u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
46
+ 25y
45
+ ··· + 87y + 1
c
2
, c
6
y
46
+ 17y
45
+ ··· + 7y + 1
c
3
, c
4
, c
9
c
10
y
46
+ 49y
45
+ ··· + 7y + 1
c
7
, c
8
, c
11
c
12
y
46
+ 53y
45
+ ··· + 311y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.664742 + 0.533075I
−7.89200 − 9.32854I −3.38258 + 7.74496I
u = 0.664742 − 0.533075I
−7.89200 + 9.32854I −3.38258 − 7.74496I
u = 0.675457 + 0.508562I
−12.18020 − 2.26977I −7.30774 + 2.96998I
u = 0.675457 − 0.508562I
−12.18020 + 2.26977I −7.30774 − 2.96998I
u = −0.656275 + 0.523642I
−6.28780 + 3.84503I −1.26707 − 3.22196I
u = −0.656275 − 0.523642I
−6.28780 − 3.84503I −1.26707 + 3.22196I
u = 0.676414 + 0.480624I
−8.04831 + 4.81861I −3.86511 − 1.90322I
u = 0.676414 − 0.480624I
−8.04831 − 4.81861I −3.86511 + 1.90322I
u = −0.663474 + 0.486446I
−6.39825 + 0.60169I −1.58447 − 2.81268I
u = −0.663474 − 0.486446I
−6.39825 − 0.60169I −1.58447 + 2.81268I
u = −0.425584 + 0.580860I
0.50678 + 6.63328I 0.39470 − 9.97215I
u = −0.425584 − 0.580860I
0.50678 − 6.63328I 0.39470 + 9.97215I
u = 0.370658 + 0.572348I
1.34286 − 1.47615I 2.76728 + 4.83936I
u = 0.370658 − 0.572348I
1.34286 + 1.47615I 2.76728 − 4.83936I
u = 0.042363 + 0.667552I
3.14066 − 2.54958I 7.36401 + 3.99068I
u = 0.042363 − 0.667552I
3.14066 + 2.54958I 7.36401 − 3.99068I
u = −0.471349 + 0.440857I
−3.50342 + 1.63744I −7.27018 − 4.90319I
u = −0.471349 − 0.440857I
−3.50342 − 1.63744I −7.27018 + 4.90319I
u = −0.04737 + 1.43621I
4.81615 − 1.87426I 0
u = −0.04737 − 1.43621I
4.81615 + 1.87426I 0
u = −0.487759 + 0.265494I
−0.43809 − 3.45776I −3.80106 + 2.57819I
u = −0.487759 − 0.265494I
−0.43809 + 3.45776I −3.80106 − 2.57819I
u = −0.11192 + 1.48925I
2.82329 + 3.62355I 0
u = −0.11192 − 1.48925I
2.82329 − 3.62355I 0
u = 0.05755 + 1.49977I
6.38122 − 1.82382I 0
u = 0.05755 − 1.49977I
6.38122 + 1.82382I 0
u = 0.21458 + 1.49604I
−1.61318 + 1.60482I 0
u = 0.21458 − 1.49604I
−1.61318 − 1.60482I 0
u = −0.20676 + 1.50200I
0.09096 + 3.73634I 0
u = −0.20676 − 1.50200I
0.09096 − 3.73634I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21685 + 1.51393I
−5.56462 − 5.50465I 0
u = 0.21685 − 1.51393I
−5.56462 + 5.50465I 0
u = −0.20731 + 1.52424I
0.43892 + 6.97774I 0
u = −0.20731 − 1.52424I
0.43892 − 6.97774I 0
u = 0.21236 + 1.52855I
−1.11770 − 12.51940I 0
u = 0.21236 − 1.52855I
−1.11770 + 12.51940I 0
u = 0.415258 + 0.188192I
0.263014 − 1.271440I −3.04057 + 3.64034I
u = 0.415258 − 0.188192I
0.263014 + 1.271440I −3.04057 − 3.64034I
u = 0.09628 + 1.54151I
8.41953 − 3.11711I 0
u = 0.09628 − 1.54151I
8.41953 + 3.11711I 0
u = 0.238736 + 0.384624I
0.049172 − 0.835852I 1.31520 + 8.15747I
u = 0.238736 − 0.384624I
0.049172 + 0.835852I 1.31520 − 8.15747I
u = −0.11146 + 1.54382I
7.60893 + 8.52667I 0
u = −0.11146 − 1.54382I
7.60893 − 8.52667I 0
u = 0.00802 + 1.55602I
10.58230 − 2.70871I 0
u = 0.00802 − 1.55602I
10.58230 + 2.70871I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
46
+ 17u
45
+ ··· + 7u + 1
c
2
, c
6
u
46
− u
45
+ ··· − u + 1
c
3
, c
4
, c
9
c
10
u
46
+ u
45
+ ··· + 3u + 1
c
7
, c
8
, c
11
c
12
u
46
+ 5u
45
+ ··· + 17u + 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
46
+ 25y
45
+ ··· + 87y + 1
c
2
, c
6
y
46
+ 17y
45
+ ··· + 7y + 1
c
3
, c
4
, c
9
c
10
y
46
+ 49y
45
+ ··· + 7y + 1
c
7
, c
8
, c
11
c
12
y
46
+ 53y
45
+ ··· + 311y + 9
8
