9
19
(K9a
3
)
A knot diagram
1
Linearized knot diagam
7 6 2 9 3 4 1 5 8
Solving Sequence
5,8
9 1 4 7 2 3 6
c
8
c
9
c
4
c
7
c
1
c
3
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
− u
19
+ ··· + u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 20 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
20
− u
19
+ 3u
18
− 2u
17
+ 9u
16
− 6u
15
+ 16u
14
− 8u
13
+ 24u
12
−
9u
11
+ 25u
10
− 6u
9
+ 21u
8
+ 10u
6
+ 4u
5
+ 3u
4
+ 3u
3
+ u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
1
=
u
2
+ 1
−u
2
a
4
=
−u
u
3
+ u
a
7
=
u
4
+ u
2
+ 1
−u
4
a
2
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
3
=
u
15
+ 2u
13
+ 6u
11
+ 8u
9
+ 10u
7
+ 8u
5
+ 4u
3
−u
15
− u
13
− 4u
11
− 3u
9
− 4u
7
− 2u
5
+ u
a
6
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
10
− 2u
8
− 3u
6
− 4u
4
− u
2
a
6
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
10
− 2u
8
− 3u
6
− 4u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
19
− 8u
17
− 4u
16
− 28u
15
− 8u
14
− 40u
13
− 24u
12
− 64u
11
−
36u
10
− 64u
9
− 44u
8
− 60u
7
− 44u
6
− 36u
5
− 24u
4
− 24u
3
− 8u
2
− 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
20
+ 5u
19
+ ··· + 2u + 1
c
2
, c
5
u
20
+ u
19
+ ··· + 2u + 1
c
3
u
20
+ 9u
19
+ ··· + 2u + 1
c
4
, c
8
u
20
− u
19
+ ··· + u
2
+ 1
c
6
u
20
− u
19
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
20
+ 21y
19
+ ··· + 10y + 1
c
2
, c
5
y
20
+ 9y
19
+ ··· + 2y + 1
c
3
y
20
+ 5y
19
+ ··· + 10y + 1
c
4
, c
8
y
20
+ 5y
19
+ ··· + 2y + 1
c
6
y
20
+ y
19
+ ··· + 18y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.362805 + 0.953641I
−2.49174 − 6.06247I −4.39660 + 7.82928I
u = −0.362805 − 0.953641I
−2.49174 + 6.06247I −4.39660 − 7.82928I
u = −0.161278 + 0.924181I
−3.63536 + 0.74806I −7.88926 − 0.17223I
u = −0.161278 − 0.924181I
−3.63536 − 0.74806I −7.88926 + 0.17223I
u = 0.351156 + 0.820236I
−0.32995 + 1.83292I −0.44386 − 4.26331I
u = 0.351156 − 0.820236I
−0.32995 − 1.83292I −0.44386 + 4.26331I
u = 0.765553 + 0.891086I
1.42388 + 2.89577I −2.31229 − 2.74717I
u = 0.765553 − 0.891086I
1.42388 − 2.89577I −2.31229 + 2.74717I
u = 0.872273 + 0.832901I
5.41964 − 3.75485I 1.74318 + 2.44199I
u = 0.872273 − 0.832901I
5.41964 + 3.75485I 1.74318 − 2.44199I
u = −0.857922 + 0.867417I
7.08907 − 1.55876I 4.11661 + 2.37917I
u = −0.857922 − 0.867417I
7.08907 + 1.55876I 4.11661 − 2.37917I
u = −0.828456 + 0.942427I
6.85240 − 4.70967I 3.63739 + 2.80351I
u = −0.828456 − 0.942427I
6.85240 + 4.70967I 3.63739 − 2.80351I
u = 0.818606 + 0.971044I
4.98583 + 10.03250I 0.83081 − 7.28178I
u = 0.818606 − 0.971044I
4.98583 − 10.03250I 0.83081 + 7.28178I
u = 0.483351 + 0.483677I
0.67976 + 1.37271I 3.12015 − 4.43993I
u = 0.483351 − 0.483677I
0.67976 − 1.37271I 3.12015 + 4.43993I
u = −0.580477 + 0.222282I
−0.25432 + 2.59904I 1.59387 − 3.16627I
u = −0.580477 − 0.222282I
−0.25432 − 2.59904I 1.59387 + 3.16627I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
20
+ 5u
19
+ ··· + 2u + 1
c
2
, c
5
u
20
+ u
19
+ ··· + 2u + 1
c
3
u
20
+ 9u
19
+ ··· + 2u + 1
c
4
, c
8
u
20
− u
19
+ ··· + u
2
+ 1
c
6
u
20
− u
19
+ ··· − 4u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
20
+ 21y
19
+ ··· + 10y + 1
c
2
, c
5
y
20
+ 9y
19
+ ··· + 2y + 1
c
3
y
20
+ 5y
19
+ ··· + 10y + 1
c
4
, c
8
y
20
+ 5y
19
+ ··· + 2y + 1
c
6
y
20
+ y
19
+ ··· + 18y + 1
7
