12a
0764
(K12a
0764
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 12 1 9 2 7 6 5 4
Solving Sequence
2,9
8 3 1 7 10 4 6 11 12 5
c
8
c
2
c
1
c
7
c
9
c
3
c
6
c
10
c
12
c
5
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
66
− u
65
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 66 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
66
− u
65
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
u
2
+ 1
u
2
a
10
=
u
4
+ u
2
+ 1
u
4
a
4
=
−u
11
− 2u
9
− 4u
7
− 4u
5
− 3u
3
−u
11
− u
9
− 2u
7
− u
5
+ u
3
+ u
a
6
=
−u
10
− u
8
− 2u
6
− u
4
+ u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 4u
6
− 3u
4
a
11
=
u
26
+ 3u
24
+ ··· + u
2
+ 1
u
28
+ 4u
26
+ ··· + 12u
8
+ u
4
a
12
=
u
27
+ 4u
25
+ ··· + 12u
7
+ u
3
u
27
+ 3u
25
+ ··· + u
3
+ u
a
5
=
−u
65
− 8u
63
+ ··· − 6u
3
− u
−u
65
+ u
64
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
65
+ 32u
63
+ ··· − 16u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
66
+ 17u
65
+ ··· + u + 1
c
2
, c
8
u
66
− u
65
+ ··· − u − 1
c
3
, c
6
u
66
− u
65
+ ··· − 36u − 40
c
4
, c
5
, c
11
u
66
+ u
65
+ ··· − 3u − 1
c
10
, c
12
u
66
− 3u
65
+ ··· + 3u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
66
+ 65y
65
+ ··· − 31y + 1
c
2
, c
8
y
66
+ 17y
65
+ ··· + y + 1
c
3
, c
6
y
66
− 35y
65
+ ··· − 32496y + 1600
c
4
, c
5
, c
11
y
66
− 55y
65
+ ··· + y + 1
c
10
, c
12
y
66
+ 37y
65
+ ··· − 3y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207533 + 0.981086I
−6.35096 + 4.33929I −15.3912 − 1.6731I
u = −0.207533 − 0.981086I
−6.35096 − 4.33929I −15.3912 + 1.6731I
u = −0.322302 + 0.940128I
−3.57030 − 2.48361I −12.14309 + 4.22745I
u = −0.322302 − 0.940128I
−3.57030 + 2.48361I −12.14309 − 4.22745I
u = −0.272653 + 0.940034I
−3.76345 − 2.65206I −14.2785 + 5.3930I
u = −0.272653 − 0.940034I
−3.76345 + 2.65206I −14.2785 − 5.3930I
u = 0.208676 + 0.955825I
−1.57258 − 0.64572I −10.64970 + 0.22730I
u = 0.208676 − 0.955825I
−1.57258 + 0.64572I −10.64970 − 0.22730I
u = 0.271816 + 0.990028I
−10.11990 + 2.95711I −17.8433 − 4.0853I
u = 0.271816 − 0.990028I
−10.11990 − 2.95711I −17.8433 + 4.0853I
u = 0.327602 + 0.976374I
−0.88010 + 6.28741I −8.00000 − 7.78129I
u = 0.327602 − 0.976374I
−0.88010 − 6.28741I −8.00000 + 7.78129I
u = −0.326605 + 0.991495I
−5.65622 − 10.20650I −13.5289 + 9.0267I
u = −0.326605 − 0.991495I
−5.65622 + 10.20650I −13.5289 − 9.0267I
u = 0.757467 + 0.819779I
−0.27528 + 5.62378I 0
u = 0.757467 − 0.819779I
−0.27528 − 5.62378I 0
u = 0.524653 + 0.709653I
−0.64902 + 5.65149I −7.27056 − 7.50619I
u = 0.524653 − 0.709653I
−0.64902 − 5.65149I −7.27056 + 7.50619I
u = −0.136824 + 0.865327I
−4.39217 − 2.36691I −15.8873 + 4.0107I
u = −0.136824 − 0.865327I
−4.39217 + 2.36691I −15.8873 − 4.0107I
u = −0.832435 + 0.793863I
−3.01879 + 1.47388I 0
u = −0.832435 − 0.793863I
−3.01879 − 1.47388I 0
u = −0.796593 + 0.845883I
