12a
1277
(K12a
1277
)
A knot diagram
1
Linearized knot diagam
5 8 9 10 12 1 11 4 3 2 7 6
Solving Sequence
1,7
6 12 5 2 11 8 3 10 4 9
c
6
c
12
c
5
c
1
c
11
c
7
c
2
c
10
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
60
+ u
59
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 60 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
60
+ u
59
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
3
+ 2u
−u
3
+ u
a
8
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
3
=
u
19
− 8u
17
+ 26u
15
− 40u
13
+ 19u
11
+ 24u
9
− 30u
7
+ 9u
3
u
19
− 7u
17
+ 20u
15
− 27u
13
+ 11u
11
+ 13u
9
− 14u
7
+ 3u
3
+ u
a
10
=
u
15
− 6u
13
+ 14u
11
− 14u
9
+ 2u
7
+ 6u
5
− 4u
3
+ 2u
−u
17
+ 7u
15
− 19u
13
+ 22u
11
− 3u
9
− 14u
7
+ 6u
5
+ 2u
3
+ u
a
4
=
u
28
− 11u
26
+ ··· + u
2
+ 1
−u
30
+ 12u
28
+ ··· + 8u
4
− u
2
a
9
=
u
55
− 22u
53
+ ··· − 4u
3
+ 2u
u
55
− 21u
53
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
58
− 92u
56
+ ··· + 28u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
11
u
60
+ 3u
59
+ ··· + 2u + 1
c
2
, c
4
u
60
− u
59
+ ··· − 30u + 53
c
3
, c
8
, c
9
u
60
+ u
59
+ ··· + 3u
2
+ 1
c
5
, c
6
, c
12
u
60
− u
59
+ ··· + 2u + 1
c
10
u
60
− 7u
59
+ ··· + 418u + 121
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
11
y
60
+ 61y
59
+ ··· − 34y + 1
c
2
, c
4
y
60
− 43y
59
+ ··· + 30370y + 2809
c
3
, c
8
, c
9
y
60
+ 49y
59
+ ··· + 6y + 1
c
5
, c
6
, c
12
y
60
− 47y
59
+ ··· + 6y + 1
c
10
y
60
− 19y
59
+ ··· + 581526y + 14641
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952891 + 0.114591I
−1.63134 − 3.97089I 0. + 3.95693I
u = 0.952891 − 0.114591I
−1.63134 + 3.97089I 0. − 3.95693I
u = −0.913578
2.26750 4.34250
u = −0.046410 + 0.879087I
11.14760 + 5.09122I 7.88188 − 3.54555I
u = −0.046410 − 0.879087I
11.14760 − 5.09122I 7.88188 + 3.54555I
u = 0.036027 + 0.879552I
7.90629 − 0.72735I 4.83751 − 0.28515I
u = 0.036027 − 0.879552I
7.90629 + 0.72735I 4.83751 + 0.28515I
u = 0.054075 + 0.877605I
6.64512 − 9.38838I 3.45721 + 5.82134I
u = 0.054075 − 0.877605I
6.64512 + 9.38838I 3.45721 − 5.82134I
u = 0.014493 + 0.848975I
5.96433 − 1.64461I 4.63229 + 3.99521I
u = 0.014493 − 0.848975I
5.96433 + 1.64461I 4.63229 − 3.99521I
u = −0.039777 + 0.829212I
0.36934 + 3.43260I −0.37711 − 3.47540I
u = −0.039777 − 0.829212I
0.36934 − 3.43260I −0.37711 + 3.47540I
u = 1.261800 + 0.016743I
−2.82969 − 0.00473I 0
u = 1.261800 − 0.016743I
−2.82969 + 0.00473I 0
u = −1.277440 + 0.123654I
−4.34670 + 2.46287I 0
u = −1.277440 − 0.123654I
−4.34670 − 2.46287I 0
u = −1.237020 + 0.366524I
−3.32294 + 0.86956I 0
u = −1.237020 − 0.366524I
−3.32294 − 0.86956I 0
u = −1.277970 + 0.198182I
−4.03371 + 1.65180I 0
