12a
0532
(K12a
0532
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 11 2 6 1 12 5 4 9
Solving Sequence
2,7
3 1 6 8 4 9 12 10 11 5
c
2
c
1
c
6
c
7
c
3
c
8
c
12
c
9
c
11
c
5
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
62
+ u
61
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 62 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
62
+ u
61
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
4
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
9
=
−u
9
+ 2u
7
− 3u
5
+ 2u
3
− u
−u
11
+ u
9
− 2u
7
+ u
5
− u
3
+ u
a
12
=
−u
16
+ 3u
14
− 7u
12
+ 10u
10
− 11u
8
+ 8u
6
− 4u
4
+ 1
−u
18
+ 2u
16
− 5u
14
+ 6u
12
− 7u
10
+ 6u
8
− 4u
6
+ 2u
4
− u
2
a
10
=
−u
23
+ 4u
21
+ ··· + 4u
3
− 2u
−u
25
+ 3u
23
+ ··· − 3u
5
+ u
a
11
=
u
34
− 5u
32
+ ··· + 3u
2
+ 1
u
34
− 6u
32
+ ··· + 8u
4
− u
2
a
5
=
u
56
− 9u
54
+ ··· + 2u
2
+ 1
u
58
− 8u
56
+ ··· − 6u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
60
− 36u
58
+ ··· + 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
62
+ 19u
61
+ ··· − 3u + 1
c
2
, c
6
u
62
− u
61
+ ··· − u + 1
c
3
u
62
+ u
61
+ ··· − 1604u + 676
c
4
, c
5
, c
10
u
62
+ u
61
+ ··· + u + 1
c
8
, c
9
, c
12
u
62
− 7u
61
+ ··· − 255u + 23
c
11
u
62
− 3u
61
+ ··· + 943u − 949
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
62
+ 49y
61
+ ··· + 7y + 1
c
2
, c
6
y
62
− 19y
61
+ ··· + 3y + 1
c
3
y
62
+ 25y
61
+ ··· + 6973656y + 456976
c
4
, c
5
, c
10
y
62
− 59y
61
+ ··· + 3y + 1
c
8
, c
9
, c
12
y
62
+ 69y
61
+ ··· + 4527y + 529
c
11
y
62
− 31y
61
+ ··· − 27237285y + 900601
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989985 + 0.122617I
1.32863 − 4.99314I −5.10286 + 6.83275I
u = 0.989985 − 0.122617I
1.32863 + 4.99314I −5.10286 − 6.83275I
u = −0.809064 + 0.581444I
3.36810 − 0.06751I −1.94023 + 0.35609I
u = −0.809064 − 0.581444I
3.36810 + 0.06751I −1.94023 − 0.35609I
u = 0.975055
−0.841645 −8.82830
u = −0.962183 + 0.082730I
−3.35982 + 2.23077I −11.92321 − 6.16182I
u = −0.962183 − 0.082730I
−3.35982 − 2.23077I −11.92321 + 6.16182I
u = 0.734854 + 0.732067I
2.04758 + 1.64642I −2.09598 − 4.37427I
u = 0.734854 − 0.732067I
2.04758 − 1.64642I −2.09598 + 4.37427I
u = 1.007400 + 0.257971I
3.02841 − 0.92384I −4.00000 + 0.56914I
u = 1.007400 − 0.257971I
3.02841 + 0.92384I −4.00000 − 0.56914I
u = −0.714319 + 0.763961I
7.22652 − 4.54026I 2.91659 + 4.06961I
u = −0.714319 − 0.763961I
7.22652 + 4.54026I 2.91659 − 4.06961I
u = −1.021670 + 0.240610I
2.88991 + 5.19815I −4.00000 − 6.77683I
u = −1.021670 − 0.240610I
2.88991 − 5.19815I −4.00000 + 6.77683I
u = −1.015640 + 0.277475I
9.38200 − 2.18146I − 60.10 − 0.620626I
u = −1.015640 − 0.277475I
9.38200 + 2.18146I − 60.10 + 0.620626I
u = 1.037690 + 0.240795I
9.12317 − 8.49284I 0. + 6.46268I
u = 1.037690 − 0.240795I
9.12317 + 8.49284I 0. − 6.46268I
u = −0.794505 + 0.726721I
3.07799 + 1.41254I 2.04320 − 3.32582I
u = −0.794505 − 0.726721I
