12a
0649
(K12a
0649
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 9 2 1 6 12 4 5 8
Solving Sequence
2,7
3 1 8 6 9 5 12 10 11 4
c
2
c
1
c
7
c
6
c
8
c
5
c
12
c
9
c
11
c
4
c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
63
+ u
62
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 63 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
63
+ u
62
+ · · · + 2u + 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
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
9
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
5
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− 3u
9
+ 6u
7
− 2u
5
+ u
u
17
− 5u
15
+ 11u
13
− 12u
11
+ 5u
9
+ 2u
7
− 2u
5
+ u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
a
10
=
u
27
− 8u
25
+ ··· − 3u
3
+ 2u
u
29
− 7u
27
+ ··· + u
3
+ u
a
11
=
u
44
− 11u
42
+ ··· + u
2
+ 1
u
44
− 12u
42
+ ··· − 3u
4
+ 2u
2
a
4
=
−u
54
+ 15u
52
+ ··· − 2u
2
+ 1
−u
56
+ 14u
54
+ ··· − 13u
8
+ 10u
6
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
61
− 64u
59
+ ··· − 8u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
+ 33u
62
+ ··· + 4u + 1
c
2
, c
6
u
63
− u
62
+ ··· + 2u − 1
c
3
, c
4
, c
10
c
11
u
63
+ u
62
+ ··· + 2u
2
− 1
c
5
, c
8
u
63
− 5u
62
+ ··· − 384u + 41
c
7
, c
12
u
63
− 3u
62
+ ··· + 164u − 9
c
9
u
63
+ 19u
62
+ ··· + 38968u + 4073
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
− 5y
62
+ ··· − 8y −1
c
2
, c
6
y
63
− 33y
62
+ ··· + 4y −1
c
3
, c
4
, c
10
c
11
y
63
− 73y
62
+ ··· + 4y −1
c
5
, c
8
y
63
+ 47y
62
+ ··· − 36224y −1681
c
7
, c
12
y
63
+ 43y
62
+ ··· + 27400y −81
c
9
y
63
− 25y
62
+ ··· + 96017920y −16589329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.807336 + 0.596819I
13.3335 + 7.7246I 10.00998 − 6.36298I
u = −0.807336 − 0.596819I
13.3335 − 7.7246I 10.00998 + 6.36298I
u = 0.797322 + 0.579716I
5.11223 − 5.63114I 8.39389 + 7.97661I
u = 0.797322 − 0.579716I
5.11223 + 5.63114I 8.39389 − 7.97661I
u = −0.971710
4.41099 −0.384110
u = −0.924847 + 0.292781I
−0.45640 + 3.17636I 1.88577 − 8.75054I
u = −0.924847 − 0.292781I
−0.45640 − 3.17636I 1.88577 + 8.75054I
u = −0.771159 + 0.561770I
2.89928 + 2.24328I 4.38244 − 3.59011I
u = −0.771159 − 0.561770I
2.89928 − 2.24328I 4.38244 + 3.59011I
u = −0.734481 + 0.605389I
13.54260 − 3.01261I 10.67968 − 0.23092I
u = −0.734481 − 0.605389I
13.54260 + 3.01261I 10.67968 + 0.23092I
u = 0.961610 + 0.434304I
7.01116 − 4.42511I 6.14172 + 6.08207I
u = 0.961610 − 0.434304I
7.01116 + 4.42511I 6.14172 − 6.08207I
u = 0.741982 + 0.582849I
5.27071 + 1.03217I 9.12178 − 1.02959I
u = 0.741982 − 0.582849I
5.27071 − 1.03217I 9.12178 + 1.02959I
u = 0.858425 + 0.141613I
−1.43959 − 0.53362I −4.53498 + 0.33396I
u = 0.858425 − 0.141613I
−1.43959 + 0.53362I −4.53498 − 0.33396I
u = 1.103660 + 0.285741I
7.32672 − 4.55583I 0
u = 1.103660 − 0.285741I
7.32672 + 4.55583I 0
u = −1.114240 + 0.357197I
−0.73485 + 3.08669I 0
u = −1.114240 − 0.357197I
−0.73485 − 3.08669I 0
u = −0.200631 + 0.794151I
