12a
0549
(K12a
0549
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 10 2 6 1 12 5 4 9
Solving Sequence
2,7
3 1 6 8 4 9 12 10 5 11
c
2
c
1
c
6
c
7
c
3
c
8
c
12
c
9
c
5
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
55
+ u
54
+ ··· − 2u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 55 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
55
+ u
54
+ · · · − 2u
2
− 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
5
=
u
49
− 8u
47
+ ··· − 6u
3
+ u
u
51
− 7u
49
+ ··· + 3u
3
+ u
a
11
=
u
34
− 5u
32
+ ··· + 3u
2
+ 1
u
34
− 6u
32
+ ··· + 8u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
53
+ 32u
51
+ ··· + 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
55
+ 17u
54
+ ··· − 4u + 1
c
2
, c
6
u
55
− u
54
+ ··· + 2u
2
+ 1
c
3
u
55
+ u
54
+ ··· + 1762u + 481
c
4
, c
5
, c
10
c
11
u
55
− u
54
+ ··· + 2u
2
+ 1
c
8
, c
9
, c
12
u
55
− 7u
54
+ ··· + 16u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
55
+ 43y
54
+ ··· − 36y −1
c
2
, c
6
y
55
− 17y
54
+ ··· − 4y −1
c
3
y
55
+ 19y
54
+ ··· − 1037728y −231361
c
4
, c
5
, c
10
c
11
y
55
+ 59y
54
+ ··· − 4y −1
c
8
, c
9
, c
12
y
55
+ 55y
54
+ ··· − 164y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684404 + 0.722826I
−5.13814 − 3.11006I −5.81726 + 2.62133I
u = −0.684404 − 0.722826I
−5.13814 + 3.11006I −5.81726 − 2.62133I
u = 1.009300 + 0.073798I
−10.64290 − 3.13922I −13.9620 + 3.8860I
u = 1.009300 − 0.073798I
−10.64290 + 3.13922I −13.9620 − 3.8860I
u = −0.983021 + 0.286921I
−3.79770 − 1.90653I −7.83144 − 0.75410I
u = −0.983021 − 0.286921I
−3.79770 + 1.90653I −7.83144 + 0.75410I
u = 0.999075 + 0.254898I
2.64629 − 0.91628I −4.31373 + 0.57035I
u = 0.999075 − 0.254898I
2.64629 + 0.91628I −4.31373 − 0.57035I
u = 0.739817 + 0.722754I
1.96614 + 1.46324I −2.76292 − 4.72881I
u = 0.739817 − 0.722754I
1.96614 − 1.46324I −2.76292 + 4.72881I
u = −0.954223 + 0.074852I
−3.31630 + 2.07955I −12.7480 − 6.4347I
u = −0.954223 − 0.074852I
−3.31630 − 2.07955I −12.7480 + 6.4347I
u = −1.016950 + 0.234947I
2.48031 + 5.10996I −4.99601 − 6.99986I
u = −1.016950 − 0.234947I
2.48031 − 5.10996I −4.99601 + 6.99986I
u = 1.033440 + 0.219903I
−4.29762 − 8.00514I −8.76672 + 6.36477I
u = 1.033440 − 0.219903I
−4.29762 + 8.00514I −8.76672 − 6.36477I
u = −0.801281 + 0.723501I
3.03409 + 1.48960I 1.90395 − 3.20693I
u = −0.801281 − 0.723501I
3.03409 − 1.48960I 1.90395 + 3.20693I
u = −0.917815 + 0.588074I
−7.81316 + 2.22017I −10.28022 − 2.96610I
u = −0.917815 − 0.588074I
−7.81316 − 2.22017I −10.28022 + 2.96610I
u = 0.882338 + 0.642245I
