9
12
(K9a
22
)
A knot diagram
1
Linearized knot diagam
5 8 7 2 9 4 3 1 6
Solving Sequence
5,9
6 1 2 4 7 3 8
c
5
c
9
c
1
c
4
c
6
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
17
+ u
16
− 4u
15
− 5u
14
+ 7u
13
+ 11u
12
− 4u
11
− 12u
10
− 3u
9
+ 5u
8
+ 6u
7
+ 2u
6
− 2u
5
− 2u
4
+ u + 1i
* 1 irreducible components of dim
C
= 0, with total 17 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
17
+ u
16
− 4u
15
− 5u
14
+ 7u
13
+ 11u
12
− 4u
11
− 12u
10
− 3u
9
+
5u
8
+ 6u
7
+ 2u
6
− 2u
5
− 2u
4
+ u + 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
4
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
7
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
−u
14
+ 4u
12
− 7u
10
+ 6u
8
− 2u
6
+ u
2
a
3
=
−u
11
+ 2u
9
− 2u
7
− u
3
−u
13
+ 3u
11
− 5u
9
+ 4u
7
− 2u
5
− u
3
+ u
a
8
=
u
3
u
5
− u
3
+ u
a
8
=
u
3
u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
16
+20u
14
+4u
13
−44u
12
−16u
11
+44u
10
+28u
9
−8u
8
−20u
7
−24u
6
+16u
4
+8u
3
−10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
17
+ 3u
16
+ ··· + 9u + 3
c
2
, c
3
, c
6
c
7
u
17
− u
16
+ ··· + u + 1
c
5
, c
9
u
17
+ u
16
+ ··· + u + 1
c
8
u
17
+ 9u
16
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
+ 11y
16
+ ··· + 57y −9
c
2
, c
3
, c
6
c
7
y
17
+ 19y
16
+ ··· + y −1
c
5
, c
9
y
17
− 9y
16
+ ··· + y −1
c
8
y
17
− y
16
+ ··· + 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774885 + 0.615952I
8.77101 + 2.39923I 0.86600 − 3.27109I
u = −0.774885 − 0.615952I
8.77101 − 2.39923I 0.86600 + 3.27109I
u = 0.758174 + 0.422247I
1.12328 − 1.83062I −0.40697 + 5.22267I
u = 0.758174 − 0.422247I
1.12328 + 1.83062I −0.40697 − 5.22267I
u = −0.231761 + 0.782357I
6.15100 − 3.91820I −0.40216 + 2.39256I
u = −0.231761 − 0.782357I
6.15100 + 3.91820I −0.40216 − 2.39256I
u = 1.172060 + 0.309872I
1.86779 + 0.50801I −5.57451 + 0.23246I
u = 1.172060 − 0.309872I
1.86779 − 0.50801I −5.57451 − 0.23246I
u = −1.151920 + 0.412149I
−4.14236 + 2.05778I −9.01930 − 0.37816I
u = −1.151920 − 0.412149I
−4.14236 − 2.05778I −9.01930 + 0.37816I
u = −0.756727
−1.00476 −10.8690
u = 1.156820 + 0.481476I
−3.64564 − 6.09306I −7.29297 + 6.87425I
u = 1.156820 − 0.481476I
−3.64564 + 6.09306I −7.29297 − 6.87425I
u = −1.162590 + 0.537552I
3.41234 + 8.83664I −3.62632 − 5.87120I
u = −1.162590 − 0.537552I
3.41234 − 8.83664I −3.62632 + 5.87120I
u = 0.112463 + 0.679715I
−0.69802 + 1.70542I −4.10923 − 4.02096I
u = 0.112463 − 0.679715I
−0.69802 − 1.70542I −4.10923 + 4.02096I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
17
+ 3u
16
+ ··· + 9u + 3
c
2
, c
3
, c
6
c
7
u
17
− u
16
+ ··· + u + 1
c
5
, c
9
u
17
+ u
16
+ ··· + u + 1
c
8
u
17
+ 9u
16
+ ··· + u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
+ 11y
16
+ ··· + 57y −9
c
2
, c
3
, c
6
c
7
y
17
+ 19y
16
+ ··· + y −1
c
5
, c
9
y
17
− 9y
16
+ ··· + y −1
c
8
y
17
− y
16
+ ··· + 9y −1
7
