9
27
(K9a
12
)
A knot diagram
1
Linearized knot diagam
5 4 7 8 9 2 3 1 6
Solving Sequence
5,9
6 1 2 7 8 4 3
c
5
c
9
c
1
c
6
c
8
c
4
c
3
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
+ u
23
+ ··· + 2u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 24 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
24
+ u
23
− 5u
22
− 6u
21
+ 13u
20
+ 18u
19
− 20u
18
− 34u
17
+ 19u
16
+
44u
15
− 10u
14
− 42u
13
+ 2u
12
+ 32u
11
− 22u
9
+ 13u
7
+ u
6
− 6u
5
− u
4
+ 2u
3
+ 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
1
=
−u
−u
3
+ u
a
2
=
−u
3
−u
3
+ u
a
7
=
u
8
− u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
8
=
u
3
u
5
− u
3
+ u
a
4
=
u
8
− u
6
+ u
4
+ 1
u
10
− 2u
8
+ 3u
6
− 2u
4
+ u
2
a
3
=
u
21
− 4u
19
+ 9u
17
− 12u
15
+ 12u
13
− 10u
11
+ 9u
9
− 6u
7
+ 3u
5
− 2u
3
+ u
u
23
− 5u
21
+ ··· − 3u
5
+ u
a
3
=
u
21
− 4u
19
+ 9u
17
− 12u
15
+ 12u
13
− 10u
11
+ 9u
9
− 6u
7
+ 3u
5
− 2u
3
+ u
u
23
− 5u
21
+ ··· − 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
+ 24u
21
+ 4u
20
− 72u
19
− 20u
18
+ 132u
17
+ 52u
16
− 160u
15
− 84u
14
+ 132u
13
+
92u
12
− 84u
11
− 72u
10
+ 52u
9
+ 44u
8
− 32u
7
− 24u
6
+ 8u
5
+ 12u
4
+ 4u
3
− 4u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
+ 3u
23
+ ··· + 4u + 1
c
2
u
24
− 13u
23
+ ··· − 2u
2
+ 1
c
3
, c
7
u
24
+ u
23
+ ··· + 2u + 1
c
4
, c
6
u
24
− u
23
+ ··· − 10u + 1
c
5
, c
9
u
24
+ u
23
+ ··· + 2u
3
+ 1
c
8
u
24
+ 11u
23
+ ··· − 2u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
+ y
23
+ ··· + 20y + 1
c
2
y
24
− 3y
23
+ ··· − 4y + 1
c
3
, c
7
y
24
+ 13y
23
+ ··· − 2y
2
+ 1
c
4
, c
6
y
24
− 19y
23
+ ··· − 48y + 1
c
5
, c
9
y
24
− 11y
23
+ ··· − 2y
2
+ 1
c
8
y
24
+ 5y
23
+ ··· − 4y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.981563 + 0.214317I
−1.74298 + 0.40841I −5.87200 − 0.75563I
u = −0.981563 − 0.214317I
−1.74298 − 0.40841I −5.87200 + 0.75563I
u = 0.803335 + 0.491088I
1.74384 − 2.05721I 4.27298 + 4.01793I
u = 0.803335 − 0.491088I
1.74384 + 2.05721I 4.27298 − 4.01793I
u = −0.527198 + 0.744803I
6.35994 + 2.92383I 5.29020 − 3.29300I
u = −0.527198 − 0.744803I
6.35994 − 2.92383I 5.29020 + 3.29300I
u = 1.085860 + 0.107562I
0.74814 + 3.77265I −1.89193 − 3.49106I
u = 1.085860 − 0.107562I
0.74814 − 3.77265I −1.89193 + 3.49106I
u = −0.433290 + 0.779547I
5.84506 − 5.78082I 4.37527 + 3.72629I
u = −0.433290 − 0.779547I
5.84506 + 5.78082I 4.37527 − 3.72629I
u = −1.062920 + 0.387157I
−2.96425 + 1.34320I −6.02964 − 0.62000I
u = −1.062920 − 0.387157I
−2.96425 − 1.34320I −6.02964 + 0.62000I
u = 0.452781 + 0.717874I
2.63437 + 1.18290I 1.39246 − 0.39910I
u = 0.452781 − 0.717874I
2.63437 − 1.18290I 1.39246 + 0.39910I
u = 1.083310 + 0.462291I
−2.43992 − 5.71321I −4.10823 + 7.50361I
u = 1.083310 − 0.462291I
−2.43992 + 5.71321I −4.10823 − 7.50361I
u = −1.041780 + 0.614710I
4.82981 + 2.24524I 3.02697 − 1.89383I
u = −1.041780 − 0.614710I
4.82981 − 2.24524I 3.02697 + 1.89383I
u = 1.075010 + 0.585259I
0.79700 − 6.17959I −1.78521 + 5.04555I
u = 1.075010 − 0.585259I
0.79700 + 6.17959I −1.78521 − 5.04555I
u = −1.097340 + 0.604979I
3.87224 + 11.00000I 1.31825 − 8.05284I
u = −1.097340 − 0.604979I
3.87224 − 11.00000I 1.31825 + 8.05284I
u = 0.143789 + 0.548880I
0.05596 + 1.77225I 0.01088 − 4.04184I
u = 0.143789 − 0.548880I
0.05596 − 1.77225I 0.01088 + 4.04184I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
24
+ 3u
23
+ ··· + 4u + 1
c
2
u
24
− 13u
23
+ ··· − 2u
2
+ 1
c
3
, c
7
u
24
+ u
23
+ ··· + 2u + 1
c
4
, c
6
u
24
− u
23
+ ··· − 10u + 1
c
5
, c
9
u
24
+ u
23
+ ··· + 2u
3
+ 1
c
8
u
24
+ 11u
23
+ ··· − 2u
2
+ 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
24
+ y
23
+ ··· + 20y + 1
c
2
y
24
− 3y
23
+ ··· − 4y + 1
c
3
, c
7
y
24
+ 13y
23
+ ··· − 2y
2
+ 1
c
4
, c
6
y
24
− 19y
23
+ ··· − 48y + 1
c
5
, c
9
y
24
− 11y
23
+ ··· − 2y
2
+ 1
c
8
y
24
+ 5y
23
+ ··· − 4y + 1
7