4.46763 − 2.52307I 0
u = −0.796593 − 0.845883I
4.46763 + 2.52307I 0
u = 0.829323 + 0.823308I
3.15412 − 0.61109I 0
u = 0.829323 − 0.823308I
3.15412 + 0.61109I 0
u = 0.866881 + 0.806451I
2.07449 − 8.47396I 0
u = 0.866881 − 0.806451I
2.07449 + 8.47396I 0
u = −0.863745 + 0.813119I
6.79180 + 4.40102I 0
u = −0.863745 − 0.813119I
6.79180 − 4.40102I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.514926 + 0.629940I
3.49483 − 1.91824I −1.30925 + 4.40205I
u = −0.514926 − 0.629940I
3.49483 + 1.91824I −1.30925 − 4.40205I
u = 0.857102 + 0.823493I
3.93034 − 0.31479I 0
u = 0.857102 − 0.823493I
3.93034 + 0.31479I 0
u = 0.752368 + 0.941982I
−0.652984 + 0.115352I 0
u = 0.752368 − 0.941982I
−0.652984 − 0.115352I 0
u = −0.774741 + 0.932829I
4.19655 − 3.39080I 0
u = −0.774741 − 0.932829I
4.19655 + 3.39080I 0
u = −0.849189 + 0.896624I
6.84678 + 0.99588I 0
u = −0.849189 − 0.896624I
6.84678 − 0.99588I 0
u = 0.845586 + 0.905987I
10.71050 + 3.14132I 0
u = 0.845586 − 0.905987I
10.71050 − 3.14132I 0
u = 0.789852 + 0.955570I
2.74573 + 6.66729I 0
u = 0.789852 − 0.955570I
2.74573 − 6.66729I 0
u = −0.842344 + 0.915164I
6.78882 − 7.27941I 0
u = −0.842344 − 0.915164I
6.78882 + 7.27941I 0
u = 0.519959 + 0.546372I
−0.16044 − 1.78515I −5.05685 + 0.I
u = 0.519959 − 0.546372I
−0.16044 + 1.78515I −5.05685 + 0.I
u = −0.779938 + 0.972264I
−3.56585 − 7.50384I 0
u = −0.779938 − 0.972264I
−3.56585 + 7.50384I 0
u = 0.804861 + 0.967797I
3.47971 + 6.50090I 0
u = 0.804861 − 0.967797I
3.47971 − 6.50090I 0
u = −0.803690 + 0.976805I
6.28091 − 10.60210I 0
u = −0.803690 − 0.976805I
6.28091 + 10.60210I 0
u = 0.802049 + 0.981776I
1.5273 + 14.6781I 0
u = 0.802049 − 0.981776I
1.5273 − 14.6781I 0
u = −0.629766 + 0.121194I
−2.95160 + 6.83126I −7.61691 − 5.02881I
u = −0.629766 − 0.121194I
−2.95160 − 6.83126I −7.61691 + 5.02881I
u = 0.175327 + 0.613584I
−0.378995 + 0.828694I −8.44183 − 8.08874I
u = 0.175327 − 0.613584I
−0.378995 − 0.828694I −8.44183 + 8.08874I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599127 + 0.137206I
1.69680 − 2.97772I −2.56592 + 3.49038I
u = 0.599127 − 0.137206I
1.69680 + 2.97772I −2.56592 − 3.49038I
u = 0.614002
−7.09939 −11.6040
u = −0.541100 + 0.190827I
−1.30250 − 0.68240I −5.55669 + 0.60358I
u = −0.541100 − 0.190827I
−1.30250 + 0.68240I −5.55669 − 0.60358I
u = −0.490541
−1.14219 −8.66240
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
66
+ 17u
65
+ ··· + u + 1
c
2
, c
8
u
66
− u
65
+ ··· − u − 1
c
3
, c
6
u
66
− u
65
+ ··· − 36u − 40
c
4
, c
5
, c
11
u
66
+ u
65
+ ··· − 3u − 1
c
10
, c
12
u
66
− 3u
65
+ ··· + 3u + 3
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
66
+ 65y
65
+ ··· − 31y + 1
c
2
, c
8
y
66
+ 17y
65
+ ··· + y + 1
c
3
, c
6
y
66
− 35y
65
+ ··· − 32496y + 1600
c
4
, c
5
, c
11
y
66
− 55y
65
+ ··· + y + 1
c
10
, c
12
y
66
+ 37y
65
+ ··· − 3y + 9
9