−0.37050 − 2.49264I −9.18106 + 2.41749I
u = 0.882338 − 0.642245I
−0.37050 + 2.49264I −9.18106 − 2.41749I
u = −0.728948 + 0.842191I
2.71025 − 7.42439I −2.34426 + 3.09843I
u = −0.728948 − 0.842191I
2.71025 + 7.42439I −2.34426 − 3.09843I
u = 0.739346 + 0.840551I
9.51060 + 4.33514I 1.19741 − 3.41520I
u = 0.739346 − 0.840551I
9.51060 − 4.33514I 1.19741 + 3.41520I
u = −0.749884 + 0.838519I
9.70470 + 0.07498I 1.76041 − 2.66320I
u = −0.749884 − 0.838519I
9.70470 − 0.07498I 1.76041 + 2.66320I
u = 0.762609 + 0.836176I
3.32526 − 3.17260I −1.67375 + 2.71266I
u = 0.762609 − 0.836176I
3.32526 + 3.17260I −1.67375 − 2.71266I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.862743
−1.53248 −4.68320
u = 0.869677 + 0.749943I
−1.90030 − 2.83935I −4.00000 + 2.97844I
u = 0.869677 − 0.749943I
−1.90030 + 2.83935I −4.00000 − 2.97844I
u = −0.925150 + 0.708021I
2.65530 + 3.98543I 0
u = −0.925150 − 0.708021I
2.65530 − 3.98543I 0
u = 0.960379 + 0.699146I
1.30494 − 6.91372I 0. + 9.95647I
u = 0.960379 − 0.699146I
1.30494 + 6.91372I 0. − 9.95647I
u = −0.982922 + 0.687300I
−6.01523 + 8.51848I 0
u = −0.982922 − 0.687300I
−6.01523 − 8.51848I 0
u = 0.984888 + 0.763099I
2.63960 − 2.80293I 0
u = 0.984888 − 0.763099I
2.63960 + 2.80293I 0
u = −0.993364 + 0.758698I
8.95425 + 5.89271I 0
u = −0.993364 − 0.758698I
8.95425 − 5.89271I 0
u = 0.999972 + 0.755227I
8.70798 − 10.29670I 0
u = 0.999972 − 0.755227I
8.70798 + 10.29670I 0
u = −1.005970 + 0.751628I
1.85795 + 13.37800I 0
u = −1.005970 − 0.751628I
1.85795 − 13.37800I 0
u = −0.045198 + 0.671804I
−0.81085 + 5.10342I −1.92119 − 3.21301I
u = −0.045198 − 0.671804I
−0.81085 − 5.10342I −1.92119 + 3.21301I
u = 0.014665 + 0.668100I
5.79986 − 2.14204I 1.76494 + 3.28212I
u = 0.014665 − 0.668100I
5.79986 + 2.14204I 1.76494 − 3.28212I
u = −0.311643 + 0.483803I
−6.70011 + 1.72964I −5.80955 − 3.62114I
u = −0.311643 − 0.483803I
−6.70011 − 1.72964I −5.80955 + 3.62114I
u = 0.173894 + 0.333363I
−0.101545 − 0.883584I −2.35912 + 7.80336I
u = 0.173894 − 0.333363I
−0.101545 + 0.883584I −2.35912 − 7.80336I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
55
+ 17u
54
+ ··· − 4u + 1
c
2
, c
6
u
55
− u
54
+ ··· + 2u
2
+ 1
c
3
u
55
+ u
54
+ ··· + 1762u + 481
c
4
, c
5
, c
10
c
11
u
55
− u
54
+ ··· + 2u
2
+ 1
c
8
, c
9
, c
12
u
55
− 7u
54
+ ··· + 16u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
55
+ 43y
54
+ ··· − 36y −1
c
2
, c
6
y
55
− 17y
54
+ ··· − 4y −1
c
3
y
55
+ 19y
54
+ ··· − 1037728y −231361
c
4
, c
5
, c
10
c
11
y
55
+ 59y
54
+ ··· − 4y −1
c
8
, c
9
, c
12
y
55
+ 55y
54
+ ··· − 164y −1
8