10.38970 − 8.95920I 8.29474 + 4.99884I
u = −0.200631 − 0.794151I
10.38970 + 8.95920I 8.29474 − 4.99884I
u = 0.193476 + 0.779461I
2.31625 + 6.69956I 6.24548 − 6.73377I
u = 0.193476 − 0.779461I
2.31625 − 6.69956I 6.24548 + 6.73377I
u = −0.254888 + 0.737304I
11.42830 + 1.53659I 9.80270 − 0.48128I
u = −0.254888 − 0.737304I
11.42830 − 1.53659I 9.80270 + 0.48128I
u = 1.166850 + 0.360700I
−3.54242 − 0.43587I 0
u = 1.166850 − 0.360700I
−3.54242 + 0.43587I 0
u = −0.186925 + 0.753807I
0.40491 − 3.15228I 2.37370 + 2.31233I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.186925 − 0.753807I
0.40491 + 3.15228I 2.37370 − 2.31233I
u = −1.181980 + 0.345078I
−1.80137 − 3.07345I 0
u = −1.181980 − 0.345078I
−1.80137 + 3.07345I 0
u = 0.070169 + 0.760914I
3.95236 + 3.34328I 4.11045 − 3.28316I
u = 0.070169 − 0.760914I
3.95236 − 3.34328I 4.11045 + 3.28316I
u = 1.191770 + 0.334933I
6.16317 + 5.31923I 0
u = 1.191770 − 0.334933I
6.16317 − 5.31923I 0
u = 0.222898 + 0.726961I
3.10820 + 0.15733I 8.25846 + 1.53332I
u = 0.222898 − 0.726961I
3.10820 − 0.15733I 8.25846 − 1.53332I
u = −1.141590 + 0.528482I
8.83894 + 3.23888I 0
u = −1.141590 − 0.528482I
8.83894 − 3.23888I 0
u = 1.179730 + 0.439001I
−5.98396 − 2.56449I 0
u = 1.179730 − 0.439001I
−5.98396 + 2.56449I 0
u = −1.190440 + 0.416970I
0.292282 + 0.762436I 0
u = −1.190440 − 0.416970I
0.292282 − 0.762436I 0
u = 1.150390 + 0.517447I
0.40909 − 4.85871I 0
u = 1.150390 − 0.517447I
0.40909 + 4.85871I 0
u = −1.180060 + 0.458564I
−5.84513 + 5.94356I 0
u = −1.180060 − 0.458564I
−5.84513 − 5.94356I 0
u = −0.027218 + 0.730004I
−2.55159 − 1.61131I −0.22743 + 4.58020I
u = −0.027218 − 0.730004I
−2.55159 + 1.61131I −0.22743 − 4.58020I
u = −1.166670 + 0.516614I
−2.45072 + 7.90304I 0
u = −1.166670 − 0.516614I
−2.45072 − 7.90304I 0
u = 1.186890 + 0.476518I
0.71091 − 7.86927I 0
u = 1.186890 − 0.476518I
0.71091 + 7.86927I 0
u = 1.172460 + 0.524704I
−0.55674 − 11.54750I 0
u = 1.172460 − 0.524704I
−0.55674 + 11.54750I 0
u = −1.175300 + 0.530872I
7.5181 + 13.8713I 0
u = −1.175300 − 0.530872I
7.5181 − 13.8713I 0
u = 0.476432 + 0.503510I
8.37645 + 0.49060I 10.31482 + 0.06254I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.476432 − 0.503510I
8.37645 − 0.49060I 10.31482 − 0.06254I
u = −0.430431 + 0.317615I
0.981121 − 0.128738I 10.38339 + 0.79799I
u = −0.430431 − 0.317615I
0.981121 + 0.128738I 10.38339 − 0.79799I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
63
+ 33u
62
+ ··· + 4u + 1
c
2
, c
6
u
63
− u
62
+ ··· + 2u − 1
c
3
, c
4
, c
10
c
11
u
63
+ u
62
+ ··· + 2u
2
− 1
c
5
, c
8
u
63
− 5u
62
+ ··· − 384u + 41
c
7
, c
12
u
63
− 3u
62
+ ··· + 164u − 9
c
9
u
63
+ 19u
62
+ ··· + 38968u + 4073
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
63
− 5y
62
+ ··· − 8y −1
c
2
, c
6
y
63
− 33y
62
+ ··· + 4y −1
c
3
, c
4
, c
10
c
11
y
63
− 73y
62
+ ··· + 4y −1
c
5
, c
8
y
63
+ 47y
62
+ ··· − 36224y −1681
c
7
, c
12
y
63
+ 43y
62
+ ··· + 27400y −81
c
9
y
63
− 25y
62
+ ··· + 96017920y −16589329
9
