12a
0744
(K12a
0744
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 11 10 2 1 7 6 5 4
Solving Sequence
6,11
5 12 4 1 10 7 9 3 8 2
c
5
c
11
c
4
c
12
c
10
c
6
c
9
c
3
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
+ u
29
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
+ u
29
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
12
=
u
u
3
+ u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
10
=
−u
u
a
7
=
u
2
+ 1
−u
2
a
9
=
−u
3
− 2u
u
3
+ u
a
3
=
−u
10
− 7u
8
− 16u
6
− 13u
4
− u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 8u
4
+ 3u
2
a
8
=
−u
11
− 8u
9
− 22u
7
− 24u
5
− 9u
3
− 2u
−u
13
− 9u
11
− 29u
9
− 40u
7
− 22u
5
− 3u
3
+ u
a
2
=
−u
25
− 18u
23
+ ··· + 6u
3
+ u
u
25
+ 17u
23
+ ··· + 5u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
28
−4u
27
−88u
26
−84u
25
−852u
24
−772u
23
−4776u
22
−4080u
21
−17160u
20
−13704u
19
−
41328u
18
−30524u
17
−67796u
16
−45664u
15
−75468u
14
−45464u
13
−55764u
12
−29136u
11
−
26120u
10
− 11080u
9
− 7012u
8
− 1872u
7
− 744u
6
+ 176u
5
+ 72u
4
+ 96u
3
+ 16u
2
+ 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 15u
29
+ ··· + u + 1
c
2
, c
7
u
30
+ u
29
+ ··· + u + 1
c
3
u
30
− u
29
+ ··· − u + 13
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
u
30
+ u
29
+ ··· + u + 1
c
8
u
30
+ 3u
29
+ ··· + 39u + 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ y
29
+ ··· + 15y + 1
c
2
, c
7
y
30
− 15y
29
+ ··· − y + 1
c
3
y
30
+ 9y
29
+ ··· − 261y + 169
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
y
30
+ 45y
29
+ ··· − y + 1
c
8
y
30
+ 13y
29
+ ··· + 2175y + 441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170414 + 0.834214I
−5.24114 + 0.43257I −4.60975 + 0.66672I
u = −0.170414 − 0.834214I
−5.24114 − 0.43257I −4.60975 − 0.66672I
u = −0.294203 + 0.768569I
−3.91612 − 7.01709I −1.64398 + 8.27896I
u = −0.294203 − 0.768569I
−3.91612 + 7.01709I −1.64398 − 8.27896I
u = 0.242623 + 0.722037I
−1.51083 + 2.43874I 1.60861 − 4.80918I
u = 0.242623 − 0.722037I
−1.51083 − 2.43874I 1.60861 + 4.80918I
u = 0.038851 + 1.290960I
−6.26416 + 2.28369I 1.00616 − 3.59603I
u = 0.038851 − 1.290960I
−6.26416 − 2.28369I 1.00616 + 3.59603I
u = 0.106749 + 1.375700I
−8.52804 + 3.68968I 0. − 2.69220I
u = 0.106749 − 1.375700I
−8.52804 − 3.68968I 0. + 2.69220I
u = −0.132490 + 1.392830I
−11.13310 − 8.56839I −3.01367 + 6.28743I
u = −0.132490 − 1.392830I
−11.13310 + 8.56839I −3.01367 − 6.28743I
u = −0.07468 + 1.41582I
−12.80400 − 0.46762I −5.38297 + 0.I
u = −0.07468 − 1.41582I
−12.80400 + 0.46762I −5.38297 + 0.I
u = 0.212525 + 0.515943I
−0.30214 + 1.56902I 3.13445 − 6.62609I
u = 0.212525 − 0.515943I
−0.30214 − 1.56902I 3.13445 + 6.62609I
u = −0.343660 + 0.336994I
−1.59918 + 2.04479I 1.77407 + 0.99321I
u = −0.343660 − 0.336994I
−1.59918 − 2.04479I 1.77407 − 0.99321I
u = −0.431998 + 0.168856I
−1.04292 − 4.61082I 4.50728 + 7.35119I
u = −0.431998 − 0.168856I
−1.04292 + 4.61082I 4.50728 − 7.35119I
u = 0.364754 + 0.087964I
0.963752 + 0.420717I 10.43938 − 2.37744I
u = 0.364754 − 0.087964I
0.963752 − 0.420717I 10.43938 + 2.37744I
u = 0.00718 + 1.81845I
−17.8624 + 2.4789I 0
u = 0.00718 − 1.81845I
−17.8624 − 2.4789I 0
u = 0.02668 + 1.83606I
18.9070 + 4.3501I 0
u = 0.02668 − 1.83606I
18.9070 − 4.3501I 0
u = −0.03325 + 1.83999I
16.2143 − 9.3978I 0
u = −0.03325 − 1.83999I
16.2143 + 9.3978I 0
u = −0.01867 + 1.84515I
14.3797 − 0.9432I 0
u = −0.01867 − 1.84515I
14.3797 + 0.9432I 0
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
30
+ 15u
29
+ ··· + u + 1
c
2
, c
7
u
30
+ u
29
+ ··· + u + 1
c
3
u
30
− u
29
+ ··· − u + 13
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
u
30
+ u
29
+ ··· + u + 1
c
8
u
30
+ 3u
29
+ ··· + 39u + 21
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
30
+ y
29
+ ··· + 15y + 1
c
2
, c
7
y
30
− 15y
29
+ ··· − y + 1
c
3
y
30
+ 9y
29
+ ··· − 261y + 169
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
y
30
+ 45y
29
+ ··· − y + 1
c
8
y
30
+ 13y
29
+ ··· + 2175y + 441
7
