12a
0732
(K12a
0732
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 12 11 2 1 4 7 6 5
Solving Sequence
7,11
6 12 5 1 10 4 9 3 2 8
c
6
c
11
c
5
c
12
c
10
c
4
c
9
c
3
c
1
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
47
+ u
46
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 47 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
47
+ u
46
+ · · · + 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
12
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
10
=
−u
u
a
4
=
−u
6
− 3u
4
+ 1
u
6
+ 4u
4
+ 3u
2
a
9
=
u
11
+ 6u
9
+ 10u
7
+ 2u
5
− 3u
3
− 2u
−u
11
− 7u
9
− 16u
7
− 13u
5
− 3u
3
+ u
a
3
=
u
16
+ 9u
14
+ 29u
12
+ 38u
10
+ 13u
8
− 10u
6
− 12u
4
− 2u
2
+ 1
−u
16
− 10u
14
− 38u
12
− 68u
10
− 58u
8
− 20u
6
+ 4u
4
+ 4u
2
a
2
=
−u
37
− 22u
35
+ ··· + 10u
3
+ u
u
37
+ 23u
35
+ ··· − u
3
+ u
a
8
=
u
19
+ 12u
17
+ ··· − 11u
3
− 2u
u
21
+ 13u
19
+ ··· − 7u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
46
+ 4u
45
+ ··· − 4u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 21u
46
+ ··· + 4u + 1
c
2
, c
7
u
47
+ u
46
+ ··· + 2u
2
− 1
c
3
, c
4
, c
9
u
47
− u
46
+ ··· + 19u
2
− 4
c
5
, c
6
, c
10
c
11
, c
12
u
47
− u
46
+ ··· + 2u − 1
c
8
u
47
+ 3u
46
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 11y
46
+ ··· − 24y −1
c
2
, c
7
y
47
− 21y
46
+ ··· + 4y −1
c
3
, c
4
, c
9
y
47
− 45y
46
+ ··· + 152y −16
c
5
, c
6
, c
10
c
11
, c
12
y
47
+ 59y
46
+ ··· + 4y −1
c
8
y
47
− y
46
+ ··· + 48y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413784 + 0.877713I
2.77094 − 10.32890I 4.55615 + 8.72539I
u = −0.413784 − 0.877713I
2.77094 + 10.32890I 4.55615 − 8.72539I
u = 0.195276 + 0.942019I
−4.26421 + 6.13092I −0.95567 − 8.26497I
u = 0.195276 − 0.942019I
−4.26421 − 6.13092I −0.95567 + 8.26497I
u = 0.413997 + 0.861943I
4.64721 + 5.04866I 7.42319 − 4.27573I
u = 0.413997 − 0.861943I
4.64721 − 5.04866I 7.42319 + 4.27573I
u = 0.088069 + 0.951448I
−5.29996 − 0.71896I −4.01239 + 0.13887I
u = 0.088069 − 0.951448I
−5.29996 + 0.71896I −4.01239 − 0.13887I
u = −0.371801 + 0.847703I
−0.66504 − 3.24376I 1.24977 + 4.19607I
u = −0.371801 − 0.847703I
−0.66504 + 3.24376I 1.24977 − 4.19607I
u = 0.418667 + 0.819399I
4.90772 + 2.01411I 7.94310 − 3.89227I
u = 0.418667 − 0.819399I
4.90772 − 2.01411I 7.94310 + 3.89227I
u = −0.422632 + 0.799038I
3.24960 + 3.24336I 5.51628 − 0.96386I
u = −0.422632 − 0.799038I
3.24960 − 3.24336I 5.51628 + 0.96386I
u = −0.166444 + 0.877591I
−2.03526 − 1.97557I 2.70543 + 4.55475I
u = −0.166444 − 0.877591I
−2.03526 + 1.97557I 2.70543 − 4.55475I
u = −0.173002 + 0.658242I
−0.78945 − 1.82375I 5.03537 + 5.41712I
u = −0.173002 − 0.658242I
−0.78945 + 1.82375I 5.03537 − 5.41712I
u = −0.632705 + 0.037024I
5.54952 − 6.80116I 9.39680 + 5.30944I
u = −0.632705 − 0.037024I
5.54952 + 6.80116I 9.39680 − 5.30944I
u = 0.631119 + 0.020188I
7.32256 + 1.52528I 12.11554 − 0.46181I
u = 0.631119 − 0.020188I
7.32256 − 1.52528I 12.11554 + 0.46181I
u = −0.585855
1.90017 6.44170
u = 0.263626 + 0.379028I
−1.33756 − 1.71540I 3.14465 − 0.50606I
u = 0.263626 − 0.379028I
−1.33756 + 1.71540I 3.14465 + 0.50606I
u = 0.408286 + 0.210597I
−0.73079 + 4.11365I 6.43864 − 8.58454I
u = 0.408286 − 0.210597I
−0.73079 − 4.11365I 6.43864 + 8.58454I
u = −0.368463 + 0.084232I
0.852973 − 0.196059I 12.38641 + 2.18387I
u = −0.368463 − 0.084232I
0.852973 + 0.196059I 12.38641 − 2.18387I
u = −0.01412 + 1.64039I
−8.92297 − 2.26281I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.01412 − 1.64039I
−8.92297 + 2.26281I 0
u = −0.10060 + 1.64581I
−5.17503 + 1.32295I 0
u = −0.10060 − 1.64581I
−5.17503 − 1.32295I 0
u = 0.10339 + 1.65410I
−3.64160 + 3.95604I 0
u = 0.10339 − 1.65410I
−3.64160 − 3.95604I 0
u = −0.09363 + 1.67036I
−9.45217 − 4.99818I 0
u = −0.09363 − 1.67036I
−9.45217 + 4.99818I 0
u = 0.10750 + 1.66999I
−4.14651 + 7.03674I 0
u = 0.10750 − 1.66999I
−4.14651 − 7.03674I 0
u = −0.10893 + 1.67541I
−6.10861 − 12.33850I 0
u = −0.10893 − 1.67541I
−6.10861 + 12.33850I 0
u = −0.03693 + 1.68229I
−11.09350 − 2.72228I 0
u = −0.03693 − 1.68229I
−11.09350 + 2.72228I 0
u = 0.04483 + 1.69525I
−13.5927 + 7.0408I 0
u = 0.04483 − 1.69525I
−13.5927 − 7.0408I 0
u = 0.02120 + 1.69620I
−14.6803 − 0.2975I 0
u = 0.02120 − 1.69620I
−14.6803 + 0.2975I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
47
+ 21u
46
+ ··· + 4u + 1
c
2
, c
7
u
47
+ u
46
+ ··· + 2u
2
− 1
c
3
, c
4
, c
9
u
47
− u
46
+ ··· + 19u
2
− 4
c
5
, c
6
, c
10
c
11
, c
12
u
47
− u
46
+ ··· + 2u − 1
c
8
u
47
+ 3u
46
+ ··· + 4u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 11y
46
+ ··· − 24y −1
c
2
, c
7
y
47
− 21y
46
+ ··· + 4y −1
c
3
, c
4
, c
9
y
47
− 45y
46
+ ··· + 152y −16
c
5
, c
6
, c
10
c
11
, c
12
y
47
+ 59y
46
+ ··· + 4y −1
c
8
y
47
− y
46
+ ··· + 48y −1
8