u = −1.277970 − 0.198182I
−4.03371 − 1.65180I 0
u = 1.226230 + 0.424129I
3.02962 + 4.73104I 0
u = 1.226230 − 0.424129I
3.02962 − 4.73104I 0
u = −1.234400 + 0.423787I
7.47969 − 0.43024I 0
u = −1.234400 − 0.423787I
7.47969 + 0.43024I 0
u = 1.244470 + 0.422086I
4.17054 − 3.92945I 0
u = 1.244470 − 0.422086I
4.17054 + 3.92945I 0
u = 1.260890 + 0.389342I
2.10105 − 2.79905I 0
u = 1.260890 − 0.389342I
2.10105 + 2.79905I 0
u = −1.323890 + 0.043080I
−7.13062 − 3.25794I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.323890 − 0.043080I
−7.13062 + 3.25794I 0
u = 1.313090 + 0.188578I
−0.90503 − 5.42632I 0
u = 1.313090 − 0.188578I
−0.90503 + 5.42632I 0
u = 1.325800 + 0.121610I
−10.07350 − 3.06520I 0
u = 1.325800 − 0.121610I
−10.07350 + 3.06520I 0
u = −1.284320 + 0.388965I
1.92305 + 6.08834I 0
u = −1.284320 − 0.388965I
1.92305 − 6.08834I 0
u = −1.329320 + 0.183577I
−5.43159 + 9.36207I 0
u = −1.329320 − 0.183577I
−5.43159 − 9.36207I 0
u = 1.300190 + 0.374913I
−3.81244 − 7.76500I 0
u = 1.300190 − 0.374913I
−3.81244 + 7.76500I 0
u = −1.303200 + 0.407332I
3.73023 + 5.33731I 0
u = −1.303200 − 0.407332I
3.73023 − 5.33731I 0
u = 1.310460 + 0.405153I
6.91172 − 9.69308I 0
u = 1.310460 − 0.405153I
6.91172 + 9.69308I 0
u = −1.315300 + 0.402754I
2.3668 + 13.9776I 0
u = −1.315300 − 0.402754I
2.3668 − 13.9776I 0
u = 0.273216 + 0.546706I
−0.44946 − 6.81706I 1.30973 + 8.19836I
u = 0.273216 − 0.546706I
−0.44946 + 6.81706I 1.30973 − 8.19836I
u = 0.576906 + 0.164637I
−1.68593 + 3.81309I −2.04506 − 2.17343I
u = 0.576906 − 0.164637I
−1.68593 − 3.81309I −2.04506 + 2.17343I
u = −0.236153 + 0.549892I
3.88620 + 2.83793I 6.61988 − 5.74267I
u = −0.236153 − 0.549892I
3.88620 − 2.83793I 6.61988 + 5.74267I
u = 0.181913 + 0.565297I
0.428112 + 1.050190I 3.41996 + 1.38655I
u = 0.181913 − 0.565297I
0.428112 − 1.050190I 3.41996 − 1.38655I
u = −0.591588
2.32006 2.71690
u = −0.345085 + 0.381413I
−4.98300 + 1.34382I −4.86472 − 5.06327I
u = −0.345085 − 0.381413I
−4.98300 − 1.34382I −4.86472 + 5.06327I
u = 0.170422 + 0.337157I
0.021675 − 0.773783I 0.67824 + 8.94296I
u = 0.170422 − 0.337157I
0.021675 + 0.773783I 0.67824 − 8.94296I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
11
u
60
+ 3u
59
+ ··· + 2u + 1
c
2
, c
4
u
60
− u
59
+ ··· − 30u + 53
c
3
, c
8
, c
9
u
60
+ u
59
+ ··· + 3u
2
+ 1
c
5
, c
6
, c
12
u
60
− u
59
+ ··· + 2u + 1
c
10
u
60
− 7u
59
+ ··· + 418u + 121
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
11
y
60
+ 61y
59
+ ··· − 34y + 1
c
2
, c
4
y
60
− 43y
59
+ ··· + 30370y + 2809
c
3
, c
8
, c
9
y
60
+ 49y
59
+ ··· + 6y + 1
c
5
, c
6
, c
12
y
60
− 47y
59
+ ··· + 6y + 1
c
10
y
60
− 19y
59
+ ··· + 581526y + 14641
8