3.07799 − 1.41254I 2.04320 + 3.32582I
u = 0.884379 + 0.631379I
−0.51363 − 2.45305I −8.70061 + 2.47945I
u = 0.884379 − 0.631379I
−0.51363 + 2.45305I −8.70061 − 2.47945I
u = 0.740332 + 0.843987I
9.98619 + 4.42504I 0
u = 0.740332 − 0.843987I
9.98619 − 4.42504I 0
u = 0.814940 + 0.773369I
9.03131 − 2.95277I 0
u = 0.814940 − 0.773369I
9.03131 + 2.95277I 0
u = −0.736127 + 0.850348I
16.3081 − 7.8313I 0
u = −0.736127 − 0.850348I
16.3081 + 7.8313I 0
u = −0.749447 + 0.842317I
10.15460 + 0.03373I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749447 − 0.842317I
10.15460 − 0.03373I 0
u = 0.870586
−1.55742 −4.71840
u = 0.756113 + 0.848275I
16.6739 − 3.2136I 0
u = 0.756113 − 0.848275I
16.6739 + 3.2136I 0
u = −0.935495 + 0.651467I
2.87996 + 4.99342I 0
u = −0.935495 − 0.651467I
2.87996 − 4.99342I 0
u = −0.930376 + 0.707827I
2.66249 + 4.07137I 0
u = −0.930376 − 0.707827I
2.66249 − 4.07137I 0
u = 0.926438 + 0.747239I
8.69067 − 2.79047I 0
u = 0.926438 − 0.747239I
8.69067 + 2.79047I 0
u = 0.965239 + 0.702224I
1.35675 − 7.13213I 0
u = 0.965239 − 0.702224I
1.35675 + 7.13213I 0
u = −0.982215 + 0.711411I
6.42370 + 10.13930I 0
u = −0.982215 − 0.711411I
6.42370 − 10.13930I 0
u = −0.995337 + 0.760558I
9.39615 + 5.95109I 0
u = −0.995337 − 0.760558I
9.39615 − 5.95109I 0
u = 1.001000 + 0.757438I
9.18276 − 10.40390I 0
u = 1.001000 − 0.757438I
9.18276 + 10.40390I 0
u = 0.994404 + 0.767003I
15.9378 − 2.8100I 0
u = 0.994404 − 0.767003I
15.9378 + 2.8100I 0
u = −1.005970 + 0.758828I
15.4757 + 13.8328I 0
u = −1.005970 − 0.758828I
15.4757 − 13.8328I 0
u = −0.620405 + 0.327589I
3.29016 − 0.22305I −0.445284 − 1.174195I
u = −0.620405 − 0.327589I
3.29016 + 0.22305I −0.445284 + 1.174195I
u = −0.024632 + 0.694041I
12.57310 + 5.42065I 5.59415 − 3.08644I
u = −0.024632 − 0.694041I
12.57310 − 5.42065I 5.59415 + 3.08644I
u = 0.012401 + 0.677140I
6.22588 − 2.17623I 2.37812 + 3.15857I
u = 0.012401 − 0.677140I
6.22588 + 2.17623I 2.37812 − 3.15857I
u = −0.163278 + 0.512817I
4.83308 + 3.11441I 3.99348 − 4.97298I
u = −0.163278 − 0.512817I
4.83308 − 3.11441I 3.99348 + 4.97298I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172662 + 0.354819I
−0.089492 − 0.934789I −1.87222 + 7.30268I
u = 0.172662 − 0.354819I
−0.089492 + 0.934789I −1.87222 − 7.30268I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
62
+ 19u
61
+ ··· − 3u + 1
c
2
, c
6
u
62
− u
61
+ ··· − u + 1
c
3
u
62
+ u
61
+ ··· − 1604u + 676
c
4
, c
5
, c
10
u
62
+ u
61
+ ··· + u + 1
c
8
, c
9
, c
12
u
62
− 7u
61
+ ··· − 255u + 23
c
11
u
62
− 3u
61
+ ··· + 943u − 949
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
62
+ 49y
61
+ ··· + 7y + 1
c
2
, c
6
y
62
− 19y
61
+ ··· + 3y + 1
c
3
y
62
+ 25y
61
+ ··· + 6973656y + 456976
c
4
, c
5
, c
10
y
62
− 59y
61
+ ··· + 3y + 1
c
8
, c
9
, c
12
y
62
+ 69y
61
+ ··· + 4527y + 529
c
11
y
62
− 31y
61
+ ··· − 27237285y + 900601
9
